An extension of the Euler Laplace transform inversion algorithm with applications in option pricing

Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering

“…The proof of (23) is similar. The Laplace transforms can be inverted numerically in the complex plane, using the two-sided extension of the Euler algorithm as described and implemented in Petrella (2004). To check the accuracy of the inversion, Kou et al (2005) compare the inversion results with the prices of call and put options under the double exponential jump-diffusion model obtained by using the closedform formulae using Hh function as in Kou (2002).…”

“…Kou et al (2005) price up-and-in calls using the two-dimensional Laplace transform (using the two-dimensional Euler algorithm developed by Choudhury et al, 1994 andPetrella, 2004) and compare the results with the onedimensional transform in Kou and Wang (2003) (based on the Gaver-Stehfest algorithm). The two-dimensional Laplace inversion matches to the fourth digit the ones obtained by the one-dimensional Gaver-Stehfest algorithm, and are all within the 95% confidence interval obtained via Monte Carlo simulation.…”

Chapter 8 Discrete Barrier and Lookback Options

“…Step 4 the Laplace transforms are inverted by using two-sided Euler inversion algorithms in Petrella (2004), which are extensions of one-sided Euler algorithms in Abate and Whitt (1992) and Choudhury et al (1994).…”

A two-dimensional, two-sided Euler inversion algorithm with computable error bounds and its financial applications

“…Petrella [23] proposed a similar algorithm with a scaling factor but without rigorous justification. As pointed out in [7], Petrella's method imposed a constraint on the scaling parameter, which may cause large errors even in the onedimensional case; see Section 4.3 in [7].…”

“…In fact, our algorithm essentially belongs to the category of Euler inversion algorithms which have enjoyed great popularity in the areas of operations research and applied probability (see, e.g., [1,11,23,7]). Motivated by applications in financial engineering, e.g., path-dependent option pricing, we extend the existing Euler inversion algorithms to the two-dimensional, twosided case.…”