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Yield to maturity modelling and a Monte Carlo Technique for pricing Derivatives on Constant Maturity Treasury (CMT) and Derivatives on forward Bonds  [PDF]
Didier Kouokap Youmbi
Quantitative Finance , 2012,
Abstract: This paper proposes a Monte Carlo technique for pricing the forward yield to maturity, when the volatility of the zero-coupon bond is known. We make the assumption of deterministic default intensity (Hazard Rate Function). We make no assumption on the volatility of the yield. We actually calculate the initial value of the forward yield, we calculate the volatility of the yield, and we write the diffusion of the yield. As direct application we price options on Constant Maturity Treasury (CMT) in the Hull and White Model for the short interest rate. Tests results with Caps and Floors on 10 years constant maturity treasury (CMT10) are satisfactory. This work can also be used for pricing options on bonds or forward bonds.
Comprehensive Unified Models of Structural and Reduced Form Models for Defaultable Fixed Income Bonds (Part 1: One factor-model, Part 2:Two factors-model)  [PDF]
Hyong-Chol O,Song-Yon Kim,Dong-Hyok Kim,Chol-Hyok Pak
Quantitative Finance , 2013, DOI: 10.2139/ssrn.2337846
Abstract: Pricing formulae for defaultable corporate bonds with discrete coupons under consideration of the government taxes in the united model of structural and reduced form models are provided. The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in [1]) into a comprehensive unified model of structural and reduced form models. Here we consider the one factor model and the two factor model. In the one factor model the bond holders receive the deterministic coupon at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under constant short rate. In the two factor model the bond holders receive the stochastic coupon (discounted value of that at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under stochastic short rate. The expected default event occurs when the equity value is not enough to pay coupon or debt at the coupon dates or maturity and unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We consider the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration and the effect of the government taxes.
Approximate formulae for pricing zero-coupon bonds and their asymptotic analysis  [PDF]
Beata Stehlikova,Daniel Sevcovic
Mathematics , 2008,
Abstract: We analyze analytic approximation formulae for pricing zero-coupon bonds in the case when the short-term interest rate is driven by a one-factor mean-reverting process with a volatility nonlinearly depending on the interest rate itself. We derive the order of accuracy of the analytical approximation due to Choi and Wirjanto. We furthermore give an explicit formula for a higher order approximation and we test both approximations numerically for a class of one-factor interest rate models.
Implications of Correlated Default For Portfolio Allocation To Corporate Bonds  [PDF]
Mark B. Wise,Vineer Bhansali
Physics , 2002,
Abstract: This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Using a multivariate normal Copula function for the joint default probabilities we show that retaining the first few moments of the portfolio default loss distribution gives an extremely good approximation to the full solution of the asset allocation problem. We provide detailed results on the convergence of the moment expansion and explore how the optimal portfolio allocation depends on recovery fractions, level of diversification and investment time horizon. Numerous numerical illustrations exhibit the results for simple portfolios and utility functions.
The Pricing of Credit Derivatives and Estimation of Default Probability  [PDF]
Hanghang Zhou, Dianli Zhao
Journal of Mathematical Finance (JMF) , 2015, DOI: 10.4236/jmf.2015.53022
Abstract: Under the native-born model of default and the circular model of default, we take the price of credit derivatives into account. It’s supposed that the short-term market interest rates are based on Vasicek model in this article. Firstly, we calculate the price of default-free bonds in zero-coupon bond. Then, we give the default-intensity expressions under the two models. We calculate the prices of default-free bonds under the two default models. For different situations, we estimate the parameters by maximum likelihood estimation method and calculate the default probability of the company. From the analysis of the result, we find that the result conforms to reality. So the models of default intensity we suppose in the bond pricing are reasonable.
Modelling Bonds & Credit Default Swaps using a Structural Model with Contagion  [PDF]
Helen Haworth,Christoph Reisinger,William Shaw
Mathematics , 2007,
Abstract: This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters.
Stepped coupon bonds and restructuring factoring in relation to net circulating capital in companies in financial difficulty
Katarzyna Kreczmańska-Gigol,Marcin Liberadzki
Perspectives of Innovations, Economics and Business , 2012,
Abstract: The instrument to be applied in order to raise net circulating capital is stepped coupon bonds, a novel solution non-existent on the Polish market. Restructuring factoring applied sporadically in Poland and Germany is an instrument reducing the demand for the corporate net circulating capital. The article presents the idea of these instruments and the possibility of using them by a company in financial difficulty
O. Slutska
Economics of Development , 2012,
Abstract: As a result of this study a common methodological approach to the evaluation of default risk of issuers of corporate bonds was formed. Key financial indices of the debtor’s solvency are determined and the vague scale is built in order to analyze them. Correlation between values of selected financial indicators of bond issuers (as a reflection of the internal condition of a borrower) and the level of market interest rates (as a reflection of the environment) on one hand, and the fact of completion of obligation or default on bonds on the other hand was ascertained.The results make possible to distribute issuers of bonds in three levels of default risk, considering the formed indefinite rules of attribution to a particular risk level. Probability values of transition to another level in the next quarter were determined and the probability of issuers’ default after a certain period of time was estimated relying on the current class of risk.The methodical approach to estimation of the default risk of corporate bonds issuers was developed. It takes into account various aspects of a borrower’s activity, dynamics of financial performance, impact of macroeconomic factors and overall market environment. In addition, makes it possible to determine risks of default with some degree of affiliation, taking into account effects of other factors on a borrower, which were not included in the model.The proposed methodical assessment of issuers’ default risk enables to estimate borrowers’ reliability properly. So that to facilitate the restoration and development of Ukrainian debt securities market.
Constant Maturity Credit Default Swap Pricing with Market Models  [PDF]
Damiano Brigo
Quantitative Finance , 2008,
Abstract: In this work we derive an approximated no-arbitrage market valuation formula for Constant Maturity Credit Default Swaps (CMCDS). We move from the CDS options market model in Brigo (2004), and derive a formula for CMCDS that is the analogous of the formula for constant maturity swaps in the default free swap market under the LIBOR market model. A "convexity adjustment"-like correction is present in the related formula. Without such correction, or with zero correlations, the formula returns an obvious deterministic-credit-spread expression for the CMCDS price. To obtain the result we derive a joint dynamics of forward CDS rates under a single pricing measure, as in Brigo (2004). Numerical examples of the "convexity adjustment" impact complete the paper.
General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application  [PDF]
Hyong-Chol O,Ji-Sok Kim
Quantitative Finance , 2013, DOI: 10.2139/ssrn.2330083
Abstract: We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results are applied in pricing defaultable discrete coupon bonds.
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