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:

Delta

-0.29846

Gamma

0.00942

Theta

-6.79811

Vega

35.62755

Rho

-33.05876

Phi

-26.88590