Maximum likelihood estimation of stochastic volatility and pricing derivatives in commodity markets

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Copyright: Lee, Damien Wai Keong
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Abstract
Financial markets worldwide have grown rapidly over the last few decades and so have the number of modelling approaches to analyse and price financial assets. With the emergence of more complex models, emphasis has also been placed on calibrating the models to market data. This thesis consists of three distinct components which investigate the estimation of financial models and the pricing of derivatives. The focus of these studies is stochastic volatility models and the crude oil futures market. The first component investigates discrete-time stochastic volatility models by comparing the estimation performance of three maximum-likelihood procedures. The analysis is conducted empirically on the fixed income and crude oil markets and also tests the validity of different stochastic volatility model specifications in-sample and out-of-sample. The study finds that the choice of estimation procedure is important if conditional volatility estimates are required. Also, a traditional AR(1) specification for the log-variance is sufficient in the fixed income and crude oil markets. The second component introduces a three-factor short/long factor commodity model which allows for mean-reversion in spot prices, expected increases in long-term prices and a time-varying market price of risk. The model is able to accurately capture the term structure of futures prices in the crude oil futures market with evidence suggesting that risk premiums are time-varying. Using the cross-section of futures prices we estimate a time-series of the market price of risk implied by the model. We find that the risk premiums in the crude oil market are driven by the same risk factors as equity and bond markets. In the final component, the short/long factor model is extended to incorporate both jumps and stochastic volatility. Semi-analytical solutions of futures and European option prices are derived for the model. The futures and option pricing performance is compared with nested specifications. The empirical results demonstrate that although introducing jumps or stochastic volatility does not impact futures pricing much, they are required for option pricing applications. When fitting the implied volatility surface of crude oil futures options, stochastic volatility is required to fit implied volatility over the maturity and moneyness dimensions but jumps are required when fitting the steep volatility smiles exhibited by short-term options.
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Author(s)
Lee, Damien Wai Keong
Supervisor(s)
Bhar, Ramaprasad
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Publication Year
2010
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Thesis
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PhD Doctorate
UNSW Faculty
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