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Valuation of spread options using the fast Fourier transform under stochastic volatility and jump diffusion models

Andersson, Max LU (2015) EXTM10 20151
Department of Economics
Abstract
Spread options have become very popular in basically every sector of the financial markets, although the pricing of these derivatives still remains a challenge. In this thesis we examine the pricing of spread options using the fast Fourier transform (FFT). We implement a FFT method derived by Hurd and Zhou [10] and investigate the performance of the method under three different market models: the 2-asset geometric Brownian motion framework, a stochastic volatility model and a stochastic volatility model including random jumps in the asset dynamics. The third model is essentially a multivariate extension of Bates model where the jumps are distributed according to a compound Poisson process with log-normally distributed jump sizes. In doing... (More)
Spread options have become very popular in basically every sector of the financial markets, although the pricing of these derivatives still remains a challenge. In this thesis we examine the pricing of spread options using the fast Fourier transform (FFT). We implement a FFT method derived by Hurd and Zhou [10] and investigate the performance of the method under three different market models: the 2-asset geometric Brownian motion framework, a stochastic volatility model and a stochastic volatility model including random jumps in the asset dynamics. The third model is essentially a multivariate extension of Bates model where the jumps are distributed according to a compound Poisson process with log-normally distributed jump sizes. In doing so we successfully extend the work of Hurd and Zhou to include random jumps in the asset dynamics. The choice of models is motivated by the diverse applications of the spread options and its widespread usage in the energy markets.

In addition to showing that the method produces accurate prices at an attractive computational expense, we provide valuable information regarding how to specify the parameters inherent in the method, which is well needed for implementation. Lastly we look at the price sensitivity to the various market parameters which is considered fundamental for the understanding of the model and can have implications for both the calibration problem and trading. (Less)
Please use this url to cite or link to this publication:
author
Andersson, Max LU
supervisor
organization
course
EXTM10 20151
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Fast Fourier transform, Spread options, Derivatives pricing, Stochastic volatility, Jump diffusion
language
English
id
5424035
date added to LUP
2015-05-20 11:27:13
date last changed
2015-05-20 11:27:13
@misc{5424035,
  abstract     = {Spread options have become very popular in basically every sector of the financial markets, although the pricing of these derivatives still remains a challenge. In this thesis we examine the pricing of spread options using the fast Fourier transform (FFT). We implement a FFT method derived by Hurd and Zhou [10] and investigate the performance of the method under three different market models: the 2-asset geometric Brownian motion framework, a stochastic volatility model and a stochastic volatility model including random jumps in the asset dynamics. The third model is essentially a multivariate extension of Bates model where the jumps are distributed according to a compound Poisson process with log-normally distributed jump sizes. In doing so we successfully extend the work of Hurd and Zhou to include random jumps in the asset dynamics. The choice of models is motivated by the diverse applications of the spread options and its widespread usage in the energy markets.

In addition to showing that the method produces accurate prices at an attractive computational expense, we provide valuable information regarding how to specify the parameters inherent in the method, which is well needed for implementation. Lastly we look at the price sensitivity to the various market parameters which is considered fundamental for the understanding of the model and can have implications for both the calibration problem and trading.},
  author       = {Andersson, Max},
  keyword      = {Fast Fourier transform,Spread options,Derivatives pricing,Stochastic volatility,Jump diffusion},
  language     = {eng},
  note         = {Student Paper},
  title        = {Valuation of spread options using the fast Fourier transform under stochastic volatility and jump diffusion models},
  year         = {2015},
}