Bond Pricing Model Research Articles

Pricing Corporate Bonds with Interest Rates Under Double Square-Root Process

This paper develops a corporate bond pricing model following the structural approach in which the dynamics of the instantaneous risk-free interest rate are governed by a double square-root (DSR) process. Credit spreads generated from this pricing model depend explicitly upon the levels of interest rates via a nonlinear effect arising from a DSR process. Given a positive correlation between interest rates and leverage ratios, the credit spreads generated by this pricing model have a negative relationship with interest rates, that is consistent with empirical findings using bond market data over the period 2008-2013 when interest rates were low.

The effects of government sponsored enterprise (GSE) status on the pricing of bonds issued by the Federal Farm Credit Banks Funding Corporation (FFCB)

PurposeMotivated by recent congressional interest in eradicating government sponsored enterprises (GSE), the purpose of this paper is to develop a framework to price the implicit government guarantee embedded in the bonds issued by the Farm Credit System.Design/methodology/approachThe paper uses the Black‐Scholes model to extract the implied volatilities of the guarantee and then substitute into the model the volatility in historical land prices. The model is developed along the lines of Merton's bond pricing formulation of implicit calls and puts on bond yield risk and default.FindingsBottom line results show that the average bond yield for a 3M Farm Credit bond from January 13th 2009 to February 10th 2011 would be 0.3744 percent if the Farm Credit System had no GSE status, which is 13.62 bps higher than the actual bond yield. The difference between the hypothetical yield and the actual yield increases with increasing maturity and reaches its peak with 10Y bond where the difference between the hypothetical yield and the actual yield is 68.81 bps. The paper concludes that given the current state of the agricultural credit market in the USA that loss of GSE status and the implied guarantee of Farm Credit bonds would have a minimal effect on short term notes, with a more substantive increase in longer term yields.Practical implicationsThe GSE status of the Farm Credit System is an important political issue. This paper provides first estimates of what impact might result from its loss of GSE status. The methods employed are consistent with current models of bond pricing and the results are of direct relevance to Farm Credit System regulators and congressional discussions.Social implicationsFarm credit is important, if the Farm Credit System loses its GSE status this might affect the competitive balance between commercial and system lenders.Originality/valueThis paper uses option price theory based upon the spread between farm credit bonds and treasury. The approach used requires daily data, but not all attributes of bonds are known. Nonetheless, the results show remarkable consistency for a problem that is largely understudied. There is a need for policy makers, including the US congress to understand the value of government guarantees whether implicit or explicit.

Determinants of the cat bond spread at issuance

The contribution at hand is a short summary of a working paper presented by Alexander Braun at the annual meeting of the German Insurance Science Association (DVfVW) in Hannover in March 2012. This working paper contains empirical evidence from the primary market for cat bonds, which provides new insights concerning the prevailing pricing practice of these instruments. For this purpose, transactional information from a multitude of sources has been collected and cross-checked in order to compile a data set comprising virtually all cat bond tranches that were issued between 1997 and 2011. In order to identify the main determinants of the cat bond spread at issuance, a series of OLS regressions with robust standard errors is run. The respective results indicate that, apart from the expected loss, the covered territory, the sponsor, the reinsurance cycle, and the spreads on comparably rated corporate bonds exhibit a significant impact. Based on these findings, a multifactor pricing model for cat bonds in the primary market is then proposed. This model is applicable across all considered territories and perils, exhibits a stable fit with regard to different subsamples used for calibration, and achieves a higher in-sample and out-of-sample accuracy than several competing specifications that have been introduced in earlier work.

The Option to Re-organize Firms with Valuable Growth Options and Risky Bond Prices

We develop a structural model of corporate bond prices which accounts for the option held by bondholders to liquidate or re-organize a firm that ends up in bankruptcy. Although there is a wide body of literature in corporate finance that examines the trade-offs between liquidation and re-organization for creditors in financially distressed firms, our paper is the first to incorporate these options into the ex-ante value of risky debt. The option to liquidate or to re-or ganize has value in our model due to the presence of valuable growth options. Liquidation value being the depreciated value of assets in place, ignores the value of these options. But were bondholders to take over control of the firm, the value of the firm is, with some ef ficiency loss, the sum of the value of assets in place and the value of future growth options.

Empirically Effective Bond Pricing Model and Analysis on Term Structures of Implied Interest Rates in Financial Crisis

In his book (1993) Kariya proposed a government bond (GB) pricing model that simultaneously values individual fixed-coupon (non-defaultable) bonds of different coupon rates and maturities via a discount function approach, and Kariya and Tsuda (Financ Eng Japanese Mark 1:1–20, 1994) verified its empirical effectiveness of the model as a pricing model for Japanese Government bonds (JGBs) though the empirical setting was limited to a simple case. In this paper we first clarify the theoretical relation between our stochastic discount function approach and the spot rate or forward rate approach in mathematical finance. Then we make a comprehensive empirical study on the capacity of the model in view of its pricing capability for individual GBs with different attributes and in view of its capacity of describing the movements of term structures of interest rates that JGBs imply as yield curves. Based on various tests of validity in a GLS (Generalized Least Squares) framework we propose a specific formulation with a polynomial of order 6 for the mean discount function that depends on maturity and coupon as attributes and a specific covariance structure. It is shown that even in the middle of the Financial Crisis, the cross-sectional model we propose is shown to be very effective for simultaneously pricing all the existing JGBs and deriving and describing zero yields.

Systematic Liquidity Risk in the Australian Bond Market

This research examines recent developments in asset pricing theories and their ability to explain Australian bond market returns. This study develops a multifactor bond pricing model in an Australian setting. We examine the Lin et al. (2011) systematic liquidity factor to evaluate its power in explaining Australian bond returns. This study shows that the term, default and liquidity factors are important systematic risk factors in explaining the variation of returns of individual bonds and bond portfolios in Australia. The Australian bond pricing model developed in this study allows market participants to evaluate the risk factors that drive Australian bond portfolio returns regardless of their credit rating, liquidity, duration or industry sector concentration. In a simple case study, the Australian bond pricing model explains more than 82 percent of the variation of returns of Public Private Partnership (PPP) bond portfolios comprising of firms that are financially solvent.

The time-varying integration of euro area government bond markets

We derive a model in which a standard international capital asset pricing model (ICAPM) for government bonds is nested within an ICAPM with impediments to invest in the local government bond markets. Excess returns or risk premiums are then driven by a country-specific or idiosyncratic stochastic factor on top of the common factor which has a time-varying idiosyncratic impact on the premiums. With this model we investigate the financial integration of government bond markets over time through two channels. First, we allow for gradual convergence from the full ICAPM with impediments to the standard model through the vanishing of the idiosyncratic factors. Second, we allow for gradual equalization of the country-specific impacts of the common factor. State space methods are used to estimate the model with weekly government bond risk premiums for Belgium, France, Italy, Germany, and the Netherlands over the period 1995–2009. Our results suggest, first, that the idiosyncratic factors were almost eliminated by 2006 in all countries but Italy but then reappeared due to the financial crisis that started in 2007. Second, the country-specific exposures to the common international risk factor have converged across countries, with no setback during the crisis.

The Equilibrium Models of Bond Pricing and Duration Measures: A New Perspective

A new approach to the conditions that a duration measure must satisfy to represent the interest rate risk adequately is proposed in this paper. These conditions are derived from an intertemporal model of utility maximization. In addition, this approach is used to provide a new perspective on the arbitrage opportunities arising from the convexity effect on hedged bond portfolios. For several decades this has been considered in the literature as the main cause of the incompatibility between the traditional duration measures of Macaulay (1938), Fisher and Weil (1971), and other “immunizing” duration measures and the equilibrium models of bond pricing. Using empirical data, this paper shows that convexity effect on the rates of return on bonds is not completely eliminated, when the duration measures derived from equilibrium models of Vasicek (1977) and of Cox, Ingersoll and Ross (1985) are used in hedging strategies. The empirical analysis also shows that the influence of convexity on bond returns depends on the magnitude of interest rate changes.

Flood Insurance Bonds Pricing Based on the Monte Carlo Simulation

China is one of the countries with most serious natural disasters where the damage caused by flood is larger than any other natural disasters. The introduction of catastrophe bonds would be a good channel for transferring the catastrophic risk. Therefore, based on the principle of non-life actuarial, this paper figured out the distribution fitting for the losses and occurrences of flood disasters and applied Monte Carlo simulation to calculate the total loss of flood disasters and its corresponding probability in China. By using the capital asset model and Catastrophe bond pricing model, the yields and prices of flood disaster bond can be obtained, which can be referred and learned for the issuance of flood disasters bonds in the future.

Dissecting Corporate Bond and CDS Spreads

In this article, the authors propose a new method to estimate the components of corporate bond and CDS spreads. They develop a CDS pricing model with default and nondefault factors and a corporate bond pricing model with default, tax, and liquidity factors using the reduced-form approach, and they jointly estimate parameters of both models from the pooled data. By formulating default intensity as a common factor in the prices of the CDS and reference bonds, the authors are able to identify the default and nondefault components of yield spreads more precisely. They find that, on average, the liquidity premium accounts for about 20–25% of corporate yield spreads across ratings and the size of the liquidity premium increases as the rating decreases. Furthermore, they find that the CDS spread contains a nontrivial nondefault component. Ignoring this component in the CDS spread thus results in a serious bias in the estimate of spread components when using the CDS information to aid in decomposition of corporate yield spreads.

Dissecting Corporate Bond and CDS Spreads

In this paper, we propose an alternative approach to estimate the components of corporate bond and CDS spreads. We develop a CDS pricing model with default and nondefault factors, and a corporate bond pricing model with default, tax and liquidity factors using the reduced-form approach, and jointly estimate parameters of both models from pooled data. By formulating default intensity as a common factor in the prices of the CDS and reference bonds, we are able to identify the liquidity and other components of yield spreads more precisely. We find that on average the liquidity premium accounts for about 23% of the corporate yield spread and the size of the liquidity premium increases as the rating decreases. Furthermore, the CDS spread contains a significant nondefault component. Results show that ignoring the nondefault component in the CDS premium results in biased estimates of corporate yield spread components when using the CDS information to aid in decomposition of yield spreads.

Default Prone Bond Prices, Valuable Growth Options and the Option to Re-Organize

There is a wide body of literature in corporate finance that examines the tradeoffs between liquidation and re-organization for creditors in financially distressed firms (Kahl (2002), Hotchkiss (1995), Gertner and Scharfstein (1991)). We incorporate salient elements from this literature into a structural model of corporate bond prices. We derive the value of perpetual coupon-paying risky debt as a function of the option held by bondholders to either liquidate or to take control when a firm becomes financially distressed. Liquidation value is the depreciated value of assets in place. Firm value under bondholders is with some efficiency loss, the sum of assets in place and future growth options. We derive ex-ante values of corporate bond prices as a function of the current values of these two competing choices.

Default Risk Characteristics of Poll-Based Bond Spreads

Poor liquidity of corporate bonds in emerging markets deters reliable estimation of credit spreads. As an alternative, credit spreads based on poll data are introduced in India. These spreads are used for pricing new credit instruments and for valuation of bond portfolios. We examine the credit risk characteristics of these spreads based on the structural models of bond pricing. We find that the spreads are largely deter-mined by the proxies of default probability and recovery rate. Also, the relation between spreads and important credit risk variables is as predicted by the models. These results support the use of poll-based credit spreads. Introducing poll-based spreads in less liquid corporate bond markets is likely to offer a reliable basis for pricing credit instruments and derivatives.

Structural models of corporate bond pricing with personal taxes

The structural approach offers an integrated framework to deal with yield spreads and default probability simultaneously. However, structural models perform poorly in predicting corporate bond spreads. It is unclear whether this poor performance is caused by characteristics of individual models, missing factors, or different calibration procedures. This study evaluates the performance of four structural models by incorporating two important factors, personal taxes and the liquidity factor, and calibrating these models to data. To ensure our results are not contingent on the calibration method, we further apply the maximum likelihood estimation method to a large sample of individual bonds. Results consistently show that the ability of structural models to predict spreads improves considerably when personal taxes and liquidity are taken into account. Our findings suggest that the poor performance of standard structural models is more likely due to missing factors than the characteristics of individual models or the calibration procedure.

Exotic put options at the diffusion bond market

The direct approach is used to obtain formulas that determine the option price, portfolios (hedging strategies) and capitals for the European put options with guaranteed income for the option holder and limited payment for the investor at the diffusion (B,P)-bond market. The properties of the solution are studied. The results are specified for the bond pricing models known as the Ho-Lee and Vasicek models.

Pricing inflation-linked bonds

This paper proposes a pricing model for inflation-linked bonds. Our proposal is developed starting from a Vasicek model of the instantaneous inflation rate process and the Cox, Ingersoll and Ross model for the nominal instantaneous risk-free interest rate process. Instead of adopting the standard approach of a cross-section estimation of the term structure of real interest rates, this work proposes a pricing model based on estimation of the inflation risk premium. The model is applied to Treasury Inflation Protected Securities, which are inflation-linked bonds issued by the U.S. Department of the Treasury. Empirical validation is carried out on data for the period 1999–2005.

An Econometric Pricing Model for CAT Bonds and the Impact of the 2005 Hurricane Season

This paper examines the impact of the hurricane season 2005, in particular hurricane Katrina, on the pricing of CAT bonds. In doing so, we examine whether highly rated CAT bonds compared to sub-investment bonds show a different relation between objective risk measures and the spread. The theoretical framework for this relationship is based on the Lance Financial (LFC) model introduced by Lane (2003). The empirical results of treed Bayesian estimation confirm that the severity component of the spread has an increased impact, indicating a shift in the perception of investors during the pricing process. While the impact of the conditional expected loss significantly increases, it contributes through its interaction with the attachment probability, however, not through the variance. Finally, we show that the influence of conditional expected loss is also increased by investment grade ratings, since investors who demand highly rated bonds may be more concerned about possible losses than junk bond investors.

Liquidity Premia in the Credit Default Swap and Corporate Bond Markets

This paper employs a new approach to estimating the size of liquidity premia in the credit default swap (CDS) and corporate bond markets. We develop a CDS pricing model with liquidity and default, and a corporate bond pricing model with default, taxes, and liquidity using the reduced-form approach, and jointly estimate parameters of both pricing models from pooled data using the generalized method of moments. By formulating default intensity as a common factor of the spreads of the CDS and reference bonds, we are able to identify the liquidity and other components of spreads more precisely. We find that both CDS and corporate bond spreads contain significant liquidity components. On average, the liquidity premium accounts for 13% of the CDS spread and 23% of the corporate yield spread. The size of the liquidity premium increases as the rating decreases. Estimates of liquidity premia in the CDS and corporate bond markets are highly correlated, and closely linked to bond-specific and aggregate liquidity measures. Results show that liquidity is important for CDS and corporate bond pricing. Ignoring CDS illiquidity results in a significant bias in estimation of corporate yield spread components when using the CDS information to aid in decomposition of spreads.

The Impact of Shareholder Control on Bondholders

This paper investigates the effect of shareholder control on bondholder wealth. While stronger shareholder control can benefit bondholders by disciplining managers, it also increases the likelihood of events that can hurt bondholders, e.g. hostile takeovers. We hypothesize that shareholder control can have contrasting effects on bond yields depending on the takeover vulnerability of a firm. Using the presence of an institutional blockholder to proxy for shareholder control and firm-level anti-takeover provisions to proxy for takeover vulnerability, we find that shareholder control is associated with lower yields if the firm is protected from takeovers. We also find that shareholder control is associated with higher yields if the firm is exposed to takeovers. The contrasting effects of shareholder control on yields are the strongest for firms that are small and have low leverage. In the presence of shareholder control, the difference in bond yields due to differences in takeover vulnerability can be as high as 93 basis points. Further, the results are insignificant for a sub-sample of firms where the bondholders are protected from takeovers through the poison put covenant. Bond ratings also appear to incorporate a similar effect of shareholder control on bondholders Finally, we find that a bond pricing model that does not account for shareholder control generates an annualized abnormal return of 1% to 1.4% for portfolios that long firms with both strong shareholder control and high takeover vulnerability and short firms without either shareholder control or takeover vulnerability. Combined, these results suggest that the use of different governance mechanisms, such as shareholder monitoring and takeover vulnerability, depends on a firm s capital structure and that bond-pricing models should account for shareholder control.

Default Characteristics of Corporate Bonds

In this paper we present a corporate bond pricing model. Based on this model we develop a construction of the default characteristics implied by historical data.