Essays in Asset Pricing under Stochastic Volatility
Date Issued
2007
Date
2007
Author(s)
Jia-Hau, Guo
DOI
en-US
Abstract
THESIS ABSTRACT
Stochastic volatility models have enjoyed an excellent reputation both theoretically and practically since introduced in the early 1990s. Lots of empirical studies provide evidence that the volatility of the price return is stochastic. The significant contribution of stochastic volatility models in asset pricing is consistently confirmed. However, there are still a few bottlenecks in asset pricing for the application of stochastic volatility models. Lots of problems remain unsolved. We consider different asset pricing problems in the two parts of the thesis, and provide the analytic solutions under stochastic volatility. We further analyze the impact of stochastic volatility on asset pricing.
The purpose of the first part is to consider the problem of pricing equity swaps in a stochastic volatility and stochastic interest rates economy. This article adds to the literature on equity swaps by presenting an equity swap pricing model that allows for non-deterministic volatility and by exploiting the relation between the swap rate and the volatility variation of underlying equity returns. The pricing formulae consider not only the correlation between interest rates and underlying equity returns but also the correlation between volatility shocks and underlying equity returns. Closed form solutions for a variety of equity swaps with constant or variable notional principal in the stochastic volatility and stochastic interest rate model are derived from the forward-neutral pricing model. No matter whether the notional principal of the equity swap is constant or variable, its swap rate in the stochastic volatility case is shown to be the same as that in the deterministic volatility case. Nevertheless, it is not the case for capped equity swaps. A capped equity swap is composed of a normal equity swap and a series of forward-start European call options. Stochastic volatility plays an important role on the valuation of capped equity swaps.
The problem of pricing American options using the quadratic approximation method with stochastic volatility and jumps is considered in the second part of the thesis. Compared to Monte Carlo simulations or other time-consumption numerical techniques, it is particularly valuable to extend the existing efficient solutions for American options from constant to stochastic volatility. Our results show that deep out of money American options with short-maturities should not be over-simplified to be treated as the European ones. Early exercise premiums are also found to be very sensitive to the changes in interest rates and dividend rates.
Subjects
隨機波動
權益交換
美式選擇權
二次近似解
遠期選擇權
Stochastic Volatility
Equity Swap
American Option
Quadratic Approximation
Forward-Start Option
Type
thesis
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