November 6th, 2011, 5:07 pm
I am an Econ PhD doing an internship and a project I have been given is to derive the underlying pdf of a futures contract based upon option prices. For the sake of simplicity, we are ignoring time considerations, insomuch as we are only looking at one contract with one expiration, i.e. I do not need to construct an entire volatility surface and then derive the corresponding pdf's for the the different expirations. I have read, and partially understood, Jim Gatheral's book "The Volatility Surface" and have read numerous papers on the topic of volatility and local volatility, so my knowledge is somewhat better than beginner, but I will make no claims of complete comprehension or understanding.Therefore, my question is twofold:1) What would be the easiest way to approximate the pdf of the underlying from option prices (should I use a local volatility model such as Dupire or Derman first then try to calculate the moments of the volatility etc?)2) What is typically the optimal way to perform such a task?My goal is first to achieve any type of results so I would prefer focus on the easiest way first. After having accomplished that, I would like to look at more techniques that would theoretically provide better goodness of fit or just be more robust in general.Any direction or input would be greatly appreciated.Glenn