Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options

@article{Cai2010OccupationTO,
  title={Occupation Times of Jump-Diffusion Processes with Double Exponential Jumps and the Pricing of Options},
  author={Ning Cai and Nan Chen and Xiangwei Wan},
  journal={Math. Oper. Res.},
  year={2010},
  volume={35},
  pages={412-437}
}
In this paper, we provide Laplace transform-based analytical solutions to pricing problems of various occupation-time-related derivatives such as step options, corridor options, and quantile options under Kou's double exponential jump diffusion model. These transforms can be inverted numerically via the Euler Laplace inversion algorithm, and the numerical results illustrate that our pricing methods are accurate and efficient. The analytical solutions can be obtained primarily because we derive… 

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References

SHOWING 1-10 OF 35 REFERENCES

First passage times of a jump diffusion process

This paper studies the first passage times to flat boundaries for a double exponential jump diffusion process, which consists of a continuous part driven by a Brownian motion and a jump part with

Option Pricing Under a Double Exponential Jump Diffusion Model

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 is proposed.

Pricing of Occupation Time Derivatives: Continuous and Discrete Monitoring

In the present work we use different numerical methods (multidimensional inverse Laplace transform, numerical solution of a PDE by finite difference scheme, Monte Carlo simulation) for pricing

A Jump-Diffusion Model for Option Pricing

  • S. Kou
  • Economics
    Manag. Sci.
  • 2002
A double exponential jump-diffusion model is proposed, for the purpose of option pricing, which is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options.

Discrete extrema of Brownian motion and pricing of exotic options

We provide a closed-form expression for the distribution of the extrema of a Brownian motion observed at discrete times. We reduce the evaluation problem to a Wiener–Hopf integral equation that we

Distribution of occupation times for CEV diffusions and pricing of α-quantile options

The main results of this paper are the derivation of the distribution functions of occupation times under the constant elasticity of variance (CEV) process. The distribution functions can then be

Distribution of Occupation Times for Cev Diffusions and Pricing of Alpha-Quantile Options

The main results of this paper are the derivation of the distribution functions of occupation times under the constant elasticity of variance (CEV) process. The distribution functions can then be

Distribution of occupation times for constant elasticity of variance diffusion and the pricing of α-quantile options

The main results of this paper are the derivation of the distribution functions of occupation times under the constant elasticity of variance process. The distribution functions can then be used to

Sample Quantiles of Stochastic Processes with Stationary and Independent Increments

Ž . This result was obtained for the special case when X t is a Brownian w x w x motion by Dassios 4 and Embrechts, Rogers and Yor 5 . Using this result, Ž . one could calculate an expression for the

General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns

When the price process for a long-lived asset is of a mixed jump-diffusion type, pricing of options on that asset by arbitrage is not possible if trading is allowed only in the underlaying asset and