March 1st, 2010, 12:05 pm
You could try the model on pg. 36 - "Fitted Heston" which is also described here on page 48ff with some comments on practical implementation and hedging performance.The basic idea is to use a given SV model, and fit it to the prevailing variance swap prices. The resulting model has a very low number of model parameters (correlation for skew, and vol of vol/mean reversion for vol of vol term structure), which can subsequently used to trade with.You basically1) Write down your preferred SV model. Heston allows for closed form. Say the short variance is u(t).2) Take the market term structure of variance swap vols, say K(x) for x maturity. Define the forward variance as m(t) := {K^2(t+dt)*(t+dt) - K^2(t)*t}/dt. Piecewise constant works really well (ie, if your variance swap vols are interpolated linearly in variance).3) Define your new pricing model as v(t) = m(t) * u(t) / EX[ u(t) ]If you do the latter formula just before your price, then your risk model will pick up perturbation of your variance swap prices (for example, if you compute BS vega), which gives you very nice risk.The above can easily be adjusted to take into account jumps.
Last edited by
probably on February 28th, 2010, 11:00 pm, edited 1 time in total.