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oRGW( ) Example 1 - Equity Call Option

Description

Consider an American call option on a stock that has a current spot price of $20, a volatility of 20%, and pays a single dividend of $2.00 on 1 September 2002. The option has a strike price of $22 and matures on 1 February 2003. The risk-free interest rate (on an actual/365 basis) is 7%. What is the value of this option as at 1 June 2002?

 

 

Function Specification

=oRGW("1/6/02", "1/2/03", 20, 22, 0.2, 0.07, "1/9/02", 2, 0)

 

 

Solution

The continuous equivalent of the actual/365 risk-free interest rate is calculated as follows:

Equation Template

Referring to the oRGW( ) model definition, the oCumNorm( ) function, and the oCumBiNorm( ) function, if S =20, X = 22, r = 0.0677, vol = 0.2, t = 0.2521 (92/365 days), and T = 1 (365/365 days), the following results are obtained:

 

 

Equation Template

 

 

 

The Roll Geske Whaley equation becomes:

Equation Template

 

 

Greeks

The following Greeks are computed using a discrete approximation of the partial derivative (see oRGW( ) Model Greeks):

Delta

0.242374

Gamma

-0.666085

Theta

-0.642848

Vega

4.269464

Rho

1.936162

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