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oGBS( ) Example 4 - Commodity Put Option

Description

Consider a European put option on Gold that has a current spot price of $300.00 per ounce and a volatility of 15%. The storage cost of gold (expressed as a yield) is 1%, while the convenience yield is 2% (net convenience yield is thus 1%). The option has a strike price of $280.00 and matures on 1 April 2004. The risk-free interest rate (on an actual/365 basis) is 6.0%. What is the value of this option as at 1 April 2002?

 

Function Specification

=oGBS(2, "1/4/02", "1/4/04", 300, 280, 0.15, 0.06, 0.05, 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):

Equation Template
Equation Template

Referring to the equations for d1 and d2 (see model definition), if S = 300, X = 280, r = 0.0583, b = 0.0483, vol = 0.15, and T = 2.0027 (731/365 days), d1 = 0.8870 and d2 = 0.6747.

 

 

As iPC = -1 (put), N(d1) is 0.1875 and N(d2) is 0.2499 (refer to the oCumNorm( ) function), the oGBS( ) equation becomes:

 

Equation Template

 

 

Greeks

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

Delta

-0.183835

Gamma

0.004144

Theta

-1.115770

Vega

112.031028

Rho

-124.710844

Phi

-110.452131

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