Feeds:
Posts

## CASE OF XOM FEB 19 2016 CALLS

Deterministic volatility models were championed by Dupire, Derman-Kani, and Rubinstein in 1994 — see dupire-PricingSmileLocalVolatilityPricing

I implemented the numerical PDE solution for the Dupire-Derman-Kani approach with parametric volatility following

$V(t) = \sigma_0^2 \int_0^t S_\alpha(s) ds$

where $S_{\alpha}(s) = s^{\alpha-1} E_{\alpha,\alpha}(-\kappa s^{\alpha})$ and also the fractional (stochastic) Heston model with a fractional volatility but with the stochastic parameters $\sigma=\rho=0$.  The latter fit the smile much better than the former in the exercise but there may be problems with the numeric solution of PDE that I have not checked yet.