## BlackScholes(call_put_flag, S, X, T, r, v)

##### Last updated May 9, 2003

**Version:** 1 |
**Requires:** CF5 |
**Library:** FinancialLib

**Description:**

Returns the value of call and put options using the Black-Scholes pricing formula. S is the current asset price, X is the exercise price, r is the risk-free interest rate, T is the time to maturity of the option in years, v is annualized volatility. This code requires the cumulative normal distribution function CND().

**Return Values:**

Returns a number.

**Example:**

```
<CFSET CallPutFlag = 'c'>
<CFSET S='49.25'>
<CFSET X='50.00'>
<CFSET T='0.1'>
<CFSET r='0.35'>
<CFSET v='0.30'>
<cfoutput>
#BlackScholes(CallPutFlag,S,X,T,r,v)#
</cfoutput>
```

**Parameters:**

Name | Description | Required |
---|---|---|

call_put_flag | The Call Put Flag. | Yes |

S | The current asset price. | Yes |

X | Exercise price. | Yes |

T | Time to maturity. | Yes |

r | Risk-free Interest rate. | Yes |

v | Annualized volatility. | Yes |

**Full UDF Source: **

```
/**
* Computes the theoretical price of an equity option.
*
* @param call_put_flag The Call Put Flag. (Required)
* @param S The current asset price. (Required)
* @param X Exercise price. (Required)
* @param T Time to maturity. (Required)
* @param r Risk-free Interest rate. (Required)
* @param v Annualized volatility. (Required)
* @return Returns a number.
* @author Alex (axs@arbornet.org)
* @version 1, May 9, 2003
*/
function BlackScholes (call_put_flag,S,X,T,r,v) {
var d1 = ( log(S / X) + (r + (v^2) / 2) * T ) / ( v * (T^0.5) );
var d2 = d1 - v * (T^0.5);
if (call_put_flag eq 'c')
return S * CND(d1) - X * exp( -r * T ) * CND(d2);
else
return X * exp( -r * T ) * CND(-d2) - S * CND(-d1);
}
```

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