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oGK( ) Example 2 - Equity Put Option

Description

Consider a European option to sell AUD / buy USD. The current exchange rate is 0.57 USD per AUD, and the rate volatility is 18%. The 'domestic' risk-free rate in the USA is 7% while the 'foreign' risk-free rate in Australia is 8% (both expressed on an actual/365 basis). The option has a strike rate of 0.55 USD per AUD and matures on 1 August 2003. What is the value of the option as at 1 March 2003?

 

 

Function Specification

=oGK(2, "1/3/03", "1/8/03", 0.57, 0.55, 0.18, 0.07, 0.08, 0)

 

Solution

This option could be equivalently valued as either a call option or a put option. The following solution treats the option as a put on the AUD.

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

Equation Template
Equation Template

Referring to the equations for d1 and d2 (see model definition), if S = 0.57, X = 0.55, r = 0.0677, rf = 0.077, vol = 0.18, and T = 0.4192 (153/365 days), d1 = 0.3313 and d2 = 0.2148.

 

 

As iPC = -1 (put), N(d1) is 0.3702 and N(d2) is 0.4150 (see oCumNorm( ) function), the Garman Kohlhagen equation becomes:

 

Equation Template

 

Greeks

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

Delta

-0.358457

Gamma

5.504513

Theta

-0.029687

Vega

0.134940

Rho

-0.092997

Phi

0.085647

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