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oGBS( ) Example 3 - Currency Call Option

Description

Consider a European call option on the New Zealand Dollar which has a current exchange rate of 2.100 (expressed in USD/NZD) and a volatility of 25%. The (local) American risk-free interest rate is 6.0% while the (foreign) New Zealand risk-free rate is 7.5% (both expressed in actual/365 terms). The option has a strike price of 2.000 and matures on 1 October 2002. What is the value of this option as at 1 February 2002?

 

 

Function Specification

=oGBS(1, "1/2/02", "1/10/02", 2.100, 2.000, 0.25, 0.06, -0.015, 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 = 2.1, X = 2.0, r = 0.0583, b = 0.0141 , vol = 0.25, and T = 0.6630 (242/365 days), d1 = 0.2957 and d2 = 0.5367.

 

 

As iPC = 1 (call), N(d1) is 0.6163 and N(d2) is 0.5367 (refer oCumNorm( ) function), the oGBS( ) equation becomes:

 

Equation Template

 

 

Greeks

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

Delta

0.587416

Gamma

0.851489

Theta

-0.088309

Vega

0.622415

Rho

0.684713

Phi

0.817876

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