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3

We assume that $\gamma(s, t)$ is differentiable with respect to $t$. Then, \begin{align*} dx_t = \left(\int_0^t \frac{\partial\gamma(s, t)}{\partial t} dW_s \right)dt + \gamma(t, t) dW_t. \end{align*}

0

Implied Volatility means the option is overpriced versus the model price. It means I'm paying more to buy an option than normally. For example, when a gap happens on the stock, the option price is high. It has no bearing on what will happen, but more on what did. The Bid and Ask price are set by people with expectations. And those prices are out of line with ...

3

You can show that "the implied variance of an ATM short maturity option is equal to the expectation under the risk neutral measure of the integrated variance over the life of the option." As you move away from the assumptions: ie not ATM, longer maturity, risk neutral measure far from true, then the forecasting power diminishes. (Google 'stochastic ...

1

1 is wrong. The implied vol is a convenient way to look at the option price, nothing more. 2 is an observed fact for equities in general but not the case for some other assets eg commodity futures. 3 is also an observed fact for equities generally (but not for single stocks with short time to expiry). If 1 and 2 were true, then 3 would naturally ...

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