Randomized Quasi-Monte Carlo Methods for Basket Option Pricing Where Underlying Assets Follow a Time-Changed Meixner Lévy Process

Detta är en Master-uppsats från Lunds universitet/Matematisk statistik

Sammanfattning: Using derivative securities can help investors increase their expected returns as well as minimize their exposure to risk. For a risk-averse investor, options can offer both insurance and leverage and for a more risk-loving investor they can be used as speculation. Basket option is a kind of option whose payoff de- pends on an arbitrary portfolio of assets. The basket is made out of a weighted sum of assets. Pricing these kinds of options require multivariate asset pricing techniques which still remains a challenge. We aim to price basket options by using different Monte Carlo methods and compare their performance. We will test both quasi-Monte Carlo methods as well as randomized quasi-Monte Carlo methods in order to try to speed up the convergance rate. We will assume a L ́evy market model with stochastic volatility through an integrated CIR-process as a stochastic time change. More specifically we are going to model the data using the Meixner distribution. In order to calibrate the model parameters we use S&P 500 index vanilla options and the fast Fourier transform (FFT).

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