Description 
Consider a European put option on a stock that has a current spot price of $90 and a volatility of 20%. The option has a strike price of $75 and matures on 1 March 2003. The riskfree interest rate (on an actual/365 basis) is 7%. What is the value of this option as at 1 March 2002? 


Function Specification 
=oBS(2, "1/3/02", "1/3/03", 90, 75, 0.20, 0.07, 0) 


Solution 
The continuous equivalent of the actual/365 riskfree interest rate is calculated as follows: Referring to the equations for d_{1} and d_{2} (see model definition), if S = 90, X = 75, r = 0.0677, vol = 0.20, and T = 1 (365/365 days), d_{1} = 1.3499 and d_{2} = 1.1499.


As iPC = 1 (put), N(d_{1}) is 0.0885 and N(d_{2}) is 0.1251 (see oCumNorm( ) function), the Black Scholes equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oBS( ) Model Greeks: 
Delta 
0.0885 
Gamma 
0.0089 
Theta 
0.8504 
Vega 
14.4364 
Rho 
8.7682 


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