# Tag Info

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If you're referring to Warren Buffett's comments, I think he believes it's due to inflation. This is not my specialty, so please take this with a flat of salt, but I have problems with the fact that as time approaches infinity, all call prices approximate half of the underlying price. Even more strangely, as time approaches infinity, all put prices ...

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Instead of a logical proof, would you accept a little bit of hand waving? Think about these two constants in Black-Scholes: $r$, interest rate $\sigma$, volatility Also think about a long-term option, say, one whose expiration date is a year from now. Will $r$ and $\sigma$ be the same over the year? Probably not. And yet a constant interest rate and ...

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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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I've ended up implementing a different model for -ve rates. I've used Bachelier's (Guassian) model that allows negative values. Most of the IR futures options are short-dated so model differences are within my tolerance.

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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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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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Just to give you two examples. Note that $dX_t =a \; dt + dW_t$ is Markov but is not a martingale. $dX_t=(\int_0^t X_s ds) \; dW_t$ is a martingale but is not Markov.

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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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5 minutes is a very short time period! If you have access to real time data of Implied Volatility and transaction Volume of the underlying of your option than you can take a look to the following article: Volatility Forecasts, Trading Volume, and the ARCH versus Option-Implied Volatility Trade-off In this article, the authors use the information from ...

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