The Math and Magic of Financial Derivatives. Klaus Volpert Villanova University March 31, 2008. Financial Derivatives have been called. . . .Engines of the Economy . . . Alan Greenspan (long-time chair of the Federal Reserve)
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Villanova UniversityMarch 31, 2008
whereS = price of underlyingdt = infinitesimal time perioddS= change in S over period dtdX = random variable with N(0,√dt)σ = volatility of Sμ = average percentage return of S
V =value of derivativeS =price of the underlyingr =riskless interest ratσ=volatilityt =time
Let’s use σ= 40%
S=102 standard normal random variable, and d1 and d2 are parameters depending on S, E, r, t,
This approach uses the discrete method of binomial trees to price derivatives
This method is mathematically much easier. It is extremely adaptable to different pay-off schemes.