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We consider a firm-value model similar to the one proposed by Black and Cox (1976) where

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for their financial backing and for giving me the opportunity to keep a toe in the credit markets. I would like to thank all those at OCIAM who have provided me with the guidance and support necessary to complete this thesis. I am particularly grateful to my supervisor, William Shaw, for allowing me the freedom to pursue my own research interests and I would especially like to thank Christoph Reisinger for more helpful discussions than I can count, not to mention the opportunity to play with his code. I would also like to mention all my friends, in Oxford and elsewhere, who have contributed in so many ways to my life over the last three years and to the ultimate form of my research. Finally, I would like to thank my family for their continued support in all my endeavours, and in particular, my sister, for giving me the impetus I needed to return to student life and Multi-asset credit derivatives trade in huge volumes, yet no models exist that are capable of properly accounting for the spread behaviour of dependent

A company’s credit spreads and default policy are analyzed in a structural model of credit risk. Agents have incomplete information about the company’s EBIT (Earnings Before Interest and Taxes) pro-cess and observe it with time delays. When all agents observe the state variable with the same delay, the delay has a minor effect on credit spreads and default policy. Asymmetric information occurs when dif-ferent agents observe the EBIT process with different time delays. Our ∗ Lindset is an Associate Professor at Trondheim Business School and an Adjunct As-

In this paper, we study the relationship between the Merton’s probability of defaut (MPD) and the first passage probability of default (FPD) defined on an (Ornstein-Uhlenbeck) OU process. We find that the FPD is twice of MPD if the default barrier is the asymptotic mean of the OU process. Three different proofs are given for this result. 1 The problem Let {Xt, t ≥ 0} be an OU process parameterized by two positive real numbers α and σ, and it follows the following stochastic differential equation (SDE): dXt = −αXtdt + σ √ 2αdBt, (1) X0 = x0> 0, where Bt is a standard Brownian motion. For fixed t, Xt specified above is

We propose to randomize the initial condition of a generalized structure model, where the solvency ratio instead of the asset value is modeled explicitly. This ini-tial randomization assumption is motivated by the fact that market players cannot observe the solvency ratio accurately. We find that positive short spreads can be produced due to imperfect observation on the risk factor. The two models we have considered, the Randomized Merton II (RM-II) and the Randomized Black-Cox II (RBC-II), both have explicit expressions for Probability of Default (PD), Loss Given Default (LGD) and Credit Spreads (CS). In the RM-II model, both PD and LGD are found to be of order of √ T, as the maturity T approaches zero. It therefore provides an example that has no well-defined default intensity but still admits positive short spreads. In the RBC-II model, the positive short spread is generated through the positive default intensity of the model. Because explicit formulas are available, these two Randomized Structure (RS) models are easily implemented and calibrated to the market data. This is illustrated by a calibration exercise on Ford Motor Corp. Credit Default Swap (CDS) spread data.

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This chapter studies structural and reduced-form credit risk models under incomplete information. Applying stochastic filtering techniques we tackle the aspect of incomplete information in different settings: starting with a brief introduction to stochastic filtering we thereafter cover the pricing of corporate securities (debt and equity) in structural models under partial information. Furthermore the construction of a dynamic reducedform credit risk model via the innovations approach is discussed; as well as pricing, calibration and hedging in that model.

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