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Indifference pricing with counterparty risk

Ngo M., Nguyen T., Duong T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 5

695--702

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.

Wnioski dla urzędów regulacyjnych rynku finansowego płynące z kryzysu lat 2008-2009

Noetzel P.

Ekonomia i Zarządzanie

2011

Vol. 3, no. 2

21-37

The article presents the genesis of the financial crisis of 2008-2009 and presents some suggestions for changes in the regulatory provisions of the financial system. These amendments relate to such issues as the use of leverage by the banks and its effect on the bank's regulatory capital, granting credits, market organization and corporate governance.