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분야
pptThe Stock Price Assumption
주가(원자산)의 움직임에 대한 가정
The Lognormal Distribution
Continuously Compounded Return (page 338)
The Expected Return
m and m−s2/2
Mutual Fund Returns(실무사례 12.1)
The Volatility
Estimating Volatility from Historical Data
Nature of Volatility
The Concepts Underlying Black-Scholes
The Derivation of the Black-Scholes Differential Equation
The Derivation of the Black-Scholes Differential Equation continuedThe Derivation of the Black-Scholes Differential Equation continued
The Black-Scholes Formulas
The N(x) Function
Properties of Black-Scholes Formula
Risk-Neutral Valuation
Applying Risk-Neutral Valuation(참고; appendix , Chapter 12)
Valuing a Forward Contract with Risk-Neutral Valuation
Implied Volatility
Dividends
American Calls
Black’s Approximation for Dealing withDividends in American Call Options
An Issue of Warrants & Executive Stock Options
Ito’s process
dx = a(x,t)dt+b(x,t)dz
Generalized Weiner process
dx = adt+bdz
Brownian motion
ds/s = μdt+σdz
랜덤워크의 시간의 간격이 매우 작다면 이는Brownian Motion에 가깝게 된다.
The Stock Price Assumption
주식의 가격을 S
매우 짧은 시간의 간격을 Dt 라 하자.
주식의 기대수익률은 평균이 m 이고 분산이 s 인 정규분포를 따른다.
주가(원자산)의 움직임에 대한 가정
결국 주가 S의 움직임은 GBM을 따른다
즉,
이 때 주가 S의 분포는 lognormal dist. 임
즉,
