Description 
Consider a European put option on a stock that has a current spot price of $80, a volatility of 25% and pays a dividend of $5.00 on 1 October 2002. The option has a strike price of $70 and matures on 1 December 2002. The riskfree interest rate is 5% (on an actual/365 basis). What is the value of this option at 1 June 2002? 


Function Specification 
=oBSdd(2, "1/6/02", "1/12/02", 80, 70, 0.25, D4:F4, D5:E5, 0) It is assumed the cell references for the zero curve and dividend schedule contain the appropriate input values. 


Solution 
The continuous equivalent of the flat actual/365 zero curve is calculated as follows: S*, the spot price less the present value of the future dividends paid during the life of the option, is calculated as follows: S* = 80  4.92 = 75.08 Referring to the equations for d_{1} and d_{2} (see model definition), if S* = 75.08, X = 70, r = 0.0488, vol = 0.25 and T = 0.5014 (183/365 days), d_{1} = 0.6225 and d_{2} 0.4455.


As iPC = 1 (call), N(d_{1}) is 0.2668 and N(d_{2}) is 0.3280 (see oCumNorm( ) function), the Black Scholes equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oBSdd() Model Greeks: 
Delta 
0.266795 
Gamma 
0.024729 
Theta 
3.263208 
Vega 
17.472822 
Rho 
11.232359 


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