Probability Density of Lognormal Fractional SABR Model

Fractional Genetic Programming with Probability Density Data

We extend the fractional genetic programming scheme with data elements that are no more scalar, but instead are similar to probability density functions. The extension straightforwardly fits into fractional programming, in which data elements are blended from several values. In the case of our previous work, the blend produced a single scalar value. The extension proposes to build an approximat...

A parallel implementation of a derivative pricing model incorporating SABR calibration and probability lookup tables

We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-αβρ) stochastic volatility model using three strike inputs. SABR calibration involves a non-linear three dimensional minimisation and parallelisation is achieved by incorporating several assumptions un...

Fractional Probability Measure and Its Properties

Based on recent studies by Guy Jumarie [1] which defines probability density of fractional order and fractional moments by using fractional calculus (fractional derivatives and fractional integration), this study expands the concept of probability density of fractional order by defining the fractional probability measure, which leads to a fractional probability theory parallel to the classical ...

Exact Simulation of the SABR Model

The SABR Model: Explicit Formulae of the Moments of the Forward Prices/Rates Variable and Series Expansions of the Transition Probability Density and of the Option Prices

The SABR stochastic volatility model with β-volatility β є (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation between the stochastic differentials that appear on the right hand side of the model equations is considered. A series expansion of the transition probability density function of the mo...