Narrow Results

Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. The Markov chain may also be interpreted to represent the credit rating of the firm whose bond we seek to price. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default and loss processes. These transforms can be calculated explicitly in case the default intensity is modeled as a linear function of a conditionally affine jump diffusion process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the nonswitching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate, and high volatility. We also model the effects of firm restructuring on the credit spread, in case of a default.

This paper proposes a simplified risky discount bond pricing model based on Longstaff and Schwartz (1995). The advantage of this model is that it yields a closed form solution for probability of default. Also, a practical feature with our model is that computing durations and other risk management tools become computationally less expensive, while the appealing properties in the LS model are preserved. The numerical comparisons show that the differences in credit spreads between this model and Longstaff and Schwartz are within a few basis points for fairly general parameter values. Moreover, the computational time is shown remarkably reduced by the simplified model. Sensitivity analysis of credit spread with respect to different parameter values is presented.

It is well known that interest rates and credit spreads are negatively correlated. Any successful model for pricing callable corporate bonds has to take this correlation into account. A new approach for the analysis of corporate bond options is developed by using two correlated geometric Brownian motion (GBM) processes for the spread and interest rate components of corporate bond yields. Analysis of the results and comparison with market prices suggest that the traditional methods of calculating the option premium overestimate the value of the call option. Our analysis can also explain why risk neutral credit spreads are significantly wider than implied by default probability and in fact justify higher spreads.

We study bond prices in Black–Cox model with jumps in asset value. We assume that the jump size distribution is arbitrary and, if default occurs, following Longstaff and Schwartz [A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance 50 (1995), 789–819] and Zhou [The Term Structure of Credit Spreads with Jump Risk. Journal of Banking & Finance 26 (2001), 2015–2040], the payoff at maturity date depends on a general write-down function. Under this general setting, we propose an integral equation approach for the bond prices. As an application of this approach, we study the analytic properties of the bond prices. Also we derive an infinite series expression for the bond prices.

The Contingent Claims Analysis (CCA) is a general approach to analyze the stakeholders of a corporation who have contingent claims on the future, uncertain cash-flows generated by the operations of the firms. The CCA allows valuing each stakeholder’s claim and also to assess the risk incurred by the stakeholders. The CCA highlights the potential conflicts of interest among the various claimholders. In this paper, we review applications of CCA including valuation of various forms of debt, rating, credit spread, probability of default and corporate events like dividends, employee stock options and M&A. The CCA framework is shown to be useful to address all these financial questions. In this approach the starting point is that the value and the risk of the firm’s assets are given. The future distribution of the assets’ rates of return is also known and given. The focus is on the liability side of the balance sheet, i.e., the funding sources of the activity of the firm, and more generally on the financial claims of the various claimholders of the firm.

In this chapter, we shall study bonds and their term structures. Bonds are a major class of investment assets distinct from equities, and they have salient features that will be explained. Continuous time stochastic processes are briefly introduced in this chapter to show their usage in modelling bond prices and therefore the resulting credit spreads and yields. Multiple regression analyses involving explanation of credit spreads and of bond returns are described.