Quantitative approaches to modelling and simulation in some problems of mathematical finance금융수학의 모델링과 시뮬레이션 문제들에 대한 계량적 접근

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We study two important issues that arise in modern mathematical finance. The first issue is the estimation of a path-dependent derivative. Unlike a vanilla option, path-dependent derivatives have no closed-form solution for its value and Greeks in general. Hence the general approach is to use the Euler scheme but it has the shortcoming that the simulation results have bias. To resolve this, we devise an exact simulation scheme for the boundary hitting time of Brownian motion, and then we use this to estimate the value and the Greeks of a path-dependent derivative efficiently. The second issue is the correlation skew in equity markets that stand out especially when market collapses. Though there have been an evident correlation skew in equity markets, most of models handle the correlation as a fixed constant derived from its historical correlation. To reflect this phenomenon to the modelling and to the estimation of multi-asset derivatives, we derive a local correlation model of which dynamic is determined by the volatilities of underlying assets. And we demonstrate from experiments that our correlation model outperforms the use of a historical correlation in its forecasting ability.
Advisors
Kang, Wanmoresearcher강완모researcher
Description
한국과학기술원 :수리과학과,
Country
한국과학기술원
Issue Date
2021
Identifier
325007
Language
eng
Article Type
Thesis(Ph.D)
URI
http://hdl.handle.net/10203/294687
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=962388&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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