Pricing power exchange options with hawkes jump diffusion processes

Puneet Pasricha; Anubha Goel

doi:10.3934/jimo.2019103

Article Contents

2021, Volume 17, Issue 1: 133-149. Doi: 10.3934/jimo.2019103

This issue Previous Article Biobjective optimization over the efficient set of multiobjective integer programming problem Next Article A SOCP relaxation based branch-and-bound method for generalized trust-region subproblem

Pricing power exchange options with hawkes jump diffusion processes

Puneet Pasricha and
Anubha Goel^,

Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, Delhi, 110016, India

^* Corresponding author: Anubha Goel
^* Corresponding author: Anubha Goel

Received: May 31, 2018

Revised: February 28, 2019

Early access: September 2019

Published: January 2021

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Abstract

In this article, we propose a jump diffusion framework to price the power exchange options. We model the price dynamics of assets using a Hawkes jump diffusion model with common factors to describe the correlated jump risk and clustering of asset price jumps. In the proposed model, the jumps, reflecting common systematic risk and idiosyncratic risk, are modeled by self-exciting Hawkes process with exponential decay. A pricing formula for valuation of power exchange option is obtained following the measure-change technique. Existing models in the literature are shown to be special cases of the proposed model. Finally, sensitivity analysis is given to illustrate the effect of jump risk and jump clustering on option prices. We observe that jump clustering significantly effects the option prices.

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Mathematics Subject Classification: Primary: 60G51; Secondary: 60G55.

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Figure 1. Option prices against time to maturity

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Figure 2. Option prices against correlation coefficient when T = 1.5

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Figure 3. Option prices against the parameters of common Hawkes process

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Figure 4. Option prices against the parameters of Hawkes process for Asset 1

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Figure 5. Option prices against the parameters of Hawkes process for Asset 2

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Figure 6. Comparison of option prices against the parameters of common Hawkes process and asset specific Hawkes processes

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Figure 7. Comparison of option prices against the parameters of amplitudes of jump sizes

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Table 1. Values of the Parameters in the Base Case

Parameters	Values	Parameters	Values
$ S_1(0) $	10	$ S_2(0) $	10
$ \sigma_1 $	0.2	$ \sigma_2 $	0.2
$ a_1 $	0	$ a_2 $	0
$ b_1 $	0.01	$ b_2 $	0.01
$ \lambda_{1, 0} $	1	$ \lambda_{2, 0} $	1
$ \theta_{1} $	1	$ \theta_2 $	1
$ \delta_1 $	2	$ \delta_2 $	2
$ \lambda_{0} $	1	$ \alpha_1 $	1
$ \theta $	1	$ \alpha_2 $	1
$ \delta $	2	$ \eta_1 $	1
$ r $	0.02	$ \eta_2 $	1

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