Bond Valuation Research Articles

Model-independent price bounds for Catastrophic Mortality Bonds

In this paper, we are concerned with the valuation of Catastrophic Mortality Bonds and, in particular, we examine the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets. This bond was the first Catastrophic Mortality Bond to be launched in the market and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders. Pricing these type of bonds is a challenging task and no closed form solution exists in the literature. In our approach, we express the payoff of such a bond in terms of the payoff of an Asian put option and present a new approach to derive model-independent bounds exploiting comonotonic theory as illustrated in Albrecher (2008), Dhaene (2002) and Simon (2000) for the pricing of Asian options. We carry out Monte Carlo simulations to estimate the bond price and illustrate the quality of the bounds.

The reinvestment risk premium in the valuation of British and Russian government bonds

This article studies the dynamic properties of the reinvestment risk premium in the UK and RF government bond markets. In a new interest rate environment when sovereign debt trades at a low and even negative yields and bond funds are struggling to earn sufficient returns, bond investors have become increasingly wary of reinvestment risk largely neglected previously. The reinvestment risk premium is quantified on the basis of replicating portfolios and further analyzed with respect to exposure to exogenous influence with the help of cointegration techniques. The findings are that in both markets investors recognize the significance of reinvestment risk. However, there are differences in the sensitivity of the reinvestment risk premium to exogenous indicators. In the UK government bond market investors tend to be guided by more conservative indicators but are ready to forecast in the medium-run; in the RF government bond market investors tend to be guided by less conservative indicators but are ready to forecast only in the short-run.

Integrity of the benchmark price for price testing of US municipal bonds

External financial market data institutions (vendors) may provide different prices for the same US municipal bond due to differences among market participants in perception about its market value. The valuation control function will include only selected vendors in the calculation of the consensus price, which enters as a benchmark price in the price testing process. Selection of vendors is largely driven by the valuation control function’s consideration of their valuation capabilities and their market coverage. Empirical analysis in this paper shows that additional pricing service may bring additional pricing information to the final consensus price, which may significantly alter the benchmark price and final price testing results. The approach described in this paper is in interest of any financial institution with US municipal bonds in the trading portfolio. Contribution of this paper to valuation of US municipal bonds is high because remaining literature does not explain alternative approach to measurement of additional pricing information in the benchmark price.

Convertible Bond Valuation with Regime Switching

We present a valuation formula for convertible bonds with regime-switching market conditions by decomposing the convertible bond into a coupon-bearing bond and the American-type exchange option. A coupon-bearing bond component is modeled with a four-factor model: a two-factor affine model for the risk-free rate and a two-factor affine model with stochastic volatility for the credit spreads on the coupon-bearing bond component. We also derive a new valuation formula for the American-type exchange option component.

A variation of Merton's corporate bond valuation model for firms with illiquid but observable assets

We introduce a new model for pricing corporate bonds, which is a modification of the classical model of Merton. In this new model, we drop the liquidity assumption of the firm's asset value process, and assume that there is a liquidly tradeable asset in the market whose value is correlated with the firm's asset value, and all portfolios can be constructed using solely this asset and the money market account. We formulate the market price of the corporate bond as the product of the price of an optimal replicating portfolio and , where κ is a non-negative constant. The interpretation is that the representative investor uses the price of the optimal replicating portfolio as a benchmark and requests compensation for the non-hedgeable risk. We show that if the replication error is measured relative to the firm's value, the resulting formula is arbitrage free with mild restrictions on the parameters.

Equity Valuation: Forecasting Earnings Based on Probability Distributions Linked to Rating Categories

The paper continues an equity valuation model based on a random process modelling of earnings and book value, coupled with rating categories and rating migration. In essence, earnings and book value probability distributions are related to rating categories, and the probability of an issue to have a certain rating category at a certain time is calculated. Based on this, earnings are forecast as probability distributions. As reflected by the output distributions, in general, given its premises, the valuation model more realistically models inherent uncertainty, particularly increased uncertainty with time. It is noted that this approach to equity valuation is rather similar to reduced form models used with bond valuation. As a consequence, the probability of default is naturally incorporated into the valuation model. The necessary input earnings per book value, and book value growth, probability distributions are simulated, in accordance with preceding research, and the resultant output earnings, and book value, probability distributions are calculated and outlined.

Bond-Valuation and Default-Risk Re-examined: A Post Reduced-Form Model Based on Integer Migration and Portfolio Migration

The study re-examines bond valuation and default risk, by considering and relaxing assumptions regarding integer rating migration, and portfolio rating migration, and consequently the implied degree of diversification. A reduced form model, based on (a) rating migration (matrix), serve as basis and starting point. The study subsequently moves towards a post reduced form bond valuation model, by considering portfolio migration and integer migration. Portfolio migration refers to actual counts of issues migrating across rating categories, between the intervals of the portfolio – the number of issues with a particular rating at a particular point in time. Integer migration considers the fact that only integer counts of issues can migrate. Both portfolio and integer migration imply more sophisticated interpretation of rating migration matrices. Portfolio migration and integer migration result in interval rating category issue count probability distributions, and issue interval rating category intensity (probability) probability distributions, and consequently cause more sophisticated issue interval cash flow distributions to form. The resultant post reduced form model issue price results are encouraging and promising, and are briefly considered.

Cyberattacks and impact on bond valuation

We examine the impact of cyberattacks on bondholder wealth. Unlike stockholders, bondholders do not react in the short-term but do experience negative returns in the one-month event window. Compared to similar firms not subject to cyberattacks, we find that bondholders lost approximately 2% of their wealth within a one-month period surrounding the attack (a loss of $3.8 million on average). In this decade of advanced cybersecurity, bondholders still suffer similar losses compared to the last decade. To our knowledge, this is the first study that analyzes the impact of cyberattacks on bondholder wealth.

A lattice-based approach to option and bond valuation under mean-reverting regime-switching diffusion processes

Nowadays, the pricing of financial instruments under continuous-time Markov switching models have received a widespread attention from researchers and practitioners in the finance industry. Lattice-based approaches are amongst the most widely used approaches to solve the pricing problem in this context. Recently, Yuen and Yang (2010) have proposed a simple and fast recombining trinomial tree method to handle the case of regime-switching geometric Brownian motion processes. In this paper, we generalize their approach to the regime-switching (exponential) mean-reverting case with state-dependent switching rates and derive the necessary conditions for the positivity of conditional branching probabilities. We employ the Hull and White’s tree-building procedure to limit tree growth away from the long-run mean of the process. We use the proposed lattice framework to price contingent claims of European, American and barrier type, and demonstrate its applicability in pricing default-free zero-coupon bonds. In the proposed tree structure, the number of nodes is substantially decreased and the computational cost is effectively reduced compared to the usual approaches. Extensive numerical experiments illustrate the efficiency and flexibility of the proposed scheme.

A Climate Risk Assessment of Sovereign Bonds' Portfolio

Climate risk brings about a new type of financial risk that standard approaches to risk management are not adequate to handle. We develop a model that allows to compute the valuation adjustment of corporate and sovereign bonds conditioned to climate transition risk, based on available forward-looking knowledge on climate policy scenarios provided by climate economic models. We investigate the impact of the endogeneity and deep uncertainty of future scenarios on both the valuation of individual bonds and on standard risk metrics for a leveraged investor, considering the role of fossil fuels and carbon intensive activities in the economy of countries. We demonstrate that an investor’s Value at Risk andExpected Shortfall have low sensitivity to key parameters such as the Probability of Default(PD) of the bond In contrast, the investor’s PD is very sensitive to these parameters, and increases with the PD of the bond and with the probability of occurrence of the adverse climate transition scenario. Choosing the wrong scenario could lead to a massive underestimation of losses. Thus, Climate stress test exercises should allow for a wide enough sets of scenarios to avoid underestimation of losses. We apply the methodology to the AustrianNational Bank’s portfolio of sovereign bonds. In carbon intensive countries, the cost of climate misalignment is reflected in a higher Climate Spread and affects sovereign risk and portfolio’s performance. These results have important implications for the selection of relevant climate transition scenarios in climate stress-testing exercises, and for the assessment of climate-related financial risk for supervisory and prudential policy purposes.

Comparing Merton model and Gram-Charlier model to capture skewness and kurtosis on bond performance

The existence of skewness and kurtosis in finance data distribution is as a generalization of the normal density. Non-normal skewness and kurtosis of underlying asset of bond issuer significantly contribute to the phenomenon of volatility smile. Merton jump diffusion model is one of the first beyond Black-Scholes model in the sense that it tries to capture the effect of skewness and kurtosis of the asset prices density by a simple addition of a compound Poisson jump process. Another approach to consider the effect of skewness and kurtosis in asset prices for bond valuation is the Gram-Charlier (G-C) expansion. Hermite polynomial is used to get an expansion of the probability distribution in G-C method. In this paper we compare Merton Jump Diffusion (MJD) Model and G-C model in the term of equity and default probability. The result showed that G-C model is more consistent than MJD model when the skewness and kurtosis are taken into account.

Interest Rate Term Structure Decomposition at the Instrument Level

The paper examines term structure decomposition at the instrument level – decomposing term structures for issues as well as the portfolio. Three different implementations are stipulated: axiomatic structural approaches, a sequential approach, and a base structure approach. The three different implementations are evaluated against a portfolio of risk-free government bonds. The goodness-of-fit and smoothness properties of instrument-level term structure decomposition are also considered. The conclusion points to remaining gaps in theory regarding instrument-level term structure decomposition, and considers areas of application – typically bond valuation.

Cyberattacks and Impact on Bond Valuation

We examine the impact of cyberattacks on bondholder wealth. Unlike stockholders, bondholders do not react in the short-term but do experience negative returns in the one-month event window. Compared to similar firms not subject to cyberattacks, we find that bondholders lost approximately 2% of their wealth within a one-month period surrounding the attack (a loss of $3.8 million on average). In this decade of advanced cybersecurity, bondholders still suffer similar losses compared to the last decade. To our knowledge, this is the first study that analyzes the impact of cyberattacks on bondholder wealth.

The Nitty Gritty of Bond Valuation

The multitude of day count conventions and the prevalence of irregular coupon periods constitute a major complication for the comparative analysis of interest accruing securities across markets. I develop the first generalized pricing methodology for straight bonds that allows for irregular coupon periods of any length and precisely accounts for any conceivable day count convention. In a comprehensive compendium, I distinguish between the individual conventions, relating them to each other in a consistent mathematical notation. Using one universal valuation formula, I derive closed form solutions for modified duration and convexity. My R-Package Bond Valuation closes the gap between theory and data.

The Valuation and Optimal Policies of Puttable Convertible Bonds

American-style convertible bonds commonly contain the put provision that allows the investors to put or sell their holdings to the issuer at preset prices and dates. The embedded put option includes a free boundary in addition to the conversion boundary. Because of the correlation of two moving boundaries with the convertible price, the valuation of puttable convertible bonds remains a classical problem in quantitative finance. This paper presents the valuation model of puttable convertible bonds under the Black-Scholes framework. We distinguish between the conventional pricing model and the current work by the realization of a jump in the put price across the hitting time. The jump condition permits the derivation of two recombining differential systems and we explore the impact of jump effect on the pricing dynamic of this innovative financial derivative.

Rating Migration and Bond Valuation: Towards Ahistorical Rating Migration Matrices and Default Probability Term Structures

The study examines rating migration, and default probability term structures obtained from rating migration matrices. It expands on the use of rating migration matrices with reduced form bond valuation models, by formally delineating the probability of default according to the likely rating paths of a bond, as implied by the rating migration matrix. Further, two alternatives are also considered. First, the cost of default is stipulated as the recovery of par according to the exit rating upon default. Also, in addition to stating the value of a bond in terms of expected cash flows, when considering the probability of default, the value of a bond is alternatively stated as the present value of all likely rating paths of the bond, discounted against the market risk-bearing bond forward rates of the different rating categories. The impact of term structure volatility and rating migration uncertainty on bond valuation is also considered.It is shown that the relationship between rating migration and default probability is complex, and the default probabilities of different rating categories are time-dependent and not isolated from each other. Also, rating migration resembles a delayed default process that influences default probabilities of subsequent intervals. The implications of a rating migration matrix may perhaps only be fully understood through simulation. This form one of the first points by which to evaluate rating migration matrices. The results of the valuation model show that historical rating migration matrices may not be optimal for pricing bonds ahistorically. A principal premise of the study is the dichotomy between historical values and ahistorical estimates, particularly with regards to rating migration. It is argued that historical estimates face two key shortcomings: they must be able to accurately forecast future rating migration and rating category intensities as a result, and they must specify a method to include rating migration uncertainty. An optimization model is delineated to extract ahistorical rating migration matrices from market prices. This too has implications that should be considered. In light of the above, reduced form models may have an advantage over structural models, in their ability to portray a far more sophisticated default process.

Rating Migration and Bond Valuation: Towards Ahistorical Rating Migration Matrices and Default Probability Term Structures

The study examines rating migration, and default probability term structures obtained from rating migration matrices. It expands on the use of rating migration matrices with reduced form bond valuation models, by formally delineating the probability of default according to the likely rating paths of a bond, as implied by the rating migration matrix. Further, two alternatives are also considered. First, the cost of default is stipulated as the recovery of par according to the exit rating upon default. Also, in addition to stating the value of a bond in terms of expected cash flows, when considering the probability of default, the value of a bond is alternatively stated as the present value of all likely rating paths of the bond, discounted against the market risk-bearing bond forward rates of the different rating categories. The impact of term structure volatility and rating migration uncertainty on bond valuation is also considered.It is shown that the relationship between rating migration and default probability is complex, and the default probabilities of different rating categories are time-dependent and not isolated from each other. Also, rating migration resembles a delayed default process that influences default probabilities of subsequent intervals. The implications of a rating migration matrix may perhaps only be fully understood through simulation. This form one of the first points by which to evaluate rating migration matrices. The results of the valuation model show that historical rating migration matrices may not be optimal for pricing bonds ahistorically. A principal premise of the study is the dichotomy between historical values and ahistorical estimates, particularly with regards to rating migration. It is argued that historical estimates face two key shortcomings: they must be able to accurately forecast future rating migration and rating category intensities as a result, and they must specify a method to include rating migration uncertainty. An optimization model is delineated to extract ahistorical rating migration matrices from market prices. This too has implications that should be considered. In light of the above, reduced form models may have an advantage over structural models, in their ability to portray a far more sophisticated default process.

Investor Sentiment and Speculative Bond Yield Spreads

Abstract The valuation of risky debt is central to theoretical and empirical work in corporate finance. Although much is known on the returns and valuation of bonds, there is hardly a consensus on the risk components of the yield spreads. This article aims to investigate the effect of investor sentiment as a systematic risk factor on speculative bond yield spreads. After applying correlation analysis to determine the strength of linear association between these two variables, a vector autoregressive (VAR) analysis and impulse response tests are used to examine the relationship between these two variables. The sample period extends from January 1997 to August 2014. In the VAR models, speculative bond spreads and consumer confidence index are used as endogenous variables. The results show that sentiment covaries with the yield spread and have a negative effect on them. The spread level of the previous period seems to be a statistically significant determinant of the current period sentiment. Empirical findings imply that investor sentiment is a systematic risk factor in risky bond markets.

Bond Valuation: Modelling Downgrade Risk and Default Risk Based on Rating Migration Variation As Uncertainty Over the Investment Horizon Through Optimization

Bond Valuation: Modelling Downgrade Risk and Default Risk Based on Rating Migration Variation As Uncertainty Over the Investment Horizon Through Optimization

BondValuation: An R Package for Fixed Coupon Bond Analysis

The purpose of this paper is to introduce the R package BondValuation for analysis of large datasets of fixed coupon bonds. The conceptual heterogeneity of fixed coupon bonds traded in the global markets imposes a high degree of complexity on their comparative analysis. Contrary to baseline fixed income theory, in practice, the majority of bonds feature coupon period irregularities. In addition, there is a multitude of day count methods, which determine the interest accrual, the cash flows and the discount factors used in bond valuation. Several R packages, e.g., fBonds, RQuantLib, and YieldCurve, provide tools for fixed income analysis. However, none of them is capable of evaluating bonds featuring irregular first and/or final coupon periods, and neither provides adequate coverage of day count conventions currently used in the global bond markets. The R package BondValuation closes this gap.