Efficient simulation for greeks and bridges under diffusion models = 확산 모형에서의 민감도와 브리지 계산을 위한 효율적인 시뮬레이션 방법

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In general, diffusions cannot be directly simulated because we hardly know enough about their probability distributions. Discretization methods can be usually used for simulating the diffusions, but introduce bias. An exact simulation technique for one-dimensional diffusions has recently been proposed by Beskos and Roberts [4] based on the acceptance-rejection method. Their method completely eliminates the bias from discretization. We propose, in this dissertation, two simulation techniques based on the Beskos-Roberts method. First, we propose unbiased Monte Carlo estimators of the Greeks by taking advantages of the Beskos-Roberts method. Some exiting methods of the Greeks provide unbiased estimators theoretically. However, their implementation still requires discretization to estimate, which causes bias inevitably. The Beskos-Roberts method can overcome such difficulty. Second, we propose an approach to improve the plain Beskos-Roberts method. Under certain scenarios, the plain method can become inefficient because of small acceptance probabilities. To improve the acceptance probabilities, we suggest a new method by adapting the localization idea of Chen and Hunag [12].
Advisors
Kang, Wanmoresearcher강완모researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2017
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2017.2,[iv, 66 p. :]

Keywords

Beskos-Roberts method; unbiased estimator; exact Monte Carlo simulation; Greeks; diffusion bridges; 베스코스-로버츠 방법; 불편추정량; 몬테카를로 시뮬레이션; 파생상품의 민감도; 확산 브리지

URI
http://hdl.handle.net/10203/241903
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=675755&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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