Pricing of Defaultable Securities Under Stochastic Interest
We reduce the problem of pricing continuously monitored defaultable securities (namely, barrier type options, corporate debts) under a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. For the case when the interest rate is governed by linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also provide an estimation for a rate of convergence of the suggested approximation as a function of number of nodes and illustrate the results by numerical examples.
|Date of creation:||01 Feb 2007|
|Date of revision:|
|Publication status:||Published as: Kordzakhia, N. and Novikov, A., 2008, "Pricing of Defaultable Securities Under Stochastic Interest", In: A. Sarychev et al (eds) Mathematical Control Theory and Finance, 251-263.|
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- Merton, Robert C., 1973.
"On the pricing of corporate debt: the risk structure of interest rates,"
684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
- G. O. Roberts & C. F. Shortland, 1997. "Pricing Barrier Options with Time-Dependent Coefficients," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 83-93.
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