Closed-Form Solutions for Pricing Credit-Risky Bonds and Bond Options
Closed-Form Solutions for Pricing Credit-Risky Bonds and Bond Options

Author: Leonard Tchuindjo

Publisher:

Published: 2013

Total Pages:

ISBN-13:

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This paper proposes closed-form solutions for pricing credit-risky discount bonds and their European call and put options in the intensity-based reduced-form framework, assuming the stochastic dynamics of both the risk-free interest rate and the credit-spread are driven by two correlated Ho-Lee models [T.S.Y. Ho, S.B. Lee, Term structure movements and pricing interest rates contingent claims, Journal of Finance 41 (5) (1986) 1011-1029]. The results are easily to implement, and require very few parameters which are directly implied from market data.

Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull - White Model
Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull - White Model

Author: Leonard Tchuindjo

Publisher:

Published: 2013

Total Pages:

ISBN-13:

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This research attempts to propose closed-form solutions for prices of credit-risky bonds, assuming a nonzero correlation between interest rates and credit spreads. The times of default of a credit-risky bond are modelled as the jump times of a Cox process, following the method of Lando, with an intensity that follows a Hull and White model, correlated with a similar model of the risk-free interest rate. Under the fractional recovery of market value assumption of Duffie and Singleton, the partial differential equation (PDE) for the price of the zero-coupon credit-risky bond is derived. Then this PDE is analytically solved, using the method of separation of variables, and easy-to-implement closed-form solutions are found. Finally, numerical examples are presented to show how these closed-form solutions can identify the magnitude and the direction of the credit-risky bond mispricing under different parameter assumptions.

Pricing Derivative Credit Risk
Pricing Derivative Credit Risk

Author: Manuel Ammann

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 238

ISBN-13: 3662223309

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Credit risk is an important consideration in most financial transactions. As for any other risk, the risk taker requires compensation for the undiversifiable part of the risk taken. In bond markets, for example, riskier issues generally promise investors a higher yield. The same principle also applies to financial derivatives. Otherwise identical derivative securities will likely have differ ent prices if the counterparties are not of the same credit quality. Although this argument seems intuitively convincing, widely used pricing models for financial derivatives do not incorporate credit risk effects. This research monograph analyzes the effect of credit risk on financial derivatives prices. Credit risk can affect derivatives prices in a variety of ways. First, financial derivatives can be subject to counterparty default risk. Second, a derivative can be written on a security which is subject to credit risk, such as a corporate bond. Third, the credit risk itself can be the un derlying of a derivative instrument. The text focuses on valuation models which take into account counterparty risk but also addresses the other two valuation problems.

Exact Solutions for Bond and Option Prices with Systematic Jump Risk
Exact Solutions for Bond and Option Prices with Systematic Jump Risk

Author: Sanjiv Ranjan Das

Publisher:

Published: 2009

Total Pages:

ISBN-13:

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A variety of realistic economic considerations make jump- diffusion models of interest rate dynamics an appealing modeling choice to price interest rate contingent claims. However, exact closed form solutions for bond prices when interest rates follow a mixed jump-diffusion process have proved very hard to derive. This paper puts forward two new models of interest rate dynamics which combine infrequent, discrete changes in the interest rate level, modeled as a jump process, with short lived, mean reverting shocks, modeled as a diffusion process. The two models differ in the way jumps affect the central tendency of interest rates; in one case shocks are temporary, in the other shocks are permanent. We derive exact closed form solutions for the price of a discount bond, and computationally tractable schemes to price bond options.

Credit Risk Valuation
Credit Risk Valuation

Author: Manuel Ammann

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 259

ISBN-13: 3662064251

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This book offers an advanced introduction to models of credit risk valuation, concentrating on firm-value and reduced-form approaches and their application. Also included are new models for valuing derivative securities with credit risk. The book provides detailed descriptions of the state-of-the-art martingale methods and advanced numerical implementations based on multivariate trees used to price derivative credit risk. Numerical examples illustrate the effects of credit risk on the prices of financial derivatives.

Perturbation Methods in Credit Derivatives
Perturbation Methods in Credit Derivatives

Author: Colin Turfus

Publisher: John Wiley & Sons

Published: 2021-03-15

Total Pages: 256

ISBN-13: 1119609615

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Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume Perturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management offers an incisive examination of a new approach to pricing credit-contingent financial instruments. Author and experienced financial engineer Dr. Colin Turfus has created an approach that allows model validators to perform rapid benchmarking of risk and pricing models while making the most efficient use possible of computing resources. The book provides innumerable benefits to a wide range of quantitative financial experts attempting to comply with increasingly burdensome regulatory stress-testing requirements, including: Replacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quants Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently Developing more efficient algorithms for generating stress scenarios for market risk quants Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.

Default-free Bond Futures and Options on Default-free Bond Futures: Theoretical and Empirical Investigation
Default-free Bond Futures and Options on Default-free Bond Futures: Theoretical and Empirical Investigation

Author: Chin-Wen Hsin

Publisher:

Published: 1990

Total Pages:

ISBN-13:

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This study investigates the pricing behaviors of default-free bond futures and American options on default-free bond futures based on the framework of Brennan and Schwartz (1979). In their model, the state space of interest-rate-dependent claims is spanned by the instantaneous spot interest rate and the long-term consol rate. This design is chosen to incorporate the features of interest-rate-dependent claims and to avoid inconsistencies in other pricing models for general assets. This study assumes that the logarithm of these two factors follow a linear transformation of an Ornstein-Uhlenbeck process. The prices of these contingent claims are solutions to a set of partial different equations subject to proper boundary conditions. As there is no closed form solutions to these equations, a finite-difference method, line-hopscotch method, is employed. To implement the pricing model, one has to empirically estimate (i) the parameters in the interest rate processes and (ii) the risk premium parameter associated with the short spot rate. An exact discrete time model is derived such that one can use discrete time empirical data to estimate parameters in the continuous interest rate processes. Maximum likelihood estimation results show that the parameter estimates are affected by the choice of proxy variable, sample period and the size of sampling interval. It is most obvious fort those parameters in the short rate process. The model prices of default-free bonds, default-free bond futures and options on default-free bond futures are solved successively by the numerical method. The empirical results indicate insignificant pricing errors for Treasury bond futures. However, the model does not perform well for pricing options on T-bond futures. A sensitivity analysis is conducted. It suggests that the long rate process is important in determining the pricing behavior of these claims. Also, the long rate affects the security prices differently than the short rate does.