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Pricing binary options with kernel density estimation

Suppose I have a large enough set of prices of an asset, from which I can extract the following function: $f:T\to\mathcal{D}$, where $T$ is a fixed finite set of time intervals (say, 1 minute, 2 ...
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Calculation of physical and risk neutral density using index options

I am asking professionals for a help. There have already been the post Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor) from Finance_Newbie. But I am wondering ...