Description

Consider an American call option on a stock that has a current spot price of $100, a volatility of 25%, and pays a dividend yield of 3% (on an actual/365 basis). The option has a strike price of $100 and matures on 1 November 2003. The risk-free interest rate (on an actual/365 basis) is 6%. What is the value of this option as at 1 November 2002?

Function Specification

=oBAW(1, "1/11/02", "1/11/03", 100, 100, 0.25, 0.06, 0.03, 0)

Solution

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

Referring to the equation for S* (see model definition), if X = 100, r = 0.0583, b = 0.0287 , vol = 0.25, T = 1 (365/365 days), and after using an initial guess of 147.5725, S* = 235.2758.

As S < S*, the Barone Adesi Whaley equation becomes:

where

Greeks

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

Delta

0.579637

Gamma

0.015964

Theta

-5.800683

Vega

37.758058

Rho

46.433199

Phi

-56.589317