Description 
Consider a European call option on a stock that has a current spot price of $100, a volatility of 30%, and pays two dividends of $4.00 on 1 September 2002 and 1 February 2003. The option has a strike price of $100 and matures on 1 March 2003. The zero curve is flat at 5% (on an actual/365 basis). What is the value of this option as at 1 April 2002? 


Function Specification 
=oBSdd(1, "1/3/02", "1/3/03", 100, 100, 0.3, 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, is calculated as follows: S* = 100  7.73 = 92.27 Referring to the equations for d_{1} and d_{2} (see model definition), if S* = 92.27, X = 100, r = 0.0488, vol = 0.3 and T = 1 (365/365 days), d_{1} = 0.0446 and d_{2} 0.2554.


As iPC = 1 (call), N(d_{1}) is 0.5178 and N(d_{2}) is 0.3992 (see oCumNorm( ) function), the Black Scholes equation becomes: 




Greeks 
The following Greeks are computed using the formulas specified in oBSdd() Model Greeks: 
Delta 
As iPC = 1 (call), the delta equation simplifies to: 


Gamma 
As T = 1, the Gamma equation simplifies to: 



The n(d_{1}) equation gives 0.398546, and since S* = 92.27 and vol = 0.3, Gamma is 0.014397 
Theta 
As iPC = T = 1, the equation for Theta becomes: 


Vega 
As T = 1, the equation for Vega becomes: 


Rho 
As iPC = T = 1, the equation for Rho becomes: 




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