Investment problem with model uncertainty and a new approach to implied volatility모델 불확실성을 고려한 투자와 내재 변동성에 대한 새로운 접근 방법

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We consider an all or nothing investment problem in finite time horizon when the investment opportunity set is changing stochastically over time, especially under a Markovian regime-switching environment, and a decision maker faces ambiguity on parameters governing profit flow dynamics of the investment. We apply $\alpha$-Maxmin Expected Utility($\alpha$-MEU) preferences to involve subjective attitude toward ambiguity and provide semi-explicit formulas for the expected value of investment and the present threshold value of the profit flow. Numerical results show that the threshold value depends on business cycle. A paramount parameter in investment decision making is related to a investment period. When investment period is short, it is important to know whether it is a recession or an expansion. With long investment period, the subjective attitude toward ambiguity make a huge difference in decision making. Furthermore, the tendency of ambiguity seeking is mitigated by introducing the regime-switching environment. Also we study an irreversible investment problem, i.e. optimal stopping time problem, under ambiguity and regime-switching environment. We provide an accurate approximation method for inverting an option price to the implied volatility under arithmetic Brownian motion, which is widely quoted in fixed income markets. The maximum error in the volatility is in the order of $10^{-10}$ of the given option price and much smaller for the near-the-money options. Thus our approximation can be used as an exact solution without further refinements of iterative methods.
Advisors
Choi, U-Jinresearcher최우진researcher
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2010
Identifier
418767/325007  / 020065805
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.2, [ vii, 59 p. ]

Keywords

산술 브라운 운동; 국면 전환; 내재 변동성; 비가역적 투자; 모델 불확실성; Arithmetic Brownian Motion; Implied Volatility; Regime-switching; Model Uncertainty; Irreversible Investment

URI
http://hdl.handle.net/10203/41933
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=418767&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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