Option Pricing Under the Heston-CIR Model with Stochastic Interest Rates and Transaction Costs
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The celebrated Black-Scholes model on pricing a European option gives a simple and elegant pricing formula for European options with the underlying price following a geometric Brownian motion. In a realistic market with transaction costs, the option pricing problem is known to lead to solving nonlinear partial differential equations even in the simplest model. The nonlinear term in these partial differential equations (PDE) reflects the presence of transaction costs. Leland developed a modified option replicating strategy which depends on the size of transaction costs and the frequency of revision. In this thesis, we consider the problem of option pricing under the Heston-CIR model, which is a combination of the stochastic volatility model discussed in Heston and the stochastic interest rates model driven by Cox-Ingersoll-Ross (CIR) processes with transaction costs. in this case, the reacted nonlinear PDE with respect to the option price does not have a closed-form solution. We use the finite-difference scheme to solve this PDE and conduct model’s performance analysis.