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Take a look at Hull's Appendix of the Volatility Smiles chapter. (Chapter 16 in my version). It gives a method to calculate the probability density function based on option prices: $$ g(K) = e^{rT} \frac{\partial ^2 c}{\partial K^2} $$ This result comes from the Breeden Litzenberger 1978 paper.


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I'll address your questions in order: 1a) For TSRV constructed using high frequency returns from NYSE market open to market close on a single day, the output should be numbers on the order of magnitude of 1e-4 to 1e-5. In other words, your numbers look about right. I got these number from calculating TSRV for IBM data myself using Kevin Sheppard's MatLab ...


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If you want a quick back of the envelop number, just use the IV of the nearest ATM option. Still the best would be to get the IV which is quite simple. However, three data points are definitely not enough to do this. Here's a matlab code that allows you to do it (credits to: volopta.com): % Variance swap calculation using the replication algorithm of % ...


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This is a somewhat ill-posed question. The "components" in your question are not components, they are just different options and all have different implied volatilities - all for the same underlying. If you are looking to get single number volatility a-la VIX without the whole VIX calculation, you should use ATM (at-the-money) implied volatility, which is ...


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See this resource at github , it uses different methods to calculate IV programmatically


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In black-scholes the option price depends not on sigma^2 but on sigma^2 T. So if volatility is going to be 20% or 21% over the next 10 years (assume for simplicity no other values are possible, just these two with equal prob, but we don't know which) then that will have a bigger impact on the option value than a 20 vs 21 uncertainty for a 1 year option. That ...


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In general, $v = \frac{\partial C}{\partial \sigma} > 0$ and $\theta = \frac{\partial C}{\partial t} < 0$. If maturity $T$ increases than $C$ increases. Suppose volatility is non-constant. Then if $T$ increases, the option value is more volatile, since the stock price is more volatile. Since $v > 0$ the option price must increase. He claims that ...



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