We present a two factor forward variance market model with jumps in returns and volatility. It allows the model user to directly control the behavior of future smiles and hence properly price forward smile risk of cliquet-style exotic products. The key idea, in order to achieve consistency...

Following a trend of sustained and accelerated growth, the VIX futures and options market has become a closely followed, active and liquid market. The standard stochastic volatility models—which focus on the modeling of instantaneous variance—are unable to fit the entire term structure of...

<title>Abstract</title>Given bid-offer quotes for a set of listed vanilla options, a fundamental need of option market makers is to interpolate and extrapolate the available quotes to a full arbitrage-free surface. We propose a methodology which directly controls the trade-off between smoothness and bid-offer...

We present a new and general technique for obtaining closed-form expansions for prices of options in the Heston model, in terms of Black-Scholes prices and Black-Scholes Greeks up to arbitrary order. We then apply the technique to solve, in detail, the cases for the second-order and third-order...

We study the pricing of options on realized variance in a general class of Log-OU (Ornstein--Ühlenbeck) stochastic volatility models. The class includes several important models proposed in the literature. Having as common feature the log-normal law of instantaneous variance, the application of...

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model by developing efficient transform-based pricing methods. This non-affine model gives prices of options on realized variance that allow upward-sloping implied...

We present a new and general technique for obtaining closed form expansions for prices of options in the Heston model, in terms of Black-Scholes prices and Black-Scholes greeks up to arbitrary orders. We then apply the technique to solve, in detail, the cases for the second order and third order...