Approximation with generalized hyperexponential distributions: weak convergence
Queueing Systems: Theory and Applications
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
A Jump-Diffusion Model for Option Pricing
Management Science
Pricing and Hedging Path-Dependent Options Under the CEV Process
Management Science
Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach
Operations Research
Option Pricing Under a Double Exponential Jump Diffusion Model
Management Science
Methods for the rapid solution of the pricing PIDEs in exponential and Merton models
Journal of Computational and Applied Mathematics
Pricing Options in Jump-Diffusion Models: An Extrapolation Approach
Operations Research
Mathematics of Operations Research
Pricing double-barrier options under a flexible jump diffusion model
Operations Research Letters
An extension of the Euler Laplace transform inversion algorithm with applications in option pricing
Operations Research Letters
On the controversy over tailweight of distributions
Operations Research Letters
Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model
Operations Research
Exit problems for jump processes with applications to dividend problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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This paper aims to extend the analytical tractability of the Black--Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and double-exponential jump diffusion models, because the mixed-exponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavy-tailed distributions. The mixed-exponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for path-dependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a high-order integro-differential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day. This paper was accepted by Michael Fu, stochastic models and simulation.