New solvable stochastic volatility models for pricing volatility derivatives

New solvable stochastic volatility models for pricing volatility derivatives

Classical solvable stochastic volatility models (SVM) use a CEV process for instantaneous variance where the CEV parameter γ takes just few values: 0 the Ornstein-Uhlenbeck process, 1/2 the Heston (or square root) process, 1GARCH, and 3/2 the 3/2 model. Some other models were discovered in Henry-Labordére (2009) by making connection between stochastic volatility and solvable diffusion processes...

Efficiently pricing double barrier derivatives in stochastic volatility models

Imposing a symmetry condition on returns, Carr and Lee [2009] show that (double) barrier derivatives can be replicated by a portfolio of European options and can thus be priced using fast Fourier techniques (FFT). We show that prices of barrier derivatives in stochastic volatility models can alternatively be represented by rapidly converging series, putting forward an idea by Hieber and Scherer...

Finite Difference Methods in Derivatives Pricing under Stochastic Volatility Models

Pricing of Volatility Derivatives using 3/2- Stochastic Models

Analytic solutions are found for prices of both variance and volatility swaps and VIX options under new 3/2stochastic models for the dynamics of the underlying assets. The main features of the new stochastic differential equations are an empirically validated cν diffusion term, a nonlinear drift providing a balancing effect of a stronger mean reversion with high volatility, and for the case of ...

Pricing and Hedging Volatility Derivatives∗

This paper studies the pricing and hedging of variance swaps and other volatility derivatives, including volatility swaps and variance options, in the Heston stochastic volatility model. Pricing and hedging results are derived using partial differential equation techniques. We formulate an optimization problem to determine the number of options required to best hedge a variance swap. We propose...