application of small vol of vol expansion formula (Lewis)

tacos · February 2nd, 2011, 5:07 pm

Hihas anyone every applied the small vol-vol expansion formula of Lewis for a stoch vol process where the instantaneous volatility is defined as an exponential of ornstein-uhlenbeck process? I am referring to the general technique that Lewis proposed in his book "option valuation under stochastic volatility". How well does it perform in practice for that specific model, for say up to 2Y?thanks

Alan · February 3rd, 2011, 1:15 am

I haven't tried it. But, the volatility x(t) = sig(t) or the variance rate x(t) = sig(t)^2 follows an sded x = x ( a - b log x) dt + c x dW(t), with (a,b,c) some constants.so your expansion parameter will be c. From dimensional analysis, you probably want c^2 T < 1.You can also use dimensional analysis to estimate c for your application if youknow the corresponding vol. of vol. for, say the Heston model.(See the discussion in my book bottom of pg 4).