network profile
| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 2 years, 3 months |
| seen | Mar 7 '11 at 23:11 | |
| stats | profile views | 16 |
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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 ? |
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Feb 9 |
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What is a martingale? A small precision : a centered random walk is a martingale :) |
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Feb 8 |
awarded | Supporter |
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Feb 8 |
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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 $\mu$. |
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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 $S$. |
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Feb 8 |
answered | Expected Growth |
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Feb 8 |
awarded | Teacher |
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Feb 8 |
answered | Is it possible to use a series of option prices to predict the most likely path of an asset? |
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Feb 8 |
comment |
What's 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). |
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Feb 8 |
answered | Probability of touching |
