Hong, Zheng HW8

Hong, Zheng HW8 - CNETzhengh HW8 Zheng Hong November 23,...

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Unformatted text preview: CNETzhengh HW8 Zheng Hong November 23, 2009 Contents 1 Computation Using Mertons (1976) Jump-Diffusion Model for European Options 2 2 Jump-Diffusion Monte Carlo Option Pricing 3 3 log-return compound process 7 4 Jump-Diffusion European Option Prices are Bigger Than Black-Scholes 7 1 1 Computation Using Mertons (1976) Jump-Diffusion Model for European Options Matlab Code: M-files 1 function In() CallPut=input(’Callput, Call = 1, Put = 0’); AssetP=input(’Underlying Asset Price’); Strike=input(’Strike Price of Option’); RiskFree=input(’Risk Free rate of interest’); Time=input(’Time to Maturity’); Vol=input(’Volatility of the Underlying’); Jumps=input(’Number of Jumps per Year’); Gamma=input(’Percent of total volatility explained by jumps’); MaxIter=input(’Max number of iterations to be used’); MertonJumpEurototal(CallPut,AssetP,Strike,RiskFree,Time,Vol,Jumps,Gamma,MaxIter) M-files 2 function = MertonJumpEurototal(CallPut, AssetP, Strike, RiskFree, Time, Vol, Jumps, Gamma, Max- Iter) Delta = sqrt((Gamma * (Vol 2 )) / Jumps); A = sqrt(Vol 2- Jumps * Delta 2 ); Value = 0; X=0; for i = 0:MaxIter VV = sqrt(A 2 + Delta 2 * (i / Time)); dt = VV * sqrt(Time); df = RiskFree + 0.5 * VV 2 ; d1 = (log( AssetP / Strike ) + df * Time ) / dt; d2 = d1 - dt; nd1 = normcdf(d1); nd2 = normcdf(d2); nnd1 = normcdf(-d1); nnd2 = normcdf(-d2); if CallPut CallPrice = AssetP * nd1 - Strike * exp(-RiskFree * Time) * nd2; X = CallPrice; end if CallPut PutPrice = Strike * exp(-RiskFree * Time) * nnd2 - AssetP * nnd1; X = PutPrice; end Value = Value + (exp(-Jumps * Time) * (Jumps * Time) i / factorial(i)) * X; end MertonJumpEuro = Value Compute results for both call and put with the two values of Vol: Vol VS CallPut 1 0.2 2.0535 6.3404 0.3 3.8459 8.2219 2 Compare results with respect to Vol: No matter the put option or the call option, the European call and put option price for the Mertons (1976) Jump-Diffusion Model is always larger when the Vol is larger with other parameters unchanged....
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This note was uploaded on 04/19/2010 for the course FIN 390 taught by Professor Hansen during the Fall '09 term at University of Illinois, Urbana Champaign.

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Hong, Zheng HW8 - CNETzhengh HW8 Zheng Hong November 23,...

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