Pricing derivatives with stochastic volatility

Chen, Jilong (2016) Pricing derivatives with stochastic volatility. PhD thesis, University of Glasgow.

Abstract

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing
Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter
6) and time dependent volatility in futures option (Chapter 7).
In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach
was investigated in the context of various benchmark models for equities and com-
modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is
the Heston stochastic volatility model, the constant elasticity of variance (CEV) model
and the Schwartz (1997) two-factor model. It is shown that the method delivers rather
tight upper bounds for the prices of Asian Options in these models and as a by-product
delivers super-hedging strategies which can be easily implemented.
In Chapter 5, two types of three-factor models were studied to give the value of com-
modities futures contracts, which allow volatility to be stochastic. Both these two
models have closed-form solutions for futures contracts price. However, it is shown
that Model 2 is better than Model 1 theoretically and also performs very well empiri-
cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the
Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages;
hence, it is also a good choice to price the value of commodity futures contracts. Fur-
thermore, if these two models are used at the same time, a more accurate price for
commodity futures contracts can be obtained in most situations.
In Chapter 6, the applicability of the asymptotic approach developed in Fouque et
al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997)
multi-factor model, featuring both stochastic convenience yield and stochastic volatility.
It is shown that the zero-order term in the expansion coincides with the Schwartz (1997)
two-factor term, with averaged volatility, and an explicit expression for the first-order
correction term is provided. With empirical data from the natural gas futures market,
it is also demonstrated that a significantly better calibration can be achieved by using
the correction term as compared to the standard Schwartz (1997) two-factor expression,
at virtually no extra effort.
In Chapter 7, a new pricing formula is derived for futures options in the Schwartz
(1997) two-factor model with time dependent spot volatility. The pricing formula can
also be used to find the result of the time dependent spot volatility with futures options
prices in the market. Furthermore, the limitations of the method that is used to find
the time dependent spot volatility will be explained, and it is also shown how to make
sure of its accuracy.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Pricing, derivatives, stochastic volatility.
• Subjects: H Social Sciences > HG Finance
• Colleges/Schools: College of Social Sciences > Adam Smith Business School
• Supervisor's Name: Ewald, Prof. Christian and Kim, Dr. Minjoo
• Date of Award: 2016
• Depositing User: Mr JILONG CHEN
• Unique ID: glathesis:2016-7703
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 27 Oct 2016 07:40
• Last Modified: 09 Dec 2016 16:41
• URI: https://theses.gla.ac.uk/id/eprint/7703