## oGBS( ) Example 2 - Equity Put Option with Continuous Dividends

Description

Consider a European put option on a stock that has a current spot price of \$120.00, a volatility of 35% and pays a continuous dividend of 3%. The option has a strike price of \$110.00 and matures on 1 September 2003. The risk-free interest rate (on an actual/365 basis) is 6.0%. What is the value of this option as at 1 December 2002?

Function Specification

=oGBS(2, "1/12/02", "1/9/03", 120, 110, 0.35, 0.06, 0.03, 0)

Solution

The continuous equivalents of the actual/365 risk-free interest rate and the cost of carry are calculated as follows (see special cases):

Referring to the equations for d1 and d2 (see model definition), if S = 120, X = 110, r = 0.0583, b = 0.0287, vol = 0.35, and T = 0.7507 (274/365 days), d1 = 0.5096 and d2 = 0.2064.

As iPC = -1 (put), N(d1) is 0.3052 and N(d2) is 0.4182 (see oCumNorm( ) function), the oGBS( ) equation becomes:

Greeks

The following Greeks are computed using the formulas specified in oGBS( ) Model Greeks:

-0.29846

0.00942

-6.79811

35.62755

-33.05876

###### Phi

-26.88590

Copyright 2013 Hedgebook Ltd.