Certain exotic options cannot be valued using closed-form solutions or even by numerical methods assuming constant volatility. Many exotics are priced in a local volatility framework. Pricing under local volatility has become a field of extensive research in finance, and various models are...

We address a number of technical problems with the popular Practitioner Black-Scholes (PBS) method for valuing options. The method amounts to a two-stage procedure in which fitted values of implied volatilities (IV) from a linear regression are plugged into the Black-Scholes formula to obtain...

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the...

VaR (Value at Risk) and CVaR (Conditional Value at Risk) are implied by option prices. Their relationships to option prices are derived initially under the pricing measure. It does not require assumptions about the distribution of portfolio returns. The effects of changes of measure are modest...

Prior research uses the basic one-period European call-option pricing model to compute default measures for individual firms and concludes that both the size and book-to-market effects are related to default risk. For example, small firms earn higher return than big firms only if they have...

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation-based least-squares Monte Carlo method by using put-call symmetry. The results show that, for a large sample of options with characteristics of relevance...

This paper develops a fully-fledged statistical arbitrage strategy based on a mean-reverting jump-diffusion model and applies it to high-frequency data of the S&P 500 constituents from January 1998-December 2015. In particular, the established stock selection and trading framework identifies...

This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under...