Since Black and Scholes published their seminal paper [2] in 1973, the pricing of options by means of deterministic partial differential equations or inequalities has become standard practise in computational finance. An option gives the right (but not the obligation) to buy (call option) or sell (put option) a share for a certain value (the exercise price K) at a certain time T (exercise date)...

Wholesale electricity market designs in practice do not provide the market participants with adequate mechanisms to hedge their financial risks. Demanders and suppliers will likely face even greater risks with the deepening penetration of variable renewable resources like wind and solar. This paper explores the design of a centralized cash-settled call option market to mitigate such risks. A ca...

This paper describes the Itô processes for the continuously compounded returns on European call and put stock options under the one-dimensional diffusion assumption and the Black Scholes pricing model. It uses the Itô processes to motivate discrete time approximations for the returns on calls and puts. Theses models are used in a simulation study to compute the probability of an option return v...

Reduced European call and put option formulas by risk-neutral valuation are given. It is shown that the European call and put options for log-uniformjump-diffusion models are worth more than that for the Black-Scholes (diffusion) model with the common parameters. Due to the complexity of the jump-diffusion models, obtaining a closed option pricing formula like that of Black-Scholes is not tract...

We summarize an experimental study on the viability of several call option trading strategies that rely on our earlier work with machine-learning-based detection and prediction of heightened volatility periods. The proposed trading strategies makes use of the connection between call options prices and volatility in the underlying.1,2 As part of these strategies, the trader would purchase call o...