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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The Math and Magic of Financial Derivatives
Villanova UniversityMarch 31, 2008
Financial Derivatives have been called. . .
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%
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.