Monte Carlo Valuation of Corporate Bonds Using Price Data

<p>Corporate debt securities play a large part in financial markets and hence accurate modeling of the prices of these securities is integral. Ericsson and Reneby (2005) state that the corporate bond market in the US doubled between 1995 and 2005 and is now larger than the market for US treasuries. Although the theoretical corporate bond pricing literature is vast, very little empirical research to test the effectiveness of these models has been published. Corporate bond pricing models are split into two families of models. The first, are the structural models which endogenise default by modeling it as an event that may eventuate due to the insolvency of the underlying firm. The second family of models is the newer class of reduced-form models that exogenise default by modeling it as some random process (default intensity). The reduced-form models have been formulated largely due to the empirical failures of the structural family to accurately model prices and spreads. However as Ericsson and Reneby (2005) point out, an inadequate estimation approach may explain the poor performance of the structural models. Structural models are, therefore, the focus of this paper. We, however, do estimate a reduced-form model in order to make a comparison between the two types of model. There are no published papers (to my knowledge) in which both types of model are implemented ...</p>

Monte Carlo Valuation of Corporate Bonds Using Price Data

<p>Corporate debt securities play a large part in financial markets and hence accurate modeling of the prices of these securities is integral. Ericsson and Reneby (2005) state that the corporate bond market in the US doubled between 1995 and 2005 and is now larger than the market for US treasuries. Although the theoretical corporate bond pricing literature is vast, very little empirical research to test the effectiveness of these models has been published. Corporate bond pricing models are split into two families of models. The first, are the structural models which endogenise default by modeling it as an event that may eventuate due to the insolvency of the underlying firm. The second family of models is the newer class of reduced-form models that exogenise default by modeling it as some random process (default intensity). The reduced-form models have been formulated largely due to the empirical failures of the structural family to accurately model prices and spreads. However as Ericsson and Reneby (2005) point out, an inadequate estimation approach may explain the poor performance of the structural models. Structural models are, therefore, the focus of this paper. We, however, do estimate a reduced-form model in order to make a comparison between the two types of model. There are no published papers (to my knowledge) in which both types of model are implemented ...</p>

Basket Credit Derivative Pricing in a Markov Chain Model with Interacting Intensities

In this paper, we propose a Markov chain model to price basket credit default swap (BCDS) and basket credit-linked note (BCLN) with counterparty and contagion risks. Suppose that the default intensity processes of reference entities and the counterparty are driven by a common external shock as well as defaults of other names in the contracts. The stochastic intensity of the external shock is a Cox process with jumps. We derive recursive formulas for the joint distribution of default times and obtain closed-form premium rates for BCDS and BCLN. Numerical experiments are performed to show how the correlated default risks may affect the premium rates.

Estimating Loss Given Default from CDS under Weak Identification*

Existing reduced-form default intensity models that jointly estimate probability of default (PD) and loss given default (LGD) from credit default swaps (CDSs) produce dissimilar results, and there is little guidance on which time series specification to choose. This article develops a model of CDS term structure without parametric time series restrictions for PD and uses weak-identification robust methods to investigate whether separate identification of PD and LGD is still possible. Consistent with intuition about the identification strategy, the model is not globally identified. However, in my empirical application, LGD is precisely estimated for half of the firm-months under study, with resulting values much lower than conventional values. This implies that the risk-neutral PD and the risk premia on PD are underestimated when LGD is set to conventional values.

OLD PROBLEMS, CLASSICAL METHODS, NEW SOLUTIONS

We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in detail: (a) calibrating the default boundary in the structural default framework to a constant default intensity; (b) calculating default probability for a representative bank in the mean-field framework; and (c) finding the hitting time probability density of an Ornstein–Uhlenbeck process. Several other problems, including pricing American put options and finding optimal mean-reverting trading strategies, are mentioned in passing. Besides, two nonfinancial applications — the supercooled Stefan problem and the integrate-and-fire neuroscience problem — are briefly discussed as well.

CREDIT DEFAULT SWAPS IN TWO-DIMENSIONAL MODELS WITH VARIOUS INFORMATIONS FLOWS

We study a credit risk model of a financial market in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions which are dependent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of both risk-free and risky credit default swaps given the reference filtration initially and progressively enlarged by the two default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.

Default Ambiguity

This paper discusses ambiguity in the context of single-name credit risk. We focus on uncertainty in the default intensity but also discuss uncertainty in the recovery in a fractional recovery of the market value. This approach is a first step towards integrating uncertainty in credit-risky term structure models and can profit from its simplicity. We derive drift conditions in a Heath–Jarrow–Morton forward rate setting in the case of ambiguous default intensity in combination with zero recovery, and in the case of ambiguous fractional recovery of the market value.

MULTI-CURRENCY CREDIT DEFAULT SWAPS

Credit default swaps (CDS) on a reference entity may be traded in multiple currencies, in that, protection upon default may be offered either in the currency where the entity resides, or in a more liquid and global foreign currency. In this situation, currency fluctuations clearly introduce a source of risk on CDS spreads. For emerging markets, but in some cases even in well-developed markets, the risk of dramatic foreign exchange (FX)-rate devaluation in conjunction with default events is relevant. We address this issue by proposing and implementing a model that considers the risk of foreign currency devaluation that is synchronous with default of the reference entity. As a fundamental case, we consider the sovereign CDSs on Italy, quoted both in EUR and USD. Preliminary results indicate that perceived risks of devaluation can induce a significant basis across domestic and foreign CDS quotes. For the Republic of Italy, a USD CDS spread quote of 440 bps can translate into an EUR quote of 350[Formula: see text]bps in the middle of the Euro-debt crisis in the first week of May 2012. More recently, from June 2013, the basis spreads between the EUR quotes and the USD quotes are in the range around 40[Formula: see text]bps. We explain in detail the sources for such discrepancies. Our modeling approach is based on the reduced form framework for credit risk, where the default time is modeled in a Cox process setting with explicit diffusion dynamics for default intensity/hazard rate and exponential jump to default. For the FX part, we include an explicit default-driven jump in the FX dynamics. As our results show, such a mechanism provides a further and more effective way to model credit/FX dependency than the instantaneous correlation that can be imposed among the driving Brownian motions of default intensity and FX rates, as it is not possible to explain the observed basis spreads during the Euro-debt crisis by using the latter mechanism alone.