BjerkStensPhi (Function)
DisclaimerThe BjerkStensPhi function is used by the BjerkStensCall function to calculate the theoretical value of American Call and Put options.
Syntax
BjerkStensPhi(AssetPr, YearsLeft, MyGamma, MyH, TriggerPr, Rate, Carry, Volty);
Returns (Double)
A numeric value representing the theoretical value of an American Call or Put option using the Bjerksund & Stensland model.
Parameters
| Name | Type | Description |
| AssetPr | Numeric | Specifies the price of the underlying asset. |
| YearsLeft | Numeric | Sets the amount of time left until option expiration in terms of years (enter 1 to stand for 365 days). |
| MyGamma | Numeric | Sets the Gamma to consider for the calculation. |
| MyH | Numeric | Sets the StrikePr or TriggerPr as determined by the calling function BjerkStensCall. |
| TriggerPr | Numeric | Sets the flat boundary of exercise strategy, as detemined by the calling function BjerkStensCall. |
| Rate | Numeric | Sets the short-term risk free interest rate, usually the 90-day T-Bill, (enter .049 for 4.9%). |
| Carry | Numeric | Sets the cost of carrying the underlying asset as a percentage in decimal points, usually the short-term risk free interest rate (enter .049 for 4.9%). |
| Volty | Numeric | Sets the volatility of the underlying asset as a percentage in decimal points (enter .225 for 22.5%). |
Remarks
The value for Carry differs based on the type of asset:
- Non-dividend paying stock - Set to the current annual risk-free interest rate.
- Dividend paying stock - Set the current annual risk-free interest rate minus the annual dividend yield percentage. Example: if the current risk-free interest rate is 4.5% and the stock's annual dividend yield is 2.4%, then the cost of carry could be approximated as 4.5% - 2.4% = 2.1%.
- Futures contract - Set to 0 (zero).
- Currency contract - Set to the current "domestic" risk-free interest rate minus current "foreign" risk-free interest rate. Note: the domestic and foreign interest rates depend on how the currency cross-rate is quoted.
The value for Volty can also be a reserved word value such as IVolatility.
BjerkStensPhi is used by the BjerkStensCall and OptionsComplex functions.
For additional information and details, you may wish to consult the following reference texts:
Chriss, Neil A. Black-Scholes and Beyond: Option Pricing Models. McGraw-Hill, 1997.
Haug, Espen Gaarder. Option Pricing Formulas. McGraw-Hill, 1998.