# 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  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
##### References:

show all references

##### 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
 [1] Wan-Hua He, Chufang Wu, Jia-Wen Gu, Wai-Ki Ching, Chi-Wing Wong. Pricing vulnerable options under a jump-diffusion model with fast mean-reverting stochastic volatility. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021057 [2] Wei Wang, Yang Shen, Linyi Qian, Zhixin Yang. Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021072 [3] Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021039 [4] Jun Moon. Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021026 [5] Zhenbing Gong, Yanping Chen, Wenyu Tao. Jump and variational inequalities for averaging operators with variable kernels. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021045 [6] Antonio Rieser. A topological approach to spectral clustering. Foundations of Data Science, 2021, 3 (1) : 49-66. doi: 10.3934/fods.2021005 [7] Xingchun Wang, Yongjin Wang. Variance-optimal hedging for target volatility options. Journal of Industrial & Management Optimization, 2014, 10 (1) : 207-218. doi: 10.3934/jimo.2014.10.207 [8] Jan Rychtář, Dewey T. Taylor. Moran process and Wright-Fisher process favor low variability. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3491-3504. doi: 10.3934/dcdsb.2020242 [9] Lei Lei, Wenli Ren, Cuiling Fan. The differential spectrum of a class of power functions over finite fields. Advances in Mathematics of Communications, 2021, 15 (3) : 525-537. doi: 10.3934/amc.2020080 [10] Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 [11] Alexander Tolstonogov. BV solutions of a convex sweeping process with a composed perturbation. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021012 [12] Ugo Bessi. Another point of view on Kusuoka's measure. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3241-3271. doi: 10.3934/dcds.2020404 [13] Xiaohong Li, Mingxin Sun, Zhaohua Gong, Enmin Feng. Multistage optimal control for microbial fed-batch fermentation process. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021040 [14] Ruchika Sehgal, Aparna Mehra. Worst-case analysis of Gini mean difference safety measure. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1613-1637. doi: 10.3934/jimo.2020037 [15] José Antonio Carrillo, Martin Parisot, Zuzanna Szymańska. Mathematical modelling of collagen fibres rearrangement during the tendon healing process. Kinetic & Related Models, 2021, 14 (2) : 283-301. doi: 10.3934/krm.2021005 [16] Muberra Allahverdi, Harun Aydilek, Asiye Aydilek, Ali Allahverdi. A better dominance relation and heuristics for Two-Machine No-Wait Flowshops with Maximum Lateness Performance Measure. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1973-1991. doi: 10.3934/jimo.2020054 [17] Yunjuan Jin, Aifang Qu, Hairong Yuan. Radon measure solutions for steady compressible hypersonic-limit Euler flows passing cylindrically symmetric conical bodies. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021048 [18] Xianbang Chen, Yang Liu, Bin Li. Adjustable robust optimization in enabling optimal day-ahead economic dispatch of CCHP-MG considering uncertainties of wind-solar power and electric vehicle. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1639-1661. doi: 10.3934/jimo.2020038 [19] Sumon Sarkar, Bibhas C. Giri. Optimal lot-sizing policy for a failure prone production system with investment in process quality improvement and lead time variance reduction. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021048 [20] Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109

2019 Impact Factor: 1.366