We investigate the effect of including variance derivatives as calibration and hedging instruments for pricing and hedging exotic structures. This is studied empirically using market data for SPX and VIX derivatives applied in a stochastic volatility jump diffusion model

We explore the use of an option selling overlay to improve portfolio rebalancing. Within a multi-asset class portfolio, portfolio weights deviate from targets as asset values fluctuate. Investors typically use a rebalancing process to bring portfolio weights back to their desired strategic...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod...

It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a...

We derive explicit formulas for pricing double (single) barrier and touch options with time-dependent rebates assuming that the asset price follows a double-exponential jump diffusion process. We also consider incorporating time-dependent volatility. Assuming risk-neutrality, the value of a...

We first discuss the positive volatility skew observed in the implied volatilities of VIX options. To model this feature, we apply the square root stochastic variance model with variance jumps for the evolution of the S&P500 index volatility. Then we develop a robust method for unified pricing...

Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and...

A one-dimensional partial differential-difference equation (pdde) under forward measure is developed to value European option under jump-diffusion, stochastic interest rate and local volatility. The corresponding forward Kolmogorov partial differential-difference equation for transition...

European option under local volatility and Cox-Ingersoll-Ross model of short rate is computed from one-dimensional partial differential equations: the Black-Scholes equation for option price and the forward Kolmogorov equation for probability transition density. Both the computations are...