Option pricing under Heston model using Monte Carlo method for Euler scheme

Siswanto, Abe Gracia Vallerian Tenno (2015) Option pricing under Heston model using Monte Carlo method for Euler scheme. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Nowadays, option is widely used as financial instrument. The pricing of option becomes very important. In this thesis, we use Heston model to price the American call option using Monte Carlo method for Euler Scheme, Steepest Descent method and Golden Ratio method. Heston model is more accurate than BlackScholes model because it does not use constant volatility, which is more approachable to the market. However, the parameters in Heston model cannot be found analytically. We use numerical approach to approximate the parameters. We divide the model into 3 phases. First, in Parameter phase, we approximate the Heston parameters using Maximum Likelihood method with Steepest Descent and Golden Ratio method. Before we do the simulation in this phase, we need to approximate the volatility of the stock because it is not observable directly. Next, in Fitting phase, we check whether the model fit with the real data using Monte Carlo for Euler scheme. One of the limitations in this phase is Feller condition. We need to deal with this condition because many stocks does not follow this condition which might affect the result. If the model fits with the real data, we can continue to the next phase. Finally, we simulate the stock movement to price option in Pricing Phase. From the simulations using 4 stocks, we found that not every stocks fit with the model. Increasing the number of Monte Carlo trials will make the error smaller. The option price from simulation does not seem to fit with the market price because the market option price is not ideal. The market price tends to be lower than simulation price. We can improve the simulation by using different method to approximate variance and change the scheme if the stock does not follow Feller condition. We have tried to use improvements and achieved better results.

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