Pricing derivatives with stochastic volatility

HG Finance

Chen, Jilong ; Ewald, Christian

University:University of Glasgow

Department:Adam Smith Business School

关键词: Pricing, derivatives, stochastic volatility.;   

Others  :  http://theses.gla.ac.uk/7703/1/2016ChenPhD.pdf

来源: University of Glasgow

【 摘 要 】

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricingAsian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter6) and time dependent volatility in futures option (Chapter 7).In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approachwas 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 isthe Heston stochastic volatility model, the constant elasticity of variance (CEV) modeland the Schwartz (1997) two-factor model. It is shown that the method delivers rathertight upper bounds for the prices of Asian Options in these models and as a by-productdelivers 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 twomodels have closed-form solutions for futures contracts price. However, it is shownthat 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 theSchwartz (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 forcommodity futures contracts can be obtained in most situations.In Chapter 6, the applicability of the asymptotic approach developed in Fouque etal.(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-ordercorrection 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 usingthe 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 canalso be used to find the result of the time dependent spot volatility with futures optionsprices in the market. Furthermore, the limitations of the method that is used to findthe time dependent spot volatility will be explained, and it is also shown how to makesure of its accuracy.