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Pricing Options Using Monte Carlo Simulation
Dutton, Ryan ; Dědek, Oldřich (advisor) ; Červinka, Michal (referee)
Monte Carlo simulation is a valuable tool in computational finance. It is widely used to evaluate portfolio management rules, to price derivatives, to simulate hedging strategies, and to estimate Value at Risk. The purpose of this thesis is to develop the mathematical foundation and an algorithmic structure to carry out Monte Carlo simulation to price a European call option, investigate Black-Scholes model to look into the parallel between Monte Carlo simulation and Black-Scholes model, provide a solution for Black-Scholes model using Lognormal distribution of a stock price rather than solving Black-Scholes original partial differential equation, and finally compare the results of Monte Carlo simulation with Black- Scholes closed-form formula. Author's contribution can be best described as developing the mathematical foundation and the algorithm for Monte Carlo simulation, comparing the simulation results with the Black-Scholes model, and investigating how path-dependent options can be implemented using simulation when closed-form formulas may not be available. JEL Classification C02, C6, G12, G17 Keywords Monte Carlo simulation, Option pricing, Black-Scholes model Author's e-mail ryandutton4@gmail.com Supervisor's e-mail oldrich.dedek@fsv.cuni.cz
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Pricing Options Using Monte Carlo Simulation
Dutton, Ryan ; Dědek, Oldřich (advisor) ; Červinka, Michal (referee)
Monte Carlo simulation is a valuable tool in computational finance. It is widely used to evaluate portfolio management rules, to price derivatives, to simulate hedging strategies, and to estimate Value at Risk. The purpose of this thesis is to develop the mathematical foundation and an algorithmic structure to carry out Monte Carlo simulation to price a European call option, investigate Black-Scholes model to look into the parallel between Monte Carlo simulation and Black-Scholes model, provide a solution for Black-Scholes model using Lognormal distribution of a stock price rather than solving Black-Scholes original partial differential equation, and finally compare the results of Monte Carlo simulation with Black- Scholes closed-form formula. Author's contribution can be best described as developing the mathematical foundation and the algorithm for Monte Carlo simulation, comparing the simulation results with the Black-Scholes model, and investigating how path-dependent options can be implemented using simulation when closed-form formulas may not be available. JEL Classification C02, C6, G12, G17 Keywords Monte Carlo simulation, Option pricing, Black-Scholes model Author's e-mail ryandutton4@gmail.com Supervisor's e-mail oldrich.dedek@fsv.cuni.cz
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