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You have been given good answers above. Basically, a stochastic process ${X_t}$ is a Markov process if $P(\{X_{t} \leq x\} | \mathcal{F}_{s}) = P(\{X_{t} \leq x\} | X_{s})$, for $s \leq t$. Here $\mathcal{F}_{s}$ is a $\sigma$-algebra, a special collection of subsets of the underlying sample space $\Omega$, containing all information about the process ...

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It's got nothing to do with you being identified as a market maker or not. It is simply that the other participants at that time are passive traders. The choice between hitting a bid or lighting a new level with a new offer are distinct and very different (especially, in some markets, in terms of fees paid or rebates received). So, you're not being ...

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Let's just deal with the aspect of probabilities. The answer is easier than you think. Consider the simplest one-step model. At the end, the stock will either be up (to $Su$) or down (to $Sd$). It will move up with a probability p or down with a probability (1-p). Here's how to calculate p: $p = \frac {e^{rT} - d}{u - d}$ For example, consider a stock ...

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It is true that you cannot infer the real World probabilities from the BSM formula directly. It is also equally true that the "right value" of the option in the real world is obtained by replacing the risk free rate with the expected return of the stock. Another example of this is simply to look at the real world price of a forward on the stock. If ...

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