# American Institute of Mathematical Sciences

January  2021, 17(1): 133-149. doi: 10.3934/jimo.2019103

## Pricing power exchange options with hawkes jump diffusion processes

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

* Corresponding author: Anubha Goel

Received  June 2018 Revised  March 2019 Published  January 2021 Early access  September 2019

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.

Citation: Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103
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##### References:
Option prices against time to maturity
Option prices against correlation coefficient when T = 1.5
Option prices against the parameters of common Hawkes process
Option prices against the parameters of Hawkes process for Asset 1
Option prices against the parameters of Hawkes process for Asset 2
Comparison of option prices against the parameters of common Hawkes process and asset specific Hawkes processes
Comparison of option prices against the parameters of amplitudes of jump sizes
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
 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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