Pricing Quanto Options And Its Applications Under Two Types Of Jump-difussion Models

Since Black and Scholes found the groundbreaking option pricing formula in 1973, the pricing problem of financial derivatives has been the main research works in Mathematical Finance. As the study moved forward in the real financial market, especially the occurrence of major financial emergencies and the growing of many questions in financial reform recently, the Black-Scholes model is found to be in-appropriate for changes of modern financial market. Modifying the Black-Scholes model to be consistent with the actual market changing is provided by many schol-ars. In 1976, Merton established firstly a jump-diffusion model in which the jump risks are assumed lo be unsystematic with a normal distribution for the jump mag-nitude of the log of the asset price. Based on the Merton's work, many research works have been gained under the jump-diffusion model. For example, S. G. Kou (2000) considered the merton's model where the jump risks are systematic and the jump magnitude of the log of the asset price is assumed to be a double exponential distribution. Meanwhile, empirical evidence has also found that the jump-diffusion model is capable of fitting the observed data and capturing both the real market changing and underlying asset fluctuation. In this dissertation, we consider the pric-ing of quanto options under the jump-diffusion model in which the jump magnitude follows both the normal distribution and the double exponential distribution, respec-tively. The main contributions are as follows:Chapter 1 provides an introduction to the necessity and significance of a re-search on option pricing and elaborates the academic literature of quanto options pricing. Furthermore, the motivations and main study topics of this dissertation are introduced. Chapter 2 discusses the pricing of European quanto options under the jump-diffusion model with two classes of jump magnitude distribution. The pricing for-mulas for four types of quanto options are derived under the jump-diffusion model by applying Fourier transform. And the closed-form pricing formulas for quanto options in the two classes of the normal jump-diffusion model and the double expo-nential jump-diffusion model are also obtained. Finally, some numerical examples are provided and the changes of option prices with model parameters are analyzed.In Chapter 3, A compound quanto option is considered under the two types of jump-diffusion model (mentioned in Chapter 2). We derive firstly pricing formulas for four types of quanto options on the Compound put options by applying Fourier transform. Second,the closed-form pricing formulas for quanto options under the two types of jump-diffusion model. Finally, we provide some numerical examples and analyze the changes of option prices with model parameters.Some applications of the Compound Quanto options are considered in Chapter4. First, we derive a pricing formula for Quanto extendible options under the two types of jump-diffusion model. Second, we consider the pricing of the American Quanto options and drive the ricing formulas for the American Quanto options. Finally, some numerical examples are provided and the changes of option prices with model parameters are also analyzed.In Chapter 5,we sum our main conclusions and suggestions for further research.