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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online