In this thesis I discuss the method of time-change and its
applications in quantitative finance.
I mainly consider the time change by writing a continuous diffusion
process as a Brownian motion subordinated by a subordinator process.
I divide the time change method into two cases: deterministic time
change and stochastic time change. The difference lies in whether
the subordinator process is a
deterministic function of time or a stochastic process of time.
Time-changed Brownian motion with deterministic time change provides
a new viewpoint to deal with option pricing under stochastic
interest rates and I utilize this idea in pricing various exotic
options under stochastic interest rates.
Time-changed Brownian motion with stochastic time change is more
complicated and I give the equivalence in law relation governing the
``original time" and the ``new stochastic time" under different
clocks. This is readily applicable in pricing a new product called
``timer option". It can also be used in
pricing barrier options under the Heston stochastic volatility model.
Conclusion and further research directions in exploring the ideas of
time change method in other areas of quantitative finance are in the last chapter.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/5096 |
| Date | January 2010 |
| Creators | Cui, Zhenyu |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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