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I want to simulate stock price paths with different stochastic processes. I started with the famous geometric brownian motion. I simulated the values with the following formula: ...
3
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1answer
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How to calculate probability of touching a take-profit without touching a stop-loss?

How to calculate probability of touching a take-profit without touching a stop-loss (no-dividend stock, infinite time)?
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Is the stock price process a martingale or a Markov process?

Some people claim that the data-generating process for stocks is a "martingale" and that is has the "Markov property". Are they unrelated? Is it that the Markov property implies some sort of ...