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oBLACK( ) Example 2 - Put Option of a Forward Contract

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:

Equation Template

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:

 

Equation Template

 

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

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