Though an analytical solution for the value of a European option in the context of the Black-Scholes model is more than 30 years old, a corresponding solution for American options has troubled practitioners and academics alike. In 2006, an analytical solution was presented for puts, however, this solution is computationally complex, requiring symbolic algebra packages, that make it impractical ...

Options or “privileges” as they were known in early 19th Century America actually appeared on the financial scene around the same times as stocks. Initially, there were numerous problems with the trading of options. The terms of the contract were different from contract to contract, contracts had to be exercised in person, and there really was no secondary market to trade. Options were eventual...

Volatility is a statistical measure that describes the amount of fluctuation in prices for a given investment; generally, the higher the volatility for an investment, the riskier it is perceived to be. Traders study volatility history so that they can make informed decisions on how to invest capital. The purpose of this article is to analyze implied volatility values, which are derived from the...

A Black-Scholes type model for American options will be considered where the underlying asset price experiences Brownian motion with random jumps. The mathematical problems is an obstacle problem for a linear one-dimensional diffusion equation with a functional source term. The problem is time discretized and solved at each time level iteratively with a Riccati method. Some numerical experiment...

One of the classic problems of mathematical finance is the pricing of American options and the behavior of the optimal exercise boundary close to expiry. For the uninitiated, financial derivatives are securities whose value is based on the value of some other underlying security, and options are an example of derivatives, carrying the right but not the obligation to enter into a specified trans...

The paper reviews options for structural design sensitivity analysis, including global finite differences, continuum derivatives, discrete derivatives, and computational or automated differentiation. The objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency, computational cost, and implementation options and effort. Linear stati...

Research was undertaken to evaluate alternative methods of selecting a sample of eligible respondents for the National Medical Expenditure Survey (NM ES) from the National Health Interview Survey (N HIS). This report presents estimates of the effects of alternative design options, obtained by statistical modeling techniques, for linking the NMES with the NH IS, The estimated survey costs for al...

This study investigates the lead-lag relationship between the option and stock markets for 17 trading-days prior to substantial earnings surprises, using the Berkeley options data base, changes in put-call parity, and a control option methodology. Before the passage of the Insider Trading Sanctions Act (ITSA) in 1984, the options market leads the stock market prior to negative surprises but tha...

Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility. This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance (CEV) diffusion model where the volatility is a function of the underlyin...

Reinforcement learning has been applied to many interesting problems such as the famous TD-gammon [1] and the inverted helicopter flight [2]. However little effort has been put into developing methods to learn policies for complex persistent tasks and tasks that are time-sensitive. In this paper we take a step towards solving this problem by using signal temporal logic (STL) as task specificati...