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

Säfwenberg, Gustav LU (2016) In Master's Theses in Mathematical Sciences FMS820 20152
Mathematical Statistics
Abstract
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... (More)
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). (Less)
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author
Säfwenberg, Gustav LU
supervisor
organization
course
FMS820 20152
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Basket options Randomized quasi-Monte Carlo Time-changed Lévy Process Meixner Distribution Fast Fourier Transform
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3303-2016
ISSN
1404-6342
other publication id
2016:E32
language
English
id
8884919
date added to LUP
2016-11-16 10:34:36
date last changed
2016-11-16 10:34:36
@misc{8884919,
  abstract     = {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).},
  author       = {Säfwenberg, Gustav},
  issn         = {1404-6342},
  keyword      = {Basket options Randomized quasi-Monte Carlo Time-changed Lévy Process Meixner Distribution Fast Fourier Transform},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {Randomized Quasi-Monte Carlo Methods for Basket Option Pricing Where Underlying Assets Follow a Time-Changed Meixner Lévy Process},
  year         = {2016},
}