Indifference pricing with counterparty risk

• Autorzy: Ngo M. , Nguyen T. , Duong T.

Identyfikatory

DOI

10.1515/bpasts-2017-0074

• Języki publikacji: EN

Abstrakty

EN

We present counterparty risk by a jump in the underlying price and a structural change of the price process after the default of the counterparty. The default time is modeled by a default-density approach. Then we study an exponential utility-indifference price of an European option whose underlying asset is exposed to this counterparty risk. Utility-indifference pricing method normally consists in solving two optimization problems. However, by using the minimal entropy martingale measure, we reduce to solving just one optimal control problem. In addition, to overcome the incompleteness obstacle generated by the possible jump and the change in structure of the price process, we employ the BSDE-decomposition approach in order to decompose the problem into a global-before-default optimal control problem and an after-default one. Each problem works in its own complete framework. We demonstrate the result by numerical simulation of an European option price under the impact of jump’s size, intensity of the default, absolute risk aversion and change in the underlying volatility.

Słowa kluczowe

EN

indifference pricing; counterparty risk; minimal entropy; BSDE

PL

ryzyko kontrahenta; entropia minimalna; BSDE

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2017
• Tom: Vol. 65, nr 5
• Strony: 695--702
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Ngo M.

• John von Neumann Institute-Vietnam National University, VNU IT Park, Linh Trung Ward, Thu Duc District, HCMC, Vietnam

autor

Nguyen T.

• John von Neumann Institute-Vietnam National University, VNU IT Park, Linh Trung Ward, Thu Duc District, HCMC, Vietnam

autor

Duong T.

• John von Neumann Institute-Vietnam National University, VNU IT Park, Linh Trung Ward, Thu Duc District, HCMC, Vietnam

Bibliografia

• [1] N. El Karoui, M. Jeanblanc, and Y. Jiao, “What happens after a default: the conditional density approach”, Stoch. Proc. Appl. 120 (7), 1011‒1032 (2010).
• [2] S. D. Hodges, “Optimal replication of contingent claims under transaction costs”, Review of Futures Markets 8, 223‒238 (1989).
• [3] M. Mania and M. Schweizer, “Dynamic exponential utility indifference valuation”, Ann. Appl. Probab. 15 (3), 2113‒2143 (2005).
• [4] Y. Jiao, I. Kharroubi, and H. Pham, “Optimal investment under multiple defaults risk: a BSDE-decomposition approach”, Ann. Appl. Probab. 23 (2), 455‒491 (2013).
• [5] M. Jeanblanc and Y. Le Cam, “Progressive enlargement of filtrations with initial times”, Stoch. Proc. Appl. 119 (8), 2523‒2543 (2009).
• [6] R. Mansuy and M. Yor, Random Times and Enlargements of Filtrations in a Brownian Setting, Springer, 2006.
• [7] P. Protter and K. Shimbo, “No arbitrage and general semimartingales” in Markov Processes and Related Topics: a Festschrift for Thomas G. Kurtz, 267‒283, Institute of Mathematical Statistics, 2008.
• [8] S. Ihara, Information Theory for Continuous Systems, vol. 2, World Scientific, 1993.
• [9] R.M. Corless, G.H. Gonnet, D.E. Hare, D.J. Jeffrey, and D.E. Knuth, “On the Lambert w function”, Adv. Comput. Math. 5 (1), 329‒359 (1996).
• [10] E. Gobet, J.-P. Lemor, and X.Warin, “A regression-based Monte Carlo method to solve backward stochastic differential equations”, Ann. Appl. Probab. 15 (3), 2172‒2202 (2005).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).