Abstract
We present fast and accurate pricing techniques for credit-derivative contracts when discrete monitoring is applied and the underlying evolves according to an exponential Lévy process. Our pricing approaches are based on the Wiener–Hopf factorization, and their computational cost is independent of the number of monitoring dates. Numerical results are presented in order to validate the pricing algorithm. Moreover, an analysis on the sensitivity of the probability of default and the credit spread term structures with respect to the process parameters is considered.
(The author was partially supported by GNCS-INDAM.)
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This is the standard framework of the so-called fractional recovery of face value. Another possibility, not considered here, is the fractional recovery of market value at default.
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For numerical purposes, it is convenient to use the symmetric Heaviside step function H(x) in place of the indicator function 1 x > 0 and 1 − H(x) in place of 1 x < 0, the only difference being for x = 0, as \(H(0) = 1/2 = 1 - H(0)\).
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Marazzina, D., Fusai, G., Germano, G. (2012). Pricing Credit Derivatives in a Wiener–Hopf Framework. In: Cummins, M., Murphy, F., Miller, J. (eds) Topics in Numerical Methods for Finance. Springer Proceedings in Mathematics & Statistics, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-3433-7_8
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