Binary call option 43

Binary Option. What is a 'Binary Option' A binary option, or asset-or-nothing option, is type of option in which the payoff is structured to be either a fixed amount of compensation if the option expires in the money, or nothing at all if the option expires out of the money. The success of a binary option is thus based on a yes or no proposition, hence “binary”. A binary option automatically exercises, meaning the option holder does not have the choice to buy or sell the underlying asset. BREAKING DOWN 'Binary Option' Difference Between Binary and Plain Vanilla Options. Binary options are significantly different from vanilla options. Plain vanilla options are a normal type of option that does not include any special features. A plain vanilla option gives the holder the right to buy or sell an underlying asset at a specified price on the expiration date, which is also known as a plain vanilla European option. While a binary option has special features and conditions, as stated previously. Binary options are occasionally traded on platforms regulated by the Securities and Exchange Commission (SEC) and other regulatory agencies, but are most likely traded over the Internet on platforms existing outside of regulations. Because these platforms operate outside of regulations, investors are at greater risk of fraud. Conversely, vanilla options are typically regulated and traded on major exchanges. For example, a binary options trading platform may require the investor to deposit a sum of money to purchase the option. If the option expires out-of-the-money, meaning the investor chose the wrong proposition, the trading platform may take the entire sum of deposited money with no refund provided.

Binary Option Real World Example. Assume the futures contracts on the Standard & Poor's 500 Index (S&P 500) is trading at 2,050.50. An investor is bullish and feels that the economic data being released at 8:30 am will push the futures contracts above 2,060 by the close of the current trading day. The binary call options on the S&P 500 Index futures contracts stipulate that the investor would receive $100 if the futures close above 2,060, but nothing if it closes below. The investor purchases one binary call option for $50. Therefore, if the futures close above 2,060, the investor would have a profit of $50, or $100 - $50. Binary Option Option Binaire. As we saw in the precedent pages, Binary options are simply a bet between two players called Traders. When a Trader bets on the underlying to go up then he has to buy a Binary Call When a Trader bets on the underlying to go down then he has to buy a Binary Put. At expiry of the option the buyer of Call or Put will get either. There are only two possibility of results this is why we called those option Binary. Binary options have however a special characteristic that differs from a normal bet. In a simple bet there is a Winner and and Loser but no one wins is the score is null. For Binary options is a little bit different because the buyer pay a premium to the seller of the option that he can keep if the score is null or if the buyer lose the bet.

In fact the seller of the option will never win more than the paid premium by the buyer while the buyer can win the full amount of the bet. To evaluate what the premium is there are différent mathematical methods but we will concentrate on one intuitive explanation. During a bet, a buyer A buy a binary call at $50 that a stock will go up. If A wins he get $100. The seller B of the option will get the $50 premium but hold the risk to give $100 to A if the stock rises. See below recapitulation. For the Buyer A: For the seller B there two possibilities to win and one chance: One chance to lose $100 if the stock goes up Two chances to win $50 if the stock stay flat or decrease. We know the value of the option at the beginning i. e. $50 and at the end ($0 or $100) but we need to know how the option price move during the time of the trader t=0 and the expiration time T. To well understand how a binary option is priced it is necessary to first understand that its value is moving with respect to several parameters that are the value of its underlying, time to expiry, the underlying volatility and finally the free risk interest rate. The value of a Binary option varies with respect to his underlying. Let’s imagine that the price of a stock is $1,000 and that a Trader bet $50 that a stock move above $1,000 by buying a Binary Call. The below table shows the price of the option versus the price of its underlying during a trading day. Note that the Option price change in % est well above its underlying change.

Below a recapitulation chart. It is logical that the value of an option increases because the probability to win the bet (Underlying > $1,000) increases when the underlying (blue line) increases. Until here this is nothing like rocket science. In trading we often look at how much an option price move with respect to its underlying move up or down in order to know how much we win or lose. For example if the underlying is worth $1,000 and rises to $1,005 then the Trader wishes to know how much he needs to add to its binary call option price to know how much money he won or lost (depending if he bought or sold this option). This measure is called the Delta. For example if a binary call with a strike of $1,000 (the strike is the underlying price at wish he starts to win) was bought for $50 and has a 50% delta. This means that if the underlying price move from $1,000 to $1,005 i. e. up $5 then its option price moves by $5 times %50 = $2.5. See below recapitulation. The underlying moved from $1000 to $1005, this is up $5 The call option price will move up as well by $5 * 50% (delta) = $2.5 The call option will be 50 + 2.5 = $52.5 (The buyer will win $2.5 and the seller will lose $2.5) The knowledge of the delta is very important because it allows to know at what speed the option price will move with respect to its underlying. Let’s take another example with a 10% delta. The underlying moved from $1000 to $1005, this is up $5 The call option price will move up as well by $5 * 10% (delta) = $0.5 The call option will be 50 + 0.5 = $50.5 (The buyer will win $0.5 and the seller will lose $0.5) The below chart shows the delta of an option with a $50 strike at three given times of its life. As we can see the delta changes with respect to the underlying bu also with respect to time.

The orange line represents the delta five days before expiry, the closer the option expiry time the more the option delta increases (i. e. the option prices move rapidly). Longer term option will move slower as the result of the bet is still very uncertain 25 and 40 days before the final result. We can notice as well than the delta stays very low when far from the strike. When the delta is far from the strike its means that the bet is already won or lost by far then it makes sense that the value of the option doesn’t move a lot. In trading terms we say that the call option is in the money when the underlying is above to the strike, out the money when the underlying is below the strike and at the money when the underlying equal the strike. For the put, the option is in the money when the underlying is below to the strike, out the money when the underlying is above the strike and at the money when the underlying equal the strike. Below we added all the same chart of delta than above (with a strike of 10 instead of 50) with all the period of time to give a 3 dimension chart. 2. The value of an option varies with respect to time. We can intuitively understand this as the longer the time the expiry the less predictable is the future. Let’s imagine that the price of a stock is $1,000 and the time to expiry 5 days. If a Trader buy a 1,000 strike call on this stock at $50, he basically bet that the stock will move above $1,000 in 5 days. Now if the stock goes to $999 the same day then the option will move from $50 to $49.8 due to the delta move. If the stock stays at $999 the following day then the option price will lose some value again because it has 1 day less chance to go above the strike of $1,000.

The real option price will be $46. If the stock is stil at $999 the fifth day until the very last second of its expiry then the option will be worth nothing as the probability for the stock to rise above $1,000 is close to zero. The below table recapitulates in details the option price move for the above losing case, I also added the wining case for education purpose: Above values charted below. Note that the binary option wins or loses a bit part of its value the very last days before its expiry. If we zoom on the last day to get the time to expiry in hours instead of days we would see the below. The price of a binary option is function of the time to expiry and as we saw above its value moves a lot when the option is closed to expiry and the underlying close to the strike. Like the delta there is a measure that allows us to know how much the option vale will increase or decrease by day, this measure is called the Theta. For example his an option has a theta of -$1 its means that the option will lose -$1 overnight when the market is closed. The below 3D chart show the theta of a binary call option during all his life. This chart recapitulates all the above explanations. 3. The value of a binary call varies with respect to the volatility to its underlying. We call the volatility the speed at which the underlying move up or down. The below chart shows the price of an underlying with three different volatility. Which one do you think is the more volatile? If you replied the orange C line then you were right.

Looking at the chart the blue line is definitely the flatter one and then the less volatile followed by the red one and by the orange line that goes much lower and higher than all other lines. If someone has to bet on one of these three stocks to go up by buying a binary call then clearly he will choose the line that move up the most (the C orange line). Why? because the stock C is so volatile that the buyer of the call has more chance than the stock will go much higher than the other two stocks given him more chance to resell the option with a larger profit than with stock A or B. ( However note that if you are forced to keep the option to expiry then the most volatile stocks is not always the optimal choice. On the above chart the stock collapses below its starting point just before the end of the trading session meaning that the binary call will lose all his value if its strike is $100 or above. One way to solve this problem is to buy a put to protect your downside when the market is above your strike. See the trading strategies pages. ) Obviously the seller of a binary option will have the opposite reasoning, he will try to sell an option on the less volatile stocks as he makes money even if the stock doesn’t move. The logic wants that one option with the same strike on A, B and C will be worth more on the most volatile market, why? Simply because the seller has more chance to lose and will ask for more money to bet are the odds are against him. When pricing binary option the underlying volatility is a very important parameter especially for the long term trading, why? Because if an option expires in a few minutes and the underlying price is $100 and the call strike $110 then there is very little chance than the underlying price will move 10% in a few minutes while if the expiry is one year then a move of 10% is more probable. An option price incorporate a larger volatility value when the time to expiry is longer.

Like the Delta and Theta an option also has a measure of how much the option price move due to an increase of decrease of the underlying volatility, this measure is called the Vega. The below 3D chart shows the Vega of a binary call with respect to the underlying price and time to expiry. The highest the Vega the more sensitive the option price is to the underlying volatility. 4. The value of an option varies with respect to the risk free interest rate. It is very important to understand that trading is all about comparing investment vehicle. Why bothering investing in an underlying that performed less than the risk free interest rate that your banker is giving you? Like all other investment option price need to incorporate in its pricing the value of the interest rate. To get the intuition let’s imagine that you invest $1,000,000 at 10% risk free at the bank and $1,000,000 on an option that expiry in one year. After a month your bank account increased by approximatively $8,300 and your option didn’t move because the underlying is not moving. The opportunity cost of this investment is then $8,300 because it is the money you could have made risk free at the bank. The option pricing model takes into account this amount of money therefore your option lost $8,300 in one month. This money is going to the seller of the option. ( remember that one of the reason to the sell an option is because you think that the underlying will not move a lot or will go the opposite direction than the buyer thinks the underlying goes ) Binary option price is also function to the risk free rate, the measure that allows to know how much the option price will move with respect to the risk free rate is called Rho.

The below chart show a $50 strike with 25 days to expiry call option Rho. The below chart shows a $10 strike Rho during a 100 days time to expiry period. 5. As we saw above the price of an option is moving with respect to. Its underlying price Its time to expiry The volatility of the underlying The risk free rate The strike of the option. To be able to price a binary option you need those five parameters (For stocks you should also use the dividend rate and substrat it to the risk free rate). In the 70’s three mathematician Black, Merton and Scholes developed an analytical formula, the formula is the following. For a binary call: For a binary put: S = Underlying price. r = Risk free rate. σ = Standard deviation of the underlying return (annualised volatility) (T - t)= Time to expiry. T-t needs to be annualised 25365 = 0.0685 year. Binary call price = 0.4908. The below 3D chart e graphique 3D shows the price of a binary call with respect to the underlying and time to expiry.

DHCP OPTION 43 for Lightweight Cisco Aironet Access Points Configuration Example. Download Options. View with Adobe Reader on a variety of devices. View in various apps on iPhone, iPad, Android, Sony Reader, or Windows Phone. View on Kindle device or Kindle app on multiple devices. Introduction. This document describes how to use DHCP Option 43 and provides sample configurations for DHCP Option 43 for lightweight Cisco Aironet access points (LAPs) for these DHCP servers: Microsoft Windows 2008 Enterprise DHCP Server. Cisco IOS ® DHCP Server. Linux Internet Systems Consortium (ISC) DHCP Server. Cisco Network Registrar DHCP Server.

Lucent QIP DHCP Server. When a Cisco Wireless Unified architecture is deployed, the LAPs can use a vendor-specific DHCP Option 43 to join specific Wireless LAN Controllers (WLCs) when the WLC is in a different subnet than the LAP. Refer to Wireless LAN Controller and Lightweight Access Point Basic Configuration Example and Lightweight AP (LAP) Registration to a Wireless LAN Controller (WLC) for information on how to configure an access point (AP) to join a WLC. Requirements. Cisco recommends that you have knowledge of these topics: Basic knowledge on Cisco Unified Wireles Network (CUWN) Basic knowledge of DHCP. This document is not restricted to specific software and hardware versions. The information in this document was created from the devices in a specific lab environment. All of the devices used in this document started with a cleared (default) configuration. If your network is live, make sure that you understand the potential impact of any command. Background Information. Vendor Specific DHCP Options. RFC 2132 defines two DHCP Options that are relevant to vendor specific options.

They are Option 60 and Option 43. DHCP Option 60 is the Vendor Class Identifier (VCI). The VCI is a text string that uniquely identifies a type of vendor device. This table lists the VCIs used by Cisco APs: Cisco Industrial Wireless 3700 Series. Cisco Aironet 1570 series. 1 Any 1500 Series AP that runs 4.1 software. 2 1500 OAP AP that runs 4.0 software. 3 1505 Model AP that runs 4.0 software. 4 1510 Model AP that runs 4.0 software. 5 Any 1500 Series AP that runs 3.2 software. 6 Any 27007001530 Series AP that runs 7.6.120.0 or later software. 7 Any 3700 Series AP that runs 7.6 or later software. 8 1540s running pre-FCS manufacturing code may use "Cisco AP c1560" Option 60 is included in the initial DHCP discover message that a DHCP client broadcasts in search of an IP address. Option 60 is used by DHCP clients (LAPs in this case) in order to identify itself to the DHCP server.

If the access point is ordered with the Service Provider option (AIR-OPT60-DHCP selected), the VCI string for that access point is different than those listed previously. The VCI string includes the ServiceProvider option. For example, a 1260 with this option returns this VCI string: Cisco AP c1260-ServiceProvider . If the Cisco AP runs 7.0.116.0 or above (12.4 (23c) JA2 or above) and if a bootloader environmental variable (env_vars) named DHCP_OPTION_60 exists in flash, the value is appended to the VCI. If you order a Cisco AP with the Service Provider option, it will (by default) include the - ServiceProvider suffix however, you can include other values into DHCP_OPTION_60 as well. In order to facilitate AP discovery of WLAN controllers that use DHCP Option 43, the DHCP server must be programmed in order to return one or more WLAN controller management interface IP addresses based on the VCI of the AP. In order to do this, program the DHCP server to recognize the VCI for each access point type, and then define the vendor specific information. On the DHCP server, the vendor specific information is mapped to VCI text strings. When the DHCP server sees a recognizable VCI in a DHCP discover from a DHCP client, it returns the mapped vendor specific information in its DHCP offer to the client as DHCP Option 43. On the DHCP server , option 43 is defined in each DHCP pool (Scope) that offers IP address to the LAPs. RFC 2132 defines that DHCP servers must return vendor specific information as DHCP Option 43. The RFC allows vendors to define encapsulated vendor-specific sub-option codes between 0 and 255. The sub-options are all included in the DHCP offer as type-length-value (TLV) blocks embedded within Option 43. The definition of the sub-option codes and their related message format is left to the vendors. When DHCP servers are programmed to offer WLAN Controller IP addresses as Option 43 for Cisco 1000 Series APs the sub-option TLV block is defined in this way: Length: - A count of the characters of the ASCII string in the Value field.

Length must include the commas if there is more than one controller specified, but not a zero-terminator. Value: - A non-zero terminated ASCII string that is a comma-separated list of controllers. No spaces should be embedded in the list. When DHCP servers are programmed to offer WLAN Controller IP addresses as Option 43 for other Cisco Aironet LAPs, the sub-option TLV block is defined in this way: Length - Number of controller IP addresses * 4. Value - List of the WLC management interfaces, typically translated to hexadecimal values. The semantics of DHCP server configuration vary based on the DHCP server vendor. This document contains specific instructions on the Microsoft DHCP server, Cisco IOS DHCP server, Linux ISC DHCP Server, Cisco Network Registrar DHCP server, and Lucent QIP DHCP Server. For other DHCP server products, consult the vendor documentation for instructions on vendor specific options. Note : Use the Command Lookup Tool (registered customers only) in order to obtain more information on the commands used in this section. Microsoft DHCP Server. This section describes the configurations necessary on the Microsoft DHCP server in order to use DHCP Option 43 for WLAN Controller discovery. Cisco 1000 Series APs. This section describes how a Windows 2008 DHCP server is configured in order to return vendor specific information to Cisco 1000 APs.

You need to know this key information: Vendor Class Identifier (VCI) Option 43 sub-option code. Management IP address(es) of WLAN controller(s) The VCI for a Cisco 1000 Series AP is always Airespace. AP1200 . As stated, the Option 43 sub-option code for the Cisco 1000 Series APs is type 102 (0x66). Create a new vendor class in order to program the DHCP server to recognize the VCI Airespace. AP1200 . In the Server Manager window, right-click the IPv4 icon, and choose Define Vendor Classes . Click Add in order to create the new class. Enter a value for the Display Name . In this example, Airespace is used as the Display Name. Also, add a short description of the vendor class in the Description field. Add the Vendor Class Identifier string. In order to do this, click the ASCII field and type in the appropriate value in this case Airespace. AP1200 .

Click OK . The new class is created. Click Close . Add an entry for the WLAN controller sub-option in the Predefined Options for the newly created Vendor Class. This is where you define the sub-option code type and the data format that is used to deliver the vendor specific information to the APs. In order to create a Predefined Option, right click the IPv4 icon and choose Set Predefined Options . A new window opens. Set the Option class to the value you configured for the vendor class. In this example, it is Airespace . Click OK in order to define the option code. The Option Type box appears.

In the Name field, enter a descriptive string value, for example, Airespace IP provision . Choose Binary as the Data Type. In the Code field, enter the sub-option value 102 . Enter a Description, if desired. Click OK . The new Predefined Option appears. Click OK . This completes the creation of the Vendor class and sub-option type needed in order to support controller discovery. Right-click the Server Options folder under the DHCP scope, and choose Configure Options . The Scope Options box appears. Click the Advanced tab. Choose the Vendor Class that you plan to use, in this case Airespace . Choose the predefined 102 sub-option to assign to this scope. In the Data Entry area, enter the controller management IP address(es) to return to the APs in the ASCII section.

This is a comma delimited list. There is a period (.) in the initial empty Data Entry area. Make sure you remove this period from the list of IP addresses added in the data entry area. This is an example of the results. Once you complete this step, the DHCP Option 43 is configured. This DHCP option is available for all the DHCP scopes that are configured in the DHCP server. So when the LAPs request for an IP address, the DHCP server sends the option 43 as well as to the LAPs. Other Cisco Lightweight Access Points. The method described in the previous section can be used if you have multiple device types on the same scope and you want them to receive different WLC IP addresses via Option 43. But, if all of the DHCP clients in the scope are Cisco IOS APs, you can use this procedure to define DHCP Option 43. Before you begin, you must know this information: Option 43 sub-option code. Management IP address(es) of WLAN controller(s) Complete these steps in order to define DHCP Option 43 on the Windows DHCP server: In the DHCP Server scope, right-click Server Options and choose Configure Options . On the General tab, scroll to Option 43 and check the 043 Vendor Specific Info check box. Enter the Option 43 sub-option in hex.

Note : TLV values for the Option 43 suboption: Type + Length + Value. Type is always the suboption code 0xf1. Length is the number of controller management IP addresses times 4 in hex. Value is the IP address of the controller listed sequentially in hex. For example, suppose there are two controllers with management interface IP addresses, 192.168.10.5 and 192.168.10.20. The type is 0xf1. The length is 2 * 4 = 8 = 0x08. The IP addresses translates to c0a80a05 (192.168.10.5) and c0a80a14 (192.168.10.20). When the string is assembled, it yields f108c0a80a05c0a80a14. The Cisco IOS command that is added to the DHCP scope is option 43 hex f108c0a80a05c0a80a14 . Once you complete this step, the DHCP Option 43 is configured and the DHCP server sends the option 43 to the LAPs. Cisco IOS DHCP Server. Cisco Aironet APs (Cisco IOS) Complete these steps in order to configure DHCP Option 43, in the embedded Cisco IOS DHCP server, for all Cisco Aironet APs that run Cisco IOS. This includes all APs except for the VxWorks 1000 Series (see the next section) and the 600 Series OEAP which does not use Option 43. Enter configuration mode at the Cisco IOS CLI. Create the DHCP pool, which includes the necessary parameters such as the default router and server name. This is an example DHCP scope: Add the Option 43 line with this syntax: The hexadecimal string in step 3 is assembled as a sequence of the TLV values for the Option 43 suboption: Type + Length + Value.

Type is always the suboption code 0xf1. Length is the number of controller management IP addresses times 4 in hex. Value is the IP address of the controller listed sequentially in hex. For example, suppose there are two controllers with management interface IP addresses, 192.168.10.5 and 192.168.10.20. The type is 0xf1. The length is 2 * 4 = 8 = 0x08. The IP addresses translate to c0a80a05 (192.168.10.5) and c0a80a14 (192.168.10.20). When the string is assembled, it yields f108c0a80a05c0a80a14. The Cisco IOS command that is added to the DHCP scope is: Cisco Aironet 1000 Series APs (VxWorks) (10101020103015051510) Series ONLY. Complete these steps in order to configure DHCP Option 43, in the embedded Cisco IOS DHCP server, for lightweight Cisco Aironet 1000 Series APs. This only applies to the 101010201030 model APs that run VxWorks, and not to APs that run IOS. Enter configuration mode at the Cisco IOS CLI. Create the DHCP pool, which includes the necessary parameters such as default router and server name. This is an example DHCP scope: Add the Option 43 line with this syntax: Note : T he quotation marks must be included.

A sub-option value does not need to be defined in the Cisco IOS DHCP server for Cisco 1000 Series APs. For example, if you configure Option 43 for Cisco 1000 Series APs with the controller IP Management IP addresses 192.168.10.5 and 192.168.10.20, add this line to the DHCP pool in the Cisco IOS CLI: Note : You must use the management interface of the WLAN controller. This video describes how to configure DHCP Option 43 on Cisco IOS DHCP Server: DHCP Option 43 on Cisco IOS DHCP Server . Linux ISC DHCP Server. The information in this section describes how the Linux ISC server is configured in order to return vendor specific information to lightweight Cisco Aironet Series APs. This example configures the Linux ISC server to return vendor specific information to the 1140, 1200, 1130 and 1240 Series Lightweight APs. This configuration can be modified and applied to other series of LAPs. Cisco Network Registrar DHCP Server. The Cisco Network Registrar DHCP server supports Vendor Specific attributes. However, the configuration of these attributes is not possible with the graphical interface. The CLI must be used.

Complete these configuration steps in order to support L3-LWAPP Discovery with DHCP Option 43: Note : The CLI Command Tool can be found in the Network registrar directory: C:\Program Files\Network Registrar\BIN\ nrcmd. bat. Log into the DHCP server. Complete these steps: Create the Vendor Class Identifier for Cisco AP1000 Series APs: Create the Vendor Class Identifier for Cisco AP1200 Series APs: Note : For other models of LAP, replace the vendor-class-id parameter with the specific VCI string from Table 1. Associate the values that can be sent in the DHCP Offer by the server when it receives a request with Option 60 set to Airespace. AP1200 . The DHCP Option 43 can support multiple values in the same Option 43 field. These options need to be identified individually by a subtype. In this case, only one value is required, without any subtype. However, the Cisco Network Registrar (CNR) configuration requires that you create a subtype option. However, in order to hide the subtype feature and send only a row string (BYTE_ARRAY) with the IP values, CNR supports specific flags in order to remove the subtype ids and length. These are no-suboption-opcode and no-suboption-len flags. Associate values based on the DHCP pools: In this example, the DHCP Pool named VLAN-52, which is already defined in CNR by the graphical interface, is configured with Option 43 10.150.1.15,10.150.50.15 when it receives a request from an Airespace.

AP1200 device. Note : 31:30:2e:31:35:30:2e:31:2e:31:35:2c:31:30:2e:31:35:30:2e:35:30:2e:31:35:2c is the hexadecimal representation of the string 10.150.1.15,10.150.50.15 . Finally, save the DHCP configuration and reload. Refer to Managing Advanced DHCP Server Properties for more information on Vendor-Options configurations on a Cisco CNR DHCP server. Lucent QIP DHCP Server. This section provides a few tips for how to configure the Lucent QIP DHCP server in order to return vendor specific information to lightweight Cisco Aironet Series APs. Note :For complete information and the steps involved, refer to the documentation provided by the vendor. The DHCP Option 43 can contain any vendor specific information. The DHCP server passes this information in the form of a hex string to the clients that receive the DHCP offer. On the Lucent QIP DHCP server, the vendor-specific information can be provided on the DHCP Option Template - Modify page. In the Active Options area, choose Vendor Specific Information , and enter the information in the Value field. In order to include the controller IP addresses in the DHCP option 43 message, enter the information to the DHCP Option template in QIP as a single hex value: ip hex .

In order to send more than one IP address with DHCP Option 43, enter the information to the DHCP Option template in QIP as a single hex value: ip hex ip hex and not ip hex,ip hex . In this case, the comma in the middle causes problems for DHCP to parse the string passed from QIP. For example, suppose there are two controllers with management interface IP addresses, 192.168.10.5 and 192.168.10.20. The type is 0xf1. The length is 2 * 4 = 8 = 0x08. The IP addresses translate to c0a80a05 (192.168.10.5) and c0a80a14 (192.168.10.20). When the string is assembled, it yields f108c0a80a05c0a80a14. On the Lucent QIP DHCP server, the hex string that needs to be added to the DHCP scope is: The hex string must be given within square brackets. The square brackets are mandatory. Once the DHCP option 43 is modified to reflect this value, the LAPs are able to find and register with the controller. Use this section in order to verify your configuration. The Output Interpreter Tool (registered customers only) supports certain show commands. Use the Output Interpreter Tool in order to view an analysis of show command output. If you use 1130 120012301240 Series LAPs, which have a console port, you can check that the WLC IP addresses are provided to the LAPs during DHCP IP address assignment. This is a sample output from a Cisco 1230 Series LAP: If you use a Cisco IOS DHCP server, enter the show ip dhcp binding command in order to view the list of the DHCP addresses assigned to DHCP clients. Here is an example: On the WLC CLI, you can enter the show ap summary command in order to verify that the APs registered with the WLC.

Here is an example: If you have Wireless LANs configured, you can enter the show client summary command in order to see the clients that are registered with the WLC: Use this section in order to troubleshoot your configuration. The Output Interpreter Tool (registered customers only) supports certain show commands. Use the Output Interpreter Tool in order to view an analysis of show command output. Enter the debug dhcp message enable command on the WLC in order to view the sequence of events that occur between the DHCP server and client. Here is an example: This is the debug lwapp packet enable command output from the WLC that indicates that DHCP option 43 is used as the discovery method in order to discover WLC IP addresses: The value of the IE 58 parameter indicates the discovery type. For DCHP Option 43 it is 3. If you use the Cisco IOS DHCP server on the router, you can enter the debug dhcp detail command and the debug ip dhcp server events command in order to view the DHCP client and server activity. Here is an example from the debug ip dhcp server events command: Enter the show ip dhcp binding command in order to view the list of the DHCP addresses assigned to DHCP clients. Binary Call Option Delta. Binary call option delta measures the change in the price of a binary call option owing to a change in the underlying asset price and is the gradient of the slope of the binary options price profile versus the underlying asset price (the ‘underlying’). Of all the Greeks, the binary call option delta could probably be considered the most useful in that it can also be interpreted as the equivalent position in the underlying, i. e. the delta translates options, whether individual options or a portfolio of options, into an equivalent position of the underlying. A binary call option with a delta of 0.5 means that if the underlying share price goes up 1¢ then the binary call will increase in value by ½¢. Another interpretation would be a short 400 contract position in S&P500 binary calls with a delta of 0.25 which would be equivalent to being short 100 S&P500 futures. It is important to realise that the delta is dynamically changing as a function of many variables, including a change in the underlying price, and that a change in any of those variables will most likely cause a change in the delta. Therefore, if any or all of the variables, including the underlying price, time to expiry and implied volatility, change then the above option will not necessarily have a delta of 0.5 and increase in value by ½¢ or the equivalent S&P position be short 100 S&P500 futures.

This practicality and simplicity of concept contributes to deltas, out of all the Greeks, being the most utilised amongst traders, especially market-makers. The following provides an analysis of: the finite difference method to evaluate deltas, examples of using the delta to hedge with, comparisons of conventional call options delta with binary call option delta, and finally a closed-form formula for the binary call option delta. Binary Call Option Delta and Finite Delta. The delta Δ of any option is defined by: P = price of the option. S = price of the underlying. δP = a change in the value of P. δS = a change in the value of S. Figure 1 shows the 1 day price profile of a binary call with Figure 2 showing (in black) the same price profile between the underlying prices of 99.78 and 99.99. Fig.1 – Binary Call Option Price Profile. Fig.2 – Fair Value & Delta Gradients. The blue ’18 tick chord’ travels between the point on the call profile 9 ticks below the price of 99.90 to 9 ticks above. The fair value of the binary call option at 99.81 is 3.4592 and at 99.99 is 46.1739 as provided in the bottom row of Table 1.. The gradient of this chord is defined by: SInc = Minimum Underlying Asset Price Change. i. e. Gradient = (46.1739-3.4592) (99.99-99.81) x 0.01. as indicated in the bottom row of the central column of Table 1. The gradients of the ‘12 tick chord’ and ‘6 tick chord’ are calculated in the same manner and are also presented in the central column of Table 1. As the price difference narrows, i. e. as δS → 0 (as reflected by δS = 0.06 and δS = 0.03) the gradient tends to the delta of 2.4149 at 99.90. The binary call option delta is therefore the first differential of the binary call option fair value with respect to the underlying and can be stated mathematically as: δS → 0, Δ = dP dS. which means that as δS falls to zero the gradient of the price profile approaches the gradient of the tangent (delta) at the underlying asset price. Binary Call Option Delta and Implied Volatility. Figure 3 illustrates 5-day binary call profiles with Figure 4 providing the associated deltas over a range of implied volatilities as in the legends.

In Figure 3 the 9% fair value profile is fairly shallow in comparison to the other four profiles which is reflected in Figure 4 where the 9% delta profile fluctuates just 0.16 from a delta of 0.22 at the wings to 0.38 when at-the-money and is the flattest of the five delta profiles. In Figure 3, with the volatility at 1% and underlying below $100, there is little chance of the binary call being a winning bet until the underlying gets close to the strike where the price profile steepens sharply to travel up through 0.5 before levelling out short of the binary call price of 100. Fig.3 – Binary Call Option Fair Value w. r.t. Volatility. The 1% delta in Figure 4 reflects this dramatic change of binary call price with the 1% delta profile showing zero delta followed by a sharply increasing delta as the binary call price changes dramatically over a small change in the underlying, followed by a sharply decreasing delta as the binary call option delta reverts to zero as the binary call levels off at the higher price. For the same volatility the delta of the binary call which is 50 ticks in-the-money is the same as the delta of the binary call 50 ticks out-of-the-money. In other words the deltas are horizontally symmetric about the underlying when at-the-money, i. e. when the underlying is at $100. Fig.4 – Binary Call Option Delta w. r.t. Implied Volatility. This feature of the binary call option delta when at the money is that of the Dirac delta function, or δ function, where the area below the profile is 1. This means that the binary call option delta when at-the-money and with time to expiry or implied volatility approaching zero can become infinitely high with a total area of one under the spike. This feature obviously renders delta-neutral hedging as impractical when the binary call option is at-the-money with very little time to expiry or extremely low implied volatility. In practice these conditions and a short at-the-money binary call position in Apple Inc would require the delta-neutral trader to bid for the company in order to get ‘flat’! Binary Call Option Delta and Time to Expiry. In the above illustration (Fig.4) the 1.00% delta peaks off the scale at 3.41 but this value increases sharply as the time to expiry decreases from 5 days.

Figures 3 & 5 illustrate binary call price profiles which always have a positive slope so the binary call options delta is always positive. Fig.5 – Binary Call Option Fair Value w. r.t. Time to Expiry. The 25-day price profile in Figure 5 has the longest time to expiry and subsequently has the lowest gearing which is illustrated in Figure 6 by the lowest value delta profile. Fig.6 – Binary Call Option Delta w. r.t. Time to Expiry. Short time to expiry binary call (and put) options provide the greatest gearing of any financial instrument as illustrated by the extremely steep price profile of Figure 5 and its associated delta in Figure 6. The 0.1-day delta peaks at 4.82 which basically offers gearing of 482% compared to the 100% gearing of a long future position. Decreasing volatility and decreasing time to expiry have a similar impact on the price of a binary option which is borne out by the similar delta profiles of Figures 4 & 6. Table 2 shows 10 day, 5% volatility binary call option prices with deltas. At $99.87 the binary call is worth 43.5921 and has a delta of 0.4764. Therefore, if the underlying rises three ticks from $99.87 to $99.90 the binary call will rise in value to: 43.5921 + 3 x 0.4764 = 45.0213. If the underlying fell 3 ticks from $99.93 to $99.90 the binary call would be worth: 46.4641 + (-3) x 0.4805 = 45.0226. At $99.90 the binary call value in Table 2 is 45.0250 so there is a slight discrepancy between the values calculated above and true value in the table. This is because the deltas of 0.4764 and 0.4805 are the deltas for just the two underlying levels of $99.87 and $99.93 respectively, i. e. the deltas change with the underlying.

At $99.90 the delta is 0.4788 so the value of 0.4764 is too low when assessing the upward move from $99.87 to $99.90, while similarly the delta of 0.4805 is too high when evaluating the change in binary call price when the underlying falls from $99.93 to $99.90. The average of the two deltas at $99.87 and $99.90 is: ( 0.4764 + 0.4788 ) 2 = 0.4772. and should this number be used in the first calculation above then the binary call at $99.90 would be estimated as: 43.5921 + 3 x 0.4772 = 45.0237. an error of 0.0013. The average delta between $99.90 and $99.93 is: ( 0.4788 + 0.4805 ) 2 = 0.47965. The second calculation above would now generate a price at $99.90 of: 46.4641 + (-3) x 0.47965 = 45.02515. an error of just 0.00015. The section on binary call option gamma will provide the answers as to why this discrepancy still exists. Hedging with Binary Call Option Delta. If the numbers in Table 2 related to a bond future then it might not be unreasonable to offer a binary option on that future with a settlement value of $1000 equating to $10 per point. Example : a binary options trader buys 100 contracts of the $100 strike binary with 10 days to expiry with the future trading at $99.87 at a price of 43.5921, costing a total of: 43.5921 x $10 x 100 contracts = $43,592.10. How does the trader hedge away the immediate directional exposure? 100 contracts of the option with delta of 0.4764 equates to a position of 47.64 futures at the futures price of $99.87 so the trader sells 48 futures to hedge (just not possible to sell 0.64 of a future…….the option price of 43.5921 was arrived at by ‘averaging in’!) 1) the future falls to $99.81 where the option is worth 40.7518 so the position P&L is now: Binary Call Option loses: 40.7518 – 43.5921 = -2.8403.

which equates to a loss of: -2.8403 x $10 x 100 contracts = -$2,840.3. which equates to a profit of: -0.060.01 x $10 x -48 = +$2,880. an overall profit of $39.70. 2) the future rises to $99.93 where the option is worth 46.4641 so the position P&L is now: Binary Call Option gains: 46.4641 – 43.5921 = 2.8720. which equates to a profit of: 2.8720 x $10 x 100 contracts = +$2,872.00. which equates to a loss of: 0.060.01 x $10 x -48 = -$2,880. an overall loss of $8.00. This loss on the upside can be explained away by the over-hedging of 48 futures as opposed to 47.64 futures. If 47.64 futures were used (a spreadbet maybe?) then the overall downside profit would be reduced to +$18.10 while the upside loss of $8.00 would turn into a profit of $13.60. The constant use of deltas for hedging in this manner is vital for an options market-maker. That using a hedge of 47.64 produces a profit on both the upside and downside is the impact of the gamma, in this case positive gamma. Binary Call Option Delta v Conventional Call Option Delta. Figures 7a-e illustrate the difference over time to expiry between the binary call option deltas and their conventional cousins for those already familiar with conventionals. Fig.7a – 25-Day Binary & Conventional Call Delta.

Fig.7b – 10-Day Binary & Conventional Call Option Delta. Fig.7c – 4-Day Binary & Conventional Call Option Delta. Fig.7d – 1-Day Binary & Conventional Call Option Delta. Fig.7e – 0.1 Day Binary & Conventional Call Option Delta. Points of note are: 1) Whereas the conventional call deltas are constrained to a value of 0.5 when the option is at-the-money, the binary call is at its highest when at-the-money and has no constraint being able to approach infinity as time to expiry approaches 0. 2) When time to expiry is greater than 1 day (Figs.7a-c) the gearing of the binary call option is lower than the conventional call option, but when time to expiry is reduced (Figs.7d-e) the delta of the binary call becomes higher than the maximum value of 1.0 of the conventional call option. 3) The conventional call option delta profile resembles the price of the binary call. 4) Substituting a range of implied volatilities instead of the times to expiry would provide a similar set of illustrations to Figs.7a-e. Summary. Binary call option delta provides instant and easily understood information on the behaviour of the price of a binary call in relation to a change in the underlying. Binary calls always have positive deltas so an increase in the underlying causes an increase in the value of the binary call. When a trader takes a position in any binary call they are immediately exposed to possible adverse movements in time, volatility and the underlying. The risk of the latter can be immediately negated by taking an opposite position in the underlying equivalent to the delta of the position. For book-runners and market-makers hedging against an adverse movement in the underlying is of prime importance and hence the delta is the most widely used of the greeks. Nevertheless, as expiry approaches the delta can reach ludicrously high numbers so one should always observe the tenet: “Beware Greeks bearing silly analysis numbers…

”. Binary Call Options. Binary call options are all-or-nothing options that settle at 100 if in-the-money at expiry, or at zero if out-of-the-money. At-the-Money Settlement Rules. If the underlying at expiry is exactly on the strike (at-the-money) settlement can be treated in numerous ways: the two obvious candidates are that the binary call options are treated as in-the-money or out-of-the-money and are settled at 100 or 0 respectively. A possibly more rational method would be to treat the settlement as a ‘dead heat’ and settle the bet at 50. This approach has a particular advantage if binary call options and puts with the same strike are being offered since the call and put settlements would sum to 100, otherwise with the first two alternatives the aggregate settlement would be 200 or zero. Another approach sometimes used with the underlying settling on the strike is to simply void all bets. Binary Call Option’s Greeks. For those looking for a high level overview of the binary call options Greeks then the ‘Descriptive’ page may be suitable, while a more in-depth understanding of the mechanics, plus formulae, are provided in the ‘Analytic’ version: Binary Call Option Formula. Binary Call Option Fair Value = e^.N\left ( d_ \right ) S = price of the underlying asset. E = strike exercise price. r = risk free interest rate. D = continuous dividend yield of the underlying asset. t = time in years to expiry. σ = annualised standard deviation of asset returns.

Binary Call Options Price Profiles. The price of binary call options could be interpreted as the probability of the event happening if there is a zero cost-of-carry, i. e. interest rates are zero. What are referred to as prediction markets are sprouting up using binary call options and are now widely seen as a more accurate assessment of the probability of an event happening than analyst’s forecasts. Binary Call Options Over Time. The first graph shows the expiry profile of Oil $100 binary call options while the graph below shows the P&L profile illustrating how the expiry profile was arrived at over time. Zero interest rates are assumed as usual. Fig.1 – Expiration Value of $100 Binary Call Option. Fig.2 – Oil $100 Binary Call Options w. r.t. Time to Expiry. The buyer of binary call options is betting that Oil will be above $100 at expiry. The 8-day profile is shallow but over time this animal changes its spots to become the most highly geared and dangerous instrument in the world of finance. It is doubtful that any other single instrument can offer a P&L profile that can exceed an angle of 45°. Indeed the angle of an at-the-money moments before expiry tends to the vertical and becomes absolutely unhedgeable.

What is also apparent from the profiles over time is that the bet decreases in value when out-of-the-money and increases in value when in-the-money, i. e. the out-of-the-money has a negative binary call options theta, the in-the-money has a positive binary call options theta while the at-the-money has a binary call options theta of zero assuming that the above ‘dead heat’ rule is applied. Binary Call Options and Implied Volatility. Implied volatility is a critical input into the pricing of binary options and the level of implied volatility determines whether one is buying the binary option cheaply or too expensively. Figure 3 displays the oil binary call price profile over a range of implied volatilities. Fig.3 – Oil $100 Binary Call Options w. r.t. Implied Volatility. At the underlying price of $97.00, as implied volatility increases, so does the value of the out-of-the-money option. This is because with a low volatility the probability of the underlying price rising above the strike is low, which in turn will lead to worthless binary call options. As volatility increases and the underlying swings around more there is a greater chance of the binary option moving in-the-money, which in turn means the option will have a better chance of being a winner. So, if an increase in implied volatility increases the value of the option the option has positive vega. Alternatively, when the underlying is above the strike the 20% implied volatility profile is worth more than the other volatilities. This is because it is in-the-money so that if the underlying remains static the option will ultimately be worth 100. Increasing the volatility increases the probability that the underlying could slide under the strike thereby ultimately generating an option with a zero final settlement price. When an increase in implied volatility leads to a decrease in the value of the option the option is said to have negative vega. The binary call option is at the root of all financial instruments.

Any other instrument invented can be constructed from a portfolio of binary call options. This simplistic instrument is the key to all financial engineering: as software code can ultimately be reduced to a series of 0’s and 1’s, so can the world of financial markets. Binary Call Option Gamma. Binary call option gamma measures the change in the binary call option delta owing to a change in the underlying price and is the gradient of the slope of the binary call options delta profile versus the underlying. Below find a Finite Gamma evaluation, followed by the gamma’s sensitivity to implied volatility and time to expiry, application of the binary call option gamma, comparisons with conventional call option gamma, and finally the closed-end formula. The gamma is the measure most commonly used by market-makers or ‘structural’ traders when referring to portfolios of options. The gamma indicates how much the delta of an option or portfolio of options will change over a one point move. Market makers will generally try to hold books that are neutral to movements in the underlying but will more often than not be a long or a short gamma player. The long or short gamma indicates the position’s exposure to swings in the delta and therefore subsequent exposure to the underlying. Gamma provides a very quick, one glance assessment of the position with respect to a change in the underlying and gamma and is subsequently a very important tool to the binary portfolio risk manager. Binary Call Option Gamma and Finite Gamma. The gamma Γ of a binary option is defined by: Δ = the delta of the binary call. S = price of the underlying. δS = a change in the value of the underlying.

δΔ = a change in the value of the delta. The gamma is therefore the ratio of the change in the option delta given a change in the price of the underlying. Furthermore, since the delta is the first derivative of a change in the binary call price with respect to a change in the underlying it follows that the gamma is the second derivative of a change in the call price with respect to a change in the underlying. So the gamma can also be written as: P = the price of the binary call. Figure 1 shows the 1 day delta profile of a binary call with Figure 2 showing (in black) the same delta profile between the underlying prices of 99.78 and 99.99. Fig.1 – Binary Call Option Delta profile. Fig.2 – Slope of the Gamma at $99.90 plus approximating Gamma ‘chords’ The blue ’18 tick chord’ in Figure 2 travels between the point on the delta profile 9 ticks below the price of 99.90 to 9 ticks above where the delta of the binary call option is provided in the bottom row of Table 1. The gradient of this chord is defined by: SInc = Minimum Underlying Price Change. i. e. Gradient = (45.1746-1.0770) (99.99-99.81) x 0.01 = 2.4499. as indicated in the bottom row of the central column of Table 1. The gradients of the ‘12 tick chord’ and ‘6 tick chord’ are calculated in the same manner and are also presented in the central column of Table 1. As the underlying price difference narrows (as reflected by δS = 0.06 and δS = 0.03) the gradient tends to the gamma of 22.0569 at 99.90. The gamma is therefore the first differential of the binary call option delta with respect to the underlying and can be stated mathematically as: δS → 0, Δ = dP dS. which means that as δS falls to zero the gradient approaches the tangent (gamma) of the delta profile of Figure 2 at 99.90. Binary Call Option Gamma w. r.t. Implied Volatility. Figure 3 illustrates 5-day binary call option delta profiles with Figure 4 providing the associated gammas over a range of implied volatilities as in the legend. The delta gradient below the strike is always positive while above the strike it is always negative: this leads directly to the first observation that binary call options gamma is always positive when out-of-the-money, always negative when in-the-money. Where implied volatility falls to as low as 1% both the delta and gamma generate numbers that are so absolutely high that as a risk management tool they become bordering on worthless. This is nothing new to at-the-money conventional options gamma when time to expiry approaches zero.

Since the peak of the delta dictates a zero gradient, the gamma always travels through zero when at-the-money. Finally, as the implied volatility increases the delta profile flattens, which in turn means that the absolute values of the gamma also decrease. Fig.3 – Binary Call Option Delta Profiles w. r.t. Implied Volatility. Fig.4 – Binary Call Option Gamma Profiles w. r.t. Implied Volatility. Binary Call Option Gamma w. r.t. Time to Expiry. Figures 5 & 6 provide delta and associated gamma profiles over a range of times to expiry. Pretty much the same observations regarding the relationship between the delta and gamma which were noted over a range of implied volatilities apply to a range of time to expiry. Fig.5 – Binary Call Options Delta w. r.t. Time to Expiry. Fig.6 – Binary Call Options Gamma w. r.t. Time to Expiry. Binary Call Option Gamma Application. Table 2 shows the Table 2 of Binary Call Option Delta with the gamma added. The table is for 10 days to expiry and 5% implied volatility. At $99.87 the delta is worth 0.4764 and has a gamma of 0.0882.

Therefore, if the underlying rises three ticks from $99.87 to $99.90 the delta will change to: 0.4764 + 0.03 x 0.0882 = 0.47905. If the underlying fell 3 ticks from $99.93 to $99.90 the delta would change to: 0.4805 + (-0.03) x 0.0468 = 0.4791. At $99.90 the delta in Table 2 is 0.4788 so there is a slight discrepancy between the values calculated above and true value in the table. This is because the gammas of 0.0882 and 0.0468 are the gammas for just the two underlying levels of $99.87 and $99.93 respectively, i. e. the gammas change with the underlying. At $99.90 the gamma is 0.0676 so the value of 0.0882 is too high when assessing the change in delta on an upward move from $99.87 to $99.90, while similarly the gamma of 0.0468 is too low when evaluating the change in delta when the underlying falls from $99.93 to $99.90. The average of the two gammas at $99.87 and $99.90 is ( 0.0882 + 0.0676 ) 2 = 0.0779 and should this number be used in the first calculation above then the binary call at $99.90 would be estimated as: 0.4764 + 0.03 x 0.0779100 = 0.4787. an error of 0.0001. The average gamma between $99.90 and $99.93 is: ( 0.0676 + 0.0468 ) 2 = 0.0572. The second calculation above would now generate a price at $99.90 of: 0.4805 + (-0.03) x 0.0572100 = 0.4788. an error of just zero. Binary Call Option Gamma v Conventional Call Option Gamma. Figures 7a-e illustrate the difference over time to expiry between the binary call option gammas and conventional call option gammas.

Fig.7a – Binary Call Option Gamma v Conventional Call Option Gamma – Expiry 25-Days. Fig.7b – Binary Call Option Gamma v Conventional Call Option Gamma – Expiry 10-Days. Fig.7c – Binary Call Option Gamma v Conventional Call Option Gamma – Expiry 4-Days. Fig.7d – Binary Call Option Gamma v Conventional Call Option Gamma – Expiry 1-Days. Fig.7e – Binary Call Option Gamma v Conventional Call Option Gamma – Expiry 0.1-Days. Points of note are: 1) The change of scale to accommodate the gamma of the binary call as time decreases. 2) Conventional gamma remains positive while the binary gamma is both positive and negative dependent on whether ‘out-of’ or ‘in-the-money’. Summary. The gamma is probably of greater use to the options portfolio manager and, as such, is a Greek for the specialist. Some options traders define themselves by their willingness to be long or short gamma, and certainly the author would be amongst that ilk being himself a religiously ‘long gamma’ player.