Description

Consider a European put option on a stock that has a current spot price of $90 and a volatility of 20%. The option has a strike price of $75 and matures on 1 March 2003. The risk-free interest rate (on an actual/365 basis) is 7%. What is the value of this option as at 1 March 2002?

Function Specification

=oBS(2, "1/3/02", "1/3/03", 90, 75, 0.20, 0.07, 0)

Solution

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

Referring to the equations for d₁ and d₂ (see model definition), if S = 90, X = 75, r = 0.0677, vol = 0.20, and T = 1 (365/365 days), d₁ = 1.3499 and d₂ = 1.1499.

As iPC = -1 (put), N(d₁) is 0.0885 and N(d₂) is 0.1251 (see oCumNorm( ) function), the Black Scholes equation becomes:

Greeks

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

Delta

-0.0885

Gamma

0.0089

Theta

-0.8504

Vega

14.4364

Rho

-8.7682