QuoteYou do not understand paul's point - which is simply that essentially all the parameters in ,say, the black scholes model are stochastic ( interest rates, volatility, dividends etc) and should be modelled as such rather than deterministically and recalibrated each day. Taking it to the extreme one should be modelling the whole implied volatility surface [or some other parameterisation] as a stochastic process. However the key issue is "how stochastic" and does it affect the option you are pricing.Agreed. This is why I have chosen to look at several models that allow the BS parameters to vary stochastically. My understanding is that these models have been criticised due to the difficulty in estimating parameters. I believe my estimation methodology overcomes this problem, allowing me to focus on the model performance.Quoteyou are saying the best prediction for tomorrow is some long term average, whereas the standard approach is to use today's market data- but in both cases you are assuming the parameters stay constant, whereas clearly they change.I think that if you specify a stochastic model of the underlying and use it to price options, then by definition the parameters shouldn't change over time. The fact that model parameters have to be reestimated regularly to get a good fit to the option surface is just evidence that the models are misspecified.What I find interesting is this: We know that the Heston or Bates model is misspecified. If we estimate the model consistently using a long set of option data we can fit the option surface with a 10% error. Alternatively we can reestimate the model each day, which gives a much better fit. However, when we do this we are just hiding the misspecification. I'm interested in whether or not the hidden misspecification of the daily reestimated model could be exploited using the more consistent estimation method. katastrofaThanks for the article. I wonder if the results would be different using my estimation method? It doesn't surprise me that the daily recalibration would lead to more accurate results over a short horizon since it is closer to the market prices.
Last edited by APablo
on November 9th, 2012, 11:00 pm, edited 1 time in total.