Description

Consider a European put option on a future that has a forward price (as of maturity) of $115 and a volatility of 30%. The option has a strike price of $90 and matures on 1 March 2003. The risk-free interest rate (on an actual/365 basis) is 6%. What is the value of this option as at 1 June 2002?

Function Specification

=oBLACK(2, "1/6/02", "1/3/03", 115, 90, 0.3, 0.06, 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 F = 115, X = 90, r = 0.0583, vol = 0.3 and T = 0.7479 (273/365 days), d₁ = 1.0745 and d₂ = 0.8150.

As iPC = -1 (put), N(d₁) is 0.1413 and N(d₂) is 0.2075 (see oCumNorm( ) function), the Black equation becomes:

Greeks

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

Delta

-0.135274

Gamma

0.007187

Theta

-4.141495

Vega

21.325985

Rho

-1.738260