Bond Valuation Research Articles

Valuing convertible bonds and the option to exchange bonds for stock

The value of a conventional convertible bond is the value of a straight bond plus the value of the option to exchange it for a specified number of shares of common stock. First, I develop a closed-form contingent-claims convertible bond valuation model that quantifies the value of the exchange option when the short-term riskless rate, the firm's credit spread, and its share price are stochastic. I model the firm's decision to force early conversion as a stopping time problem in which the firm forces conversion as soon as the conversion value reaches the forced conversion barrier. I empirically validate the model by comparing model and market prices for a sample of 148 corporate convertible bonds issued between 2006 and 2010. The average median and mean pricing errors are −0.18% and 0.21%, respectively, which are within the average bid–ask spread for convertible bonds during the sample period. I use the model to quantify the disruptive impact that the prohibition on short selling during the recent financial crisis had on convertible bond prices.

Valuation and analysis of zero-coupon contingent capital bonds

We consider the valuation and analysis of zero-coupon contingent capital bonds (CCBs) in the structural framework. Making virtually no assumptions on asset value dynamics, the terms of conversion or the conversion trigger, we express the value of the CCB in terms of the effective loss imposed on CCB investors at conversion and quantify the impact that contingent capital has on traditional debt and equity. We show how a variety of conversion terms can be incorporated into a single framework and describe how they can be calibrated to ensure that seniority is respected and/or equity investors are not rewarded for poor performance. We provide numerical evidence indicating that the terms of conversion can fundamentally alter the nature of the CCB, a phenomenon that is of clear interest to investors, issuers and regulators.

Regime-switching shot-noise processes and longevity bond pricing

In this paper, we consider the valuation of longevity bonds under a regime-switching interest rate and a regimeswitching force of mortality model. The model assumes that the interest rate is driven by economic and environmental conditions described by a homogenous Markov chain and that the stochastic force of mortality is modeled by the sum of a regime-switching Gompertz–Makeham model and a regime-switching shot-noise process. Using the conditional Laplace transform of the regime-switching shot-noise process, we give a formula for the longevity bond price in terms of a couple of system partial differential equations. The pricing formula is also derived by using the concept of stochastic flows and the idea of change of measure.

Convertible bond valuation in a jump diffusion setting with stochastic interest rates

This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffie et al. [Econometrica, 2000, 68, 1343–1376] with tractable behaviour. We define the firm’s optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates.

Valuation and Analysis of Zero-Coupon Contingent Capital Bonds

We consider the valuation and analysis of zero-coupon contingent capital bonds (CCBs) in the structural framework. Using Doob's Optional Sampling Theorem (and making virtually no assumptions on asset value dynamics, the terms of conversion or the conversion trigger) we express the value of the CCB in terms of the effective loss imposed on CCB investors at conversion and quantify the impact that contingent capital has on traditional debt and equity. We show how a variety of conversion terms can be incorporated into a single framework and describe how they can be calibrated to ensure that seniority is respected and/or equity investors are not rewarded for poor performance. We provide numerical evidence indicating that the terms of conversion can fundamentally alter the nature of the CCB, a phenomenon that is of clear interest to investors, issuers and regulators.

Financial Contracting as Behavior Towards Risk

This paper describes a business cycle model where financial contracting with interrelated covenants is the mechanism by which bondholders and stockholders confront the risks associated with future production-investment decisions and financing decisions of the firm and in the process resolves a conflict of interest problem between them. In resolving this conflict of interest problem the interrelated covenants in the financial contract shape the financial facts of business cycles. The model set-up includes two agents (bondholders and stockholders), two decisions (production-investment decisions and financing decisions), and two equilibrium conditions (market equals economic book value for both bonds and stocks). In this 2x2x2 set-up the manager of the representative firm should always make production-investment decisions that conform to the risk aversion of stockholders and then use financing decisions to offset any effect of a change in operating risk on the market valuation of bonds. Preliminary evidence from the U.S. nonfinancial corporate sector does not reject the predictions of the model.

The valuation of catastrophe bonds with exposure to currency exchange risk

In this paper, we present a new model that takes an arbitrage approach to the valuation of catastrophic risk bonds (CAT bonds). The model considers the sponsor's exposure to currency exchange risk and the risk of catastrophic events. We use a jump-diffusion process for catastrophic events, a three-dimensional stochastic process for the exchange rate and domestic and foreign interest rates, and a hedging cost for the currency risk to derive a semi-closed-form formula for the CAT bond price. We also extend to three factors Joshi and Leung's (2007) Monte Carlo simulation approach to obtain numerical results showing the following: in addition to catastrophic risk, the CAT bond price is affected mainly by the volatility of the exchange rate and its correlations with domestic and foreign interest rates. The first two factors have a negative impact while the third has a positive impact.

The Valuation of Catastrophe Bonds with Exposure to Currency Exchange Risk

In this paper, we present a new model that takes an arbitrage approach to the valuation of catastrophic risk bonds (CAT bonds). The model considers the sponsor’s exposure to currency exchange risk and the risk of catastrophic events. We use a jump-diffusion process for catastrophic events, a three-dimensional stochastic process for the exchange rate and domestic and foreign interest rates, and a hedging cost for the currency risk to derive a semi-closed-form formula for the CAT bond price. We also extend to three factors Joshi and Leung’s (2007) Monte Carlo simulation approach to obtain numerical results showing the following: in addition to catastrophic risk, the CAT bond price is affected mainly by the volatility of the exchange rate and its correlations with domestic and foreign interest rates. The first two factors have a negative impact while the third has a positive impact.

The Analysis of Corporate Bond Valuation under an Infinite Dimensional Compound Poisson Framework

This paper analyzes the firm bond valuation and credit spread with an endogenous model for the pure default and callable default corporate bond. Regarding the stochastic instantaneous forward rates and the firm value as an infinite dimensional Poisson process, we provide some analytical results for the embedded American options and firm bond valuations.

On the conditional default probability in a regulated market with jump risk

In this paper, we introduce tractable dynamic models for financial variables (such as interest rates, foreign exchange rates, commodity prices, etc.) with capturing both jump risk and boundedness of the price fluctuation in a regulated market. For the jump risk, we use a compound Poisson process with double exponential jump amplitude to describe the jumps. As for the boundedness of the fluctuation, we introduce two regulators to regulate (or control) the price dynamics. Based on such a dynamics, we then study the default events under the structural framework for credit risk. The explicit expression for the Laplace transform of the default time is derived. For exploring the effect of the jump risk and the regulation, we perform some numerical simulation. As a practical application, an analytic valuation of defaultable zero-coupon bonds is presented. It turns out that our model can produce a variety of strictly positive credit spread term structures, including downward, humped and upward styles.

Valuation and choice of convertible bonds based on MCDM

The pricing model of convertible bonds has emerged as an important assessment model for financial investment in recent years. This model suggests that the pricing model of convertible bonds can be decomposed into the Options Pricing Theory and Pure Bonds Theory. Literature in the past did not explain therelative weight and factors affecting these two models. This research is anattempt to explore the unexplained portion of the pricing model of convertiblebonds by adopting Decision-Making Trial and Evaluation Laboratory, Analytic Network Process, and Multiple Criteria Decision-Making of the VlseKriterijumska Optimizacija I Kompromisno Resenje. The model has been referred to three Taiwanese technology firms issuing convertible bonds for verification. The result indicated that the aforementioned two models are inter-affecting each other and in self-regression. Of the eight criteria, conversion price remains the critical factor affecting the pricing of convertible bonds. It was followed by stock price and yiel...

Commercial and investment banking and the international credit and capital markets: a guide to the global finance industry and its governance

Preface PART 1: THE FUNDAMENTALS OF FINANCE, MARKETS AND THE FINANCIAL FIRMS The Price Mechanism and the Three Pillars of Finance Appendix - Valuation Models, Issues in Bank Asset Valuation, Discounted Cash Flow Valuation of Bonds and Equities Balance Sheets: The Key to Understanding Financial Intermediation Financial Intermediation: Industry Sectors, Products and Markets Financial Intermediation: Commercial and Investment Bank Structure PART 2: PRIMARY MARKETS: FUNDING LIQUIDITY AND EXTERNAL CAPITAL ALLOCATION THROUGH CREDIT AND CAPITAL MARKETS Liquidity: What is it? Financing the Four Sectors: Companies, Households, Governments and Overseas through Credit and Capital Markets Banking: Credit Intermediation through Depository Institutions Bank Liquidity Management Converting Loans to Securities: Securitisation as a Financing Tool Shadow Banking: Credit Intermediation through Non-depository IPOs and Corporate Bond Origination PART 3: SECONDARY MARKETS: MARKET LIQUIDITY AND MARKET FAILURE Market Liquidity: Order-driven Auction Markets and Quote-driven Dealer Markets The New Secondary Market Structure: Competition, Dark Pools, Algorithmic and High Frequency Trading Clearing and Settlement of Securities Transactions Market Failure: Sub-optimal Allocation of Resources by Credit and Capital Markets, Banking and Sovereign Debt Crises Assessing Risk and Return for Investors in Bank and Sovereign Debt Case Study: Lehman - What might have been Case Study: Greece in Default in 2011 Case Study: Italy, Illiquid or Insolvent in 2011 PART 4: ASSESSING AND MANAGING RISK IN ASSET PORTFOLIOS Investment Management and Portfolio Structuring Investment Management Practice: Funds - Pension, Insurance, Sovereign Wealth, Long-Only, Hedge, Mutual, Cash and Synthetic ETF's and Delta One Trading Desks PART 5: INTERNAL CAPITAL ALLOCATION: THE ROLE OF DIRECTORS, INVESTORS AND THE MARKET FOR CORPORATE CONTROL The Internal Capital Market & Investor Governance of Capital Allocation The Market for Corporate Control: Mergers and Acquisitions Private Equity PART 6: INTERNAL RISK MANAGEMENT AND EXTERNAL REGULATION OF FINANCIAL INTERMEDIARIES AND MARKETS Risk Management in Credit Intermediaries and Investment Banks Regulation of Banks and Investment Banks: Basel I, II, and III Regulation of Securities Markets PART 7: THE ROLE OF GOVERNANCE AND STRATEGY IN RESOURCE ALLOCATION, FIRM AND INDUSTRY STRUCTURE: CASE STUDIES IN FINANCIAL SERVICES Strategy, Governance and Firm and Industry Structure Case Studies in Financial Services - Success and Failures The Future Structure of the Industry: Implications of Re-regulation The Fatal Flaw in Capital Allocation - The Shift from a Trust Model to a Transactional Model The Global Economic and Financial Outlook: 2020 Vision

Market Transparency and the Marking Precision of Bond Mutual Fund Managers

We analyze the dispersion of month-end prices simultaneously placed on identical corporate bonds by different US mutual fund managers before and after initiations of TRACE and introductions of issuers into Markit’s CDS database. Disseminated bonds show large and statistically significant decreases in mark dispersion around three key TRACE system rollout events, including important spillover effects for non-disseminated bonds. Dispersion for large, investment grade bonds fell 20% to 83% after the start of TRACE reporting. A difference-in-differences regression analysis of the two-stage rollout of BBB-rated bonds provides clearer evidence suggesting that TRACE led to a decrease in mark dispersion for all bonds via a matrix pricing channel in addition to any direct dissemination impact. TRACE-associated improvement in bond valuation precision provides indirect support for Bessembinder, Maxwell, and Venkataraman’s (2006) information-based channel relating transparency and pricing. During the pre-TRACE period, we also find some evidence that mark dispersion fell for investment grade issuers after introductions into Markit’s database.

A Binomial-Tree Model for Convertible Bond Pricing

In this article, we derive a binary tree–based model for convertible bond valuation subject to credit risk modeling. Our model, which belongs to the framework known as equity to credit risk, is based on the so-called reduced-form (constant intensity of default model for the underlying) and so-called synthesis (variable intensity of default model for the underlying) credit risk models. We show that our model converges in continuous time to the Ayache–Forsyth–Vetzal convertible bond valuation model introduced in 2003. We highlight and quantify certain issues that arise, such as transition probability analysis and threshold values of model inputs (tree step and underlying stock price). The model we propose provides an alternative way to develop the price dynamics model suggested by the Ayache–Forsyth–Vetzal model for convertible bonds, taking into account credit risk. <b>TOPICS:</b>Fixed income and structured finance, fixed-income portfolio management, options, factor-based models

Credit spreads, endogenous bankruptcy and liquidity risk

In this paper, we consider a bond valuation model with both credit risk and liquidity risk to show that credit spreads are not negligible for short maturities. We adopt the structural approach to model credit risk, where the default triggering barrier is determined endogenously by maximizing equity value. As for liquidity risk, we assume that bondholders may encounter liquidity shocks during the lifetime of corporate bonds, and have to sell the bond immediately at the price, which is assumed to be a fraction of the price in a perfectly liquid market. Under this framework, we derive explicit expressions for corporate bond, firm value and bankruptcy trigger. Finally, numerical illustrations are presented.

Valuing Companies by Cash Flow Discounting: Fundamental Relationships and Unnecessary Complications

La version espanola de este articulo se puede encontrar en: http://ssrn.com/abstract=2089397.Company valuation using discounted cash flows is based on the valuation of the Government bonds: it consists of applying the procedure used to value the Government bonds to the debt and shares of a company. This is easy to understand (sections 1, 2 and 3). But company valuation is complicated by ‘additions’ (formulae, concepts, theories…) to complicate its understanding (see sections 4 to 15) and to provide a more “scientific”, “serious”, “intriguing”, “impenetrable”, …appearance. Among the most commonly used ‘additions’ are: WACC, beta (B), market risk premium, beta levered and beta unlevered.

Interest Rate Derivatives: Features, Valuation and Benefits

Interest rate derivatives have become some of the most important derivative instruments, making up a higher proportion of financial market deals. Although financial markets are dominated by stock and stock indices in terms of activity, the bond market, and consequently the interest rate derivatives markets dominate in terms of value. However, most of the bond and interest rate derivatives transaction occur in over-the-counter markets. Additionally, there are well developed exchange markets for interest rate derivatives, such as the Chicago Mercantile Exchange. Noteworthy, is also the fact that interest rate derivatives are an essential ingredient in the management of interest rate risk. This paper highlights a number of such instruments including swaps, caps, collars, and floors. The paper further explores the modelling of interest rates, as well as the significance of interest rates in bond valuation.

Continuous-time evolutionary stock and bond markets with time-dependent strategies

This paper develops a general continuous-time evolutionary finance model with time-dependent strategies based on evolutionary game theory. We show that the continuous model, which is a limit of a general discrete model, is well-defined and if there exists one completely diversified strategy in the market, then there is no sudden bankruptcy. We study in detail, a deterministic evolutionary bond market and certify that a bond market is evolutionary stable if and only if the total returns across all assets are the same. By this way, we derive an explicit expression for the bond valuation and provide an approach to recover the benchmark interest rate from an effective bond market. Key words: Evolutionary finance, evolutionary bond market, continuous-time model, time-dependent strategies.

Pricing and Valuation Challenges for Mutual Funds

The panel emphasized the importance of transparency across the valuation process. One of the biggest changes after the financial crisis is the regulatory requirements on consistency, transparency, and auditability. Transparency has been frequently discussed in the industry. Transparency is important when pricing vendors provide bond valuation. Information, such as assumptions used and influence of market color, are needed. However, transparency is not only about the valuation but also about the process to derive bond valuations, including the use of both mark-to-market and mark-to-model. Information, such as valuation process, compliance process, and methodology used are all important to clients. It is also critical to use consistent processes across valuations, with complete auditability into the chosen methodology. <b>TOPICS:</b>Mutual fund performance, volatility measures

Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance

The valuation of many financial securities can be formulated as high-dimensional integrals for which quasi-Monte Carlo (QMC) methods are becoming indispensable numerical tools. It is known that some typical high-dimensional problems in finance and in many other fields have a strong additive nature. This paper investigates the enhancement of QMC methods by exploiting the additive approximation in combination with suitable transformation methods. To this end, we study (a) the approximation of a multivariate function by a sum of one-dimensional functions; and (b) the effective use of the possible strong additive property inherent in finance problems to enhance QMC. For problem (a), we establish a relationship between the approximation quality resulting from anchored decomposition and the global sensitivity indices. For problem (b), we propose new methods for efficiency improvement—the additive weighted uniform sampling and the additive control variate, which exactly exploit the strong additive structure. The required importance distribution and control variate are found constructively based on the anchored additive approximation with a suitably chosen anchor. Numerical examples on bond valuation and option pricing illustrate that the proposed methods reduce the variance by huge factors in QMC. Transformation methods play a crucial role, since they may enhance the degree of additivity of a function. Traditional methods, such as Brownian bridge and principal component analysis, do not necessarily work well, whereas methods that take into account the underlying functions are robust and powerful.