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EnglishWe obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Lévy-driven SDE. The stock jumps to zero at default with a hazard rate given by a negative power of the stock price. We recover the characteristic function of the terminal log price as the solution of an infinite-dimensional system of complex-valued first-order ordinary differential equations. We provide an explicit eigenfunction expansion representation of the characteristic function in a suitably chosen Banach space and use it to price defaultable bonds and stock options. We present numerical results to demonstrate the accuracy and efficiency of the method.
| Titolo: | Pricing vulnerable claims in a Lévy-driven model |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Abstract: | We obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Lévy-driven SDE. The stock jumps to zero at default with a hazard rate given by a negative power of the stock price. We recover the characteristic function of the terminal log price as the solution of an infinite-dimensional system of complex-valued first-order ordinary differential equations. We provide an explicit eigenfunction expansion representation of the characteristic function in a suitably chosen Banach space and use it to price defaultable bonds and stock options. We present numerical results to demonstrate the accuracy and efficiency of the method. |
| Handle: | http://hdl.handle.net/11368/2886131 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00780-014-0239-6 |
| URL: | http://link.springer.com/article/10.1007/s00780-014-0239-6 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |