Valuing Credit Risky Bonds

2013 ◽  
pp. 453-472
Keyword(s):  
Risky Bonds

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

An Explicit, Multi-Factor Credit Default Swap Pricing Model with Correlated Factors

2008 ◽  
Vol 43 (1) ◽  
pp. 123-160 ◽  
Author(s):  
Ren-Raw Chen ◽  
Xiaolin Cheng ◽  
Frank J. Fabozzi ◽  
Bo Liu
Keyword(s):  
Goodness Of Fit ◽  
Credit Default Swap ◽  
Change Of Measure ◽  
Computationally Efficient ◽  
Period 2 ◽  
Credit Default ◽  
Risky Bonds ◽  
Default Swap ◽  
The Interest Rate ◽  
Correlated Factors

AbstractWith the recent significant growth in the single-name credit default swap (CDS) market has come the need for accurate and computationally efficient models to value these instruments. While the model developed by Duffie, Pan, and Singleton (2000) can be used, the solution is numerical (solving a series of ordinary differential equations) rather than explicit. In this paper, we provide an explicit solution to the valuation of a credit default swap when the interest rate and the hazard rate are correlated by using the “change of measure” approach and solving a bivariate Riccati equation. CDS transaction data for the period 2/15/2000 through 4/8/2003 for 60 firms are used to test both the goodness of fit of the model and provide estimates of the influence of economic variables in the market for credit-risky bonds.

scholarly journals Sovereign Default Risk and Banks in a Monetary Union

2014 ◽  
Vol 15 (1) ◽  
pp. 23-41 ◽  
Author(s):  
Harald Uhlig
Keyword(s):  
Central Bank ◽  
Monetary Union ◽  
Default Risk ◽  
Bank Regulation ◽  
Sovereign Default ◽  
Sovereign Bonds ◽  
Sovereign Default Risk ◽  
Risky Bonds ◽  
The Common ◽  
Repurchase Agreements

Abstract This study seeks to understand the interplay between banks, bank regulation, sovereign default risk and central bank guarantees in a monetary union. I assume that banks can use sovereign bonds for repurchase agreements with a common central bank, and that their sovereign partially backs up any losses should the banks not be able to repurchase the bonds. I argue that regulators in risky countries have an incentive to allow their banks to hold home risky bonds and risk defaults, whereas regulators in other ‘safe’ countries will impose tighter regulation. As a result, governments in risky countries get to borrow more cheaply, effectively shifting the risk of some of the potential sovereign default losses on the common central bank.

scholarly journals Fund Managers, Career Concerns, and Asset Price Volatility

2012 ◽  
Vol 102 (5) ◽  
pp. 1986-2017 ◽  
Author(s):  
Veronica Guerrieri ◽  
Péter Kondor
Keyword(s):  
Portfolio Management ◽  
Default Risk ◽  
Asset Price ◽  
Price Volatility ◽  
Career Concerns ◽  
Past Performance ◽  
Fund Managers ◽  
Risky Bonds ◽  
Delegated Portfolio Management ◽  
Changes Over Time

We propose a model of delegated portfolio management with career concerns. Investors hire fund managers to invest their capital either in risky bonds or in riskless assets. Some managers have superior information on default risk. Based on past performance, investors update beliefs on managers and make firing decisions. This leads to career concerns that affect managers' investment decisions, generating a countercyclical “reputational premium.” When default risk is high, return on bonds is high to compensate uninformed managers for the high risk of being fired. As default risk changes over time, the reputational premium amplifies price volatility. (JEL G11, G12, G23, L84)

Testing the Elasticity of Corporate Yield Spreads

2009 ◽  
Vol 44 (3) ◽  
pp. 641-656 ◽  
Author(s):  
Gady Jacoby ◽  
Rose C. Liao ◽  
Jonathan A. Batten
Keyword(s):  
Interest Rates ◽  
Corporate Bond ◽  
Reduced Form ◽  
Time Varying ◽  
Yield Spreads ◽  
Asset Value ◽  
Key Factor ◽  
Risky Bonds ◽  
Bond Spreads ◽  
Hazard Process

AbstractWhat drives the compensation demanded by investors in risky bonds? Longstaff and Schwartz (1995) predict that one key factor is the time-varying negative correlation between interest rates and the yield spreads on corporate bonds. However, the effects of callability and taxes also need to be considered in empirical analyses. Canadian bonds have no tax effects, yet, after controlling for callability, the correlation between riskless interest rates and corporate bond spreads remains negligible. Our results provide support for reduced-form models that explicitly define a default hazard process and untie the relation between the firm’s asset value and default probability.

A "COHERENT STATE TRANSFORM" APPROACH TO DERIVATIVE PRICING

2009 ◽  
Vol 12 (02) ◽  
pp. 125-151
Author(s):  
LUDOVICO PERISSINOTTO ◽  
CLAUDIO TEBALDI
Keyword(s):  
Coherent State ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Group Invariant ◽  
Jump Diffusion Processes ◽  
Markov Generator ◽  
The Family ◽  
Risky Bonds ◽  
Spread Option ◽  
Positive State

We propose an extension of the transform approach to option pricing introduced in Duffie, Pan and Singleton (Econometrica68(6) (2000) 1343–1376) and in Carr and Madan (Journal of Computational Finance2(4) (1999) 61–73). We term this extension the "coherent state transform" approach, it applies when the Markov generator of the factor process can be decomposed as a linear combination of generators of a Lie symmetry group. Then the family of group invariant coherent states determine the transform to price derivatives. We exemplify this procedure deriving a coherent state transform for affine jump-diffusion processes with positive state space. It improves the traditional FFT because inversion of the latter requires integration over an unbounded domain, while inversion of the coherent state transform requires integration over unit ball. We explicitly perform the pricing exercise for some contracts like the plain vanilla options on (credit) risky bonds and on the spread option.

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