egoroff
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 Feb 10 comment Probability - Generating fair outcome using unfair coin Right, but this could be (and probably is) an interview question for a quant job, so ? Feb 9 comment What is a martingale? A small precision : a centered random walk is a martingale :) Feb 8 awarded Supporter Feb 8 comment Expected Growth Plus, what shabbychef describes is a bona fide arbitrage opportunity only if the stock has a deterministic rate of return, equal to $\mu$. As soon as the future value of the stock is random, the probability of a negative terminal value is nonzero. What the reasoning does prove is that the forward price of the stock does not depend on $\mu$. Feb 8 comment Probability of touching OK. An approach without tedious computations is as follows : first find a nonzero real number $\gamma$ such that $X_t=S_t^{\gamma}$ is a martingale. This process $X$ now satisfies a "multiplicative reflection principle" : for any stopping time $T$, $X_{T+s}$ has the same law as $X_T^2/X_{T+s}$. Use this at $T_H$ (first hitting time of $H$) and mimic the classic reasoning for standard Brownian motion to find an expression of $P(T_H < t)$ as a function of $P(X_t > H)$, and finally, go back to $S$. Feb 8 answered Expected Growth Feb 8 awarded Teacher Feb 8 answered Is it possible to use a series of option prices to predict the most likely path of an asset? Feb 8 comment What is the difference between volatility and variance? I think you missed the point, Harpreet. If you take e.g. a standard Brownian motion and an Ornstein-Uhlenbeck (aka Vasicek) process, they both have the same (constant) instantaneous volatility. But their variances are different ; in the BM case the variance grows like time, whereas in the OU case the variance converges rapidly to a finite limit (stationary regime). Feb 8 answered Probability of touching