Asset or Nothing Function |
  
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Asset or Nothing Function |
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The AssetOrNothing function calculates the theoretical price, sensitivities, the implied volatility, and the implied strike value of a European asset-or-nothing option using the Cox and Rubinstein’s model. See Binary Options for a further explanation.
AssetOrNothing |
(OptionType, ModelStatistic, Asset, Strike, TimeExpire, Volatility, InterestRate, YieldRate, MarketPrice, TimeFormat, InterestType, YieldType) |
Note: Optional arguments are shown in Italics. MarketPrice is not Optional for the Implied Calculations.
Argument |
Description |
OptionType |
Alphanumeric value indicating the type of option: •Call = 1 or "c" (case insensitive) •Put = 2 or "p" (case insensitive) |
ModelStatistic |
Numeric value indicating the type of function required for the return value: •Theoretical = 1 •Delta = 2 •Gamma = 3 •Theta = 4 •ImpliedVol = 5 •Vega = 6 •Rho = 7 •Psi = 8 •Lambda = 9 •StrikeSensitivity = 11 •ImpliedStrike = 13 |
Asset |
The price of the underlying asset. Must be > 0. |
Strike |
The price at which the asset can be purchased if the option is a call or sold if the option is a put. Must be > 0. |
TimeExpire |
Time, expressed in either Days or Years (depending on the TimeFormat value), until the options expiration. Must be > 0. |
Volatility |
Annualized volatility of the underlying security. Must be > 0. |
InterestRate |
Risk-free interest rate expressed as a percentage. This rate is interpreted as a continuously compounded rate unless otherwise specified in the InterestType argument. Must be > 0. |
YieldRate |
Yield, expressed as a percentage (dividends or interest yield), of the underlying asset price. This rate is interpreted as a continuously compounded rate unless specified otherwise in the YieldType argument. |
MarketPrice |
Optional. The selling price of the option in the marketplace. This input is required when implied volatility and strike are calculated. Price must be > 0. |
TimeFormat |
Optional. Alphanumeric value indicating the format of the time arguments (i.e. TimeExpire). If omitted, Days are used as the default. Specified as either: •Days = 0 or "D" (case insensitive) •Years = 1 or "Y" (case insensitive) |
InterestType |
Optional. Alphanumeric value indicating the type of InterestRate to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a Continuously Compounded rate is used. |
YieldType |
Optional. Alphanumeric value indicating the type of YieldRate to use when evaluating the option. This value is converted to Continuously Compounded for the calculations. If omitted, a Continuously Compounded rate is used. |
Example
Calculate all of functions for an asset-or-nothing call option whose asset price 150 days from expiration is $38, the exercise price is $40, the risk-free interest rate is 8% per annum, the yield rate is 5% per annum, and the annual volatility is 25%. All of the rates are considered continuous. So, |
Input |
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Output |
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Variable |
Value |
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Function |
Name |
Value |
OptionType |
Call |
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1 |
Theoretical: |
16.203564 |
Asset |
38 |
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2 |
Delta: |
2.832861 |
Strike |
40 |
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3 |
Gamma: |
0.127732 |
InterestRate |
8% |
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4 |
Theta: |
-0.021088 |
YieldRate |
5% |
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5 |
Implied Vol.: |
0.239586 |
TimeExpire |
150 |
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6 |
Vega: |
0.189500 |
Volatility |
25% |
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7 |
Rho: |
0.375802 |
TimeFormat |
Days |
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8 |
Psi: |
-0.442392 |
MarketPrice |
16 |
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9 |
Lambda: |
6.643522 |
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11 |
Strike Sensitivity: |
-2.286129 |
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13 |
Implied Strike: |
40.089247 |