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Matlab Report

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MathLab
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Miami University
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Assignment Report ABSTRACT In thie report, we introduce the Heston model, For this problem, your job is to simulate the stock price S, and volatility process V, under correlation model simulate the Heston model using the following baseline parameters: So = 10, Vo = 0.06. = 0.1. x = 5, 9 = 0.04, o = 0.5, and the correlateon between two Brownian Motions p = - 0.6. Simulate from time 0 to 7 = 10, and use N = 10, 000 number of steps. which is a special case of the constant elasticity of variance stochastic volatility (CEV-SV) models. When the feller condition fails, the volitility is no longer strictly positive. In this case, the Euler discretization with four schemes can be used to fix this issue. We investigate the errors and performance of these four schemes. Finally, a well-commented matlab implementation of the Heston model for pricing European call option is provided. Keywords: Stochastic volatility, Heston, Euler discretization Introduction The Heston stochastic volatility models1 has been widely applied by practitioners in today’s financial market. It can be described as following: dS(t) = rS(t)dt +λpV(t)S(t)dWS(t), dV(t) = −κ(V(t)−θ)dt +ωpV(t)dWV(t), dWS(t)dWV(t) = ρdt, % % My implementation of the Heston model for strike price and vitality process % Date: 7th March 2018 % % Input: S_0 - Spot price of the underlying asset % K - Strike price % T - Time interval (years) % r - Risk-free rate % V_0 - Initial variance % theta - Long-term average variance % ...
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