Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity...

In this financial engineering research, we study the behaviour of an option premium of a call/put option which is embedded in a typical fixed coupon bond with finite maturity. The contribution of the research is the conclusion about the dynamics of premium changes; represented by direction and...

Replacing equity return (as in the equity risk premium) with returns on an arbitrary contingent claim, we obtain a new class of economic risk premiums to impose upon candidate models. These risk premiums reflect the distance between the physical and risk-neutral moments for asset returns, can be...

Finance researchers keep producing increasingly complex and computationally-intensive models of stock returns. Separately, professional analysts forecast stock returns daily for their clients. Are the sophisticated methods of researchers achieving better forecasts or are we better off relying on...

Today there are many equity derivatives that are traded on organized and over-the-counter markets. The models that allow market participants to value them and manage the associated risks on a daily basis are numerous. The idea of this study is, for vanilla equity options, to understand the Black...

Here, we introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability...

The market risk premium is central in finance, and has been analyzed by numerous studies in the time-series predictability literature and by growing studies in the options literature. In this paper, we provide a novel link between the two literatures. Theoretically, we derive a lower bound on...

A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may...

A relatively simple approach to correlating unit period returns of Lévy processes is developed. We write the Lévy process as a time changed Brownian motion and correlate the Brownian motions. It is shown that sample correlations understate the required correlation between the Brownian motions...

The concept of stress levels embedded in S&P 500 options are defined and illustrated with explicit constructions. The particular example of a stress function used is MINMAXVAR. Seven joint laws for the top 50 stocks in the index are considered. The first time changes a Gaussian one factor...