# Geometric Step Options with Jumps: Parity Relations, PIDEs, and Semi-Analytical Pricing

@article{Farkas2020GeometricSO, title={Geometric Step Options with Jumps: Parity Relations, PIDEs, and Semi-Analytical Pricing}, author={Walter Farkas and Ludovic Mathys}, journal={Risk Management eJournal}, year={2020} }

The present article studies geometric step options in exponential Levy markets. Our contribution is manifold and extends several aspects of the geometric step option pricing literature. First, we provide symmetry and parity relations and derive various characterizations for both European-type and American-type geometric double barrier step options. In particular, we are able to obtain a jump-diffusion disentanglement for the early exercise premium of American-type geometric double barrier step… Expand

#### 2 Citations

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#### References

SHOWING 1-10 OF 69 REFERENCES

Option Pricing Under a Double Exponential Jump Diffusion Model

- Economics, Computer Science
- Manag. Sci.
- 2004

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. Expand

Option Pricing Under a Mixed-Exponential Jump Diffusion Model

- Computer Science
- Manag. Sci.
- 2011

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. Expand

Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model

- Economics
- 2015

We analyze American put options in a hyper-exponential jump-diffusion model. Our contribution is threefold. Firstly, by following a maturity randomization approach, we solve the partial… Expand

PRICING STEP OPTIONS UNDER THE CEV AND OTHER SOLVABLE DIFFUSION MODELS

- Mathematics, Economics
- 2013

We consider a special family of occupation-time derivatives, namely proportional step options introduced by [18]. We develop new closed-form spectral expansions for pricing such options under a class… Expand

Double Barrier Options in Regime-Switching Hyper-Exponential Jump-Diffusion Models

- Mathematics
- 2009

We present a very fast and accurate algorithm for calculating prices of finite lived double barrier options with arbitrary terminal payoff functions under regime-switching hyper-exponential… Expand

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

- Mathematics, Computer Science
- Math. Oper. Res.
- 2010

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 are provided. Expand

Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model

- Economics, Computer Science
- Oper. Res.
- 2012

A closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model is obtained and it is shown that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. Expand

PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES

- Mathematics
- 2004

We consider the American put with finite time horizonT, assuming that, under an EMM chosen by the market, the stock returns follow a regular Levy process of exponential type. We formulate the free… Expand

American type geometric step options

- Mathematics
- 2013

The step option is a special contact whose value decreases gradually in proportional to the spending time outside a barrier of the asset price. European step options were introduced and studied by… Expand

Parisian options with jumps: a maturity–excursion randomization approach

- Computer Science
- 2018

An analytically tractable method for the pricing of European and American Parisian options in a flexible jump–diffusion model and the non-monotonic effects of volatility and jump intensity close to the excursion barrier are studied. Expand