American and exotic option pricing with jump diffusions and other Levy processes

2018 ◽  
Vol 22 (3) ◽  
pp. 89-148 ◽  
Author(s):  
Justin Lars Kirkby
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Levy Processes ◽  
Jump Diffusions ◽  
Exotic Option ◽  
Exotic Option Pricing

APPROXIMATING LÉVY PROCESSES WITH A VIEW TO OPTION PRICING

2010 ◽  
Vol 13 (01) ◽  
pp. 63-91 ◽  
Author(s):  
JOHN CROSBY ◽  
NOLWENN LE SAUX ◽  
ALEKSANDAR MIJATOVIĆ
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Jump Diffusion ◽  
Levy Processes ◽  
Poisson Processes ◽  
Exotic Options ◽  
Option Prices ◽  
Barrier Option ◽  
Systematic Methodology ◽  
The Mean

We examine how to approximate a Lévy process by a hyperexponential jump-diffusion (HEJD) process, composed of Brownian motion and of an arbitrary number of sums of compound Poisson processes with double exponentially distributed jumps. This approximation will facilitate the pricing of exotic options since HEJD processes have a degree of tractability that other Lévy processes do not have. The idea behind this approximation has been applied to option pricing by Asmussen et al. (2007) and Jeannin and Pistorius (2008). In this paper we introduce a more systematic methodology for constructing this approximation which allow us to compute the intensity rates, the mean jump sizes and the volatility of the approximating HEJD process (almost) analytically. Our methodology is very easy to implement. We compute vanilla option prices and barrier option prices using the approximating HEJD process and we compare our results to those obtained from other methodologies in the literature. We demonstrate that our methodology gives very accurate option prices and that these prices are more accurate than those obtained from existing methodologies for approximating Lévy processes by HEJD processes.

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