Transform Approximations for Event Timing Models Vibhav Bukkapatanam ∗ Kay Giesecke † November 7, 2011 Abstract Financial institutions are often exposed to credit-sensitive assets such as loans and corporate bonds. Positions involving these securities could be entered into for hedging, speculation or diversification purposes. An important consideration in the design and risk management of these credit-linked portfolios is the ability to calculate the distribution of the total loss. In this paper, we develop analytical approximations for the distribution of the total loss due to defaults in a loan portfolio at a fixed time horizon. We first consider a small-time expansion of the Laplace transform of the total loss; which we invert using the saddlepoint method. We handle specific cases for the loss specification and analyze approximation methods which are more suitable for longer time horizons. Our approximation method is generic in that it can handle a large class of models of default timing, and it addresses other important features of the loan portfolio, including stochastic volatility and state-dependent jumps at and between defaults. We illustrate our approximations for common types of portfolio loss specification. We also provide error bounds to our approximation and evaluate the methods by numerical simulation. * Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, email vibhav@stanford.edu. This work is supported by a B.C. and E.J. Eaves Stanford Graduate Fellowship. † Corresponding author. Department of Management Science & Engineering, Stanford University, Stanford, CA 94305, phone (650) 723 9265, fax (650) 723 1614, email: giesecke@stanford.edu, web: www.stanford.edu/∼giesecke. 1