Time change method in quantitative finance

time change;stochastic volatility;stochastic interest rates;exotic option;Quantitative Finance

Cui, Zhenyu

University of Waterloo

关键词: time change;    stochastic volatility;    stochastic interest rates;    exotic option;    Quantitative Finance;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5096/1/Cui_Zhenyu.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis I discuss the method of time-change and itsapplications in quantitative finance.I mainly consider the time change by writing a continuous diffusionprocess as a Brownian motion subordinated by a subordinator process.I divide the time change method into two cases: deterministic timechange and stochastic time change. The difference lies in whetherthe subordinator process is adeterministic function of time or a stochastic process of time.Time-changed Brownian motion with deterministic time change providesa new viewpoint to deal with option pricing under stochasticinterest rates and I utilize this idea in pricing various exoticoptions understochastic interest rates.Time-changed Brownian motion with stochastic time change is morecomplicated and I give the equivalence in law relation governing the``original time;; and the ``new stochastic time;; under differentclocks. This is readily applicable in pricing a new product called``timer option;;. It can also be used inpricing barrier options under the Heston stochastic volatility model.Conclusion and further research directions in exploring the ideas oftime change method in other areas of quantitative finance are in the last chapter.