The volatility manager makes it easy to control parameters for any of Tbricks by Itiviti’s volatility curve parameterization functions, as well as to fit the parameters to implied market volatilities and visualizing the result.
The Black–Scholes option pricing model assumes that the underlying volatility is constant over the life of the derivative, and unaffected by the changes in the price level of the underlying security. However, long-observed features of the implied volatility surface such as the volatility smile, shows that implied volatility does vary with respect to strike price and expiry.
Tbricks offers three models to describe and handle this pricing flaw, the SVI (Stochastic Volatility Inspired), the CCS (Clamped Cubic Spline) curve and the Wing volatility model.
The SVI model is based on work done by Jim Gatheral. This model fits certain markets extremely well, even for short expirations, making it highly practical. The SVI model does not give rise to arbitrage: if it is fitted to actual option price data, negative vertical spreads or butterflies never arise. Also calendar spread arbitrage can be excluded. SVI is in a sense compatible with stochastic volatility models such as Heston.
The CCS interpolation is a standard spline interpolation, where the number of spline points can be chosen freely.
The call/put Wing volatility model is a parabolic volatility curve defined by parameters such as height (ATM volatility level), slope (modeling the slope of volatility curve’s tangent at ATM), call and put wing curvatures and cutoffs beyond which the model behaves according to Lee’s rule for implied volatilities at extreme strikes.
The fitting of the curves to market volatilities, either manually or automatically, is based on proprietary algorithms for the SVI, extending work done by Zeliade Systems. For CCS, a standard mathematical least square fitting algorithm is used. For the wing model, a nonlinear least square fitting is used generically.
Both the volatility curve manager and the volatility models are fully implemented on top of Tbricks’ Application Framework infrastructure, which allows for seamless customization or adoption of other volatility curve models. Of course, the full source code is included, allowing you to see how the models are implemented in detail.