Since the seminar work by Black and Sholes on option pricing early 1970’s, many alternative option pricing models have appeared to address some key stylized facts for option markets such as volatility smile, fat-tail, volatility clustering, and so on. Most of the successful option models are parametric models based on diffusion processes with jumps usually called the Lévy processes and the para...

Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The convergence rate of the COS method is exponential and the computational complexity is linear. It has a wide range of applicability for different underlying dynamics, including Lévy processes and Heston’s stochastic volatility model, and for various types of option co...

This paper investigates the valuation of European option with credit risk in a reduced formmodel when the stock price is driven by the so-called Markov-modulated jump-diffusion process, in which the arrival rate of rare events and the volatility rate of stock are controlled by a continuous-time Markov chain. We also assume that the interest rate and the default intensity follow the Vasicek mode...

This paper considers the pricing of European options on assets that follow a stochastic differential equation with a quadratic volatility term. We correct several errors in the existing literature, extend the pricing formulas to arbitrary root configurations, and list alternative representations of option pricing formulas to improve computational performance. Our exposition is based entirely on...

In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained from Ethiopia commodity exchange (ECX) market to analyse the prices fluctuations.The natures of log-returns of the prices exhibit a...

This paper applies real option pricing theory to the analysis of a sample of 15 recent mergers and acquisitions in the European Financial Services industry. Overall, it is found that those acquisitions were not on average overpaid. Nevertheless, further analysis, assuming the option premium equalled the takeover premium, shows that either the implicitly assumed volatility was too low, the assum...

A master equation approach to the numerical solution of option pricing models is developed. The basic idea of the approach is to consider the Black–Scholes equation as the macroscopic equation of an underlying mesoscopic stochastic option price variable. The dynamics of the latter is constructed and formulated in terms of a master equation. The numerical efficiency of the approach is demonstrat...

We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic numerical method. Then, we apply the latter to some specific financial problems. In particular, we consider the pricing of a European option, a zero-coupon bond...