University essay from Lunds universitet/Matematisk statistik

Abstract: On the financial markets, there are a large number of financial instruments. Two of these instruments is the European and Bermudan option, where the Bermudan option can be seen as a discrete version of the American option. Meaning, if one can price the Bermudan option one can also estimate the price of an American option. A method used to estimate the Bermudan option price is the Least-square Monte Carlo approach. It is a numerical approach that uses simulated values of the underlying asset and fits a polynomial for each date exercise is possible. The function is used to estimate the holding value of the option, by which one can determine whether to exercise the option. Using four different price movement models to simulate the value of the underlying asset, European option prices were estimated using the standard Monte Carlo method and Bermudan option prices were estimated using the Least-square Monte Carlo approach. The results show that the pricing of the European options frequently results in options prices outside the ASK/BID-spread. It also shows tendencies towards better estimations using price movement models containing more parameters, but that these models do not always show better results. Probably, it is because of external problems such as parameter fitting. The results also show that the Least-square Monte Carlo approach works sufficiently well when pricing the Bermudan option, but that in some cases incorrect estimations are made stemming from the fitted polynomials. To conclude, the Monte Carlo based option pricing methods are considered to work and result largely in satisfactory estimations, but contain problems such as the choice and fitting of polynomials and parameter calibration.

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