APPROXIMATING GARCH-JUMP MODELS, JUMP-DIFFUSION PROCESSES, AND OPTION PRICING

Approximating GARCH-Jump Models, Jump-Diffusion Processes, and Option Pricing

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering limiting models for our resulting approximating GARCH-Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffus...

Option Pricing on Commodity Prices Using Jump Diffusion Models

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...

A Jump-Diffusion Model for Option Pricing

Brownian motion and normal distribution have been widely used in the Black–Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called...

Asymmetric Jump Processes: Option Pricing Implications

Option pricing in jump diffusion models with quadratic spline collocation

In this paper, we develop a robust numerical method in pricing options, when the underlying asset follows a jump diffusion model. We demonstrate that, with the quadratic spline collocation method, the integral approximation in the pricing PIDE is intuitively simple, and comes down to the evaluation of the probabilistic moments of the jump density. When combined with a Picard iteration scheme, t...