An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds

Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior are accommodated within this approach. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects, showing that uncertain volatility can capture the call premia so often observed in issuer’s call policies. Increasingly pessimistic values for the issuer’s substitution asset obtain as we introduce more uncertainty during the notice period. Volatility uncertainty is thus a useful mechanism to explain issuers delayed call policies.call notice period, call premium, convertible bond, delayed calls, equity-linked default, stochastic interest rates, volatility uncertainty

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Convertible Bonds: Risks and Optimal Strategies

Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasi˘cekâmodel is applied to incorporate interest rate risk into the firmâs value process which follows a geometric Brownian motion. Finally, we derive pricing bounds for convertible bonds in an uncertain volatility model, i.e. when the volatility of the firm value process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk

Market Valuation of Convertible Securities of U.S. Airlines

The airlines have enormous needs for capital. Historically, capital spending was accountable for about 15 percent of annual airline revenues, more than double the average for manufacturing companies (Arpey, 1995). Access to capital is essential to the long-term viability and growth of the airline industry especially due to the capital-intensive nature of its business. However, highly cyclical nature of the airline business and its severe dependence on general economic condition make investments in the industry risky and uncertain. The airline\u27s junk bond credit rating and enormous amounts of debt result in extremely high costs of capital. In addition, the airlines find very difficult to raise funds on equity markets since investors are not impressed with poorly performing airline stocks. To satisfy their needs for capital the airlines have turned towards convertible securities. The important feature of convertibles is the relative insensitivity of their value to the risk of the issuing company (Brennan and Schwartz, 1988). This separation is achieved by selecting appropriate convertible contract parameters. Pricing of interest rate derivatives and instruments with embedded options, such as callable convertible bonds and preferred stocks, is typically performed utilizing models of the term structure of interest rates. Ramanlal, Mann, and Moore (1998) test several contingent claims valuation models adapted to callable convertible preferred stocks. Based on their large scale testing, the best performing valuation model produced mean pricing errors of about -0.18%. In this study this model is utilized to assess market valuation of airline convertible preferred stocks. The sample consists of 11 convertible preferred stocks issued by U.S. airlines in 1980 - 1991. For each convertible daily model prices are estimated for two years after issuance and compared with market prices by calculating pricing errors. It turns out that mean pricing error for our sample is 2.63 %, indicating that market undervalues airline convertible preferred stocks by about 2.63 %. In addition, a panel data analysis of pricing errors suggests that market undervaluation in much more severe immediately after issuance and persists for approximately 6 months. The mean pricing error for a subsample containing first six months of daily prices is 8.01 %, while for a sub-sample of convertible daily prices for 7-24 months after issuance the mean pricing error is 0.10 %. There are two potential explanations of observed discrepancy between market and model pricing of airline convertibles shortly after issuance: model mispricing or market undervaluation. Since utilized model was extensively tested and found to be superior in pricing convertible preferred stocks market undervaluation seems to be a plausible explanation. Pricing model cannot capture investor sentiment towards traded securities. Probably, market perception of airlines as higher risk companies, influences prices of newly issued convertibles. However, in about six months of trading, the insensitivity of properly designed convertibles to the risks of issuing companies becomes obvious and the market and theoretical values of convertibles converge. Market undervaluation of airline convertibles at issuance suggests that, probably due to their reputation, airlines cannot efficiently raise capital even with convertibles

Valuation of Convertible Bonds

Convertible bonds are hybrid financial instruments with complex features. They have characteristics of both debts and equities, and usually several options are embedded in this kind of contracts. The optimality of the conversion decision depends on equity price, interest rate and default probability of the issuer. The decision making can be further complicated by the fact that most convertible bonds have call provisions allowing the bond issuer to call back the bond at a predetermined call price. In this thesis, we first adopt a structural approach where the Vasicek-model is applied to incorporate interest rate risk into the firm's value process which follows a geometric Brownian motion. Default is triggered when the firm's value hits a lower boundary. The complex nature of the firm's capital structure and information asymmetry may make it hard to model the firm's value and the capital structure. In this case, reduced-form models are applied for the study of convertible bonds. We adopt a parsimonious, intensity-based default model, in which the default intensity is modeled as a function of the pre-default stock price. We first analyze the contract features of the convertible bonds and show that callable and convertible bonds can be decomposed into a straight bond and a game option component. Then the no-arbitrage prices of the European- and American-style callable and convertible bonds are derived. In American-style contracts, the focus is on the analysis of the strategic optimal behavior. The bondholder and issuer choose their stopping times to maximize or minimize the expected payoff respectively. For the bondholder it is optimal to select the stopping time which maximizes the expected payoff given the minimizing strategy of the issuer, while the issuer will choose the stopping time that minimizes the expected payoff given the maximizing strategy of the bondholder. The no-arbitrage price can be approximated numerically by means of backward induction. In the structural model, the recursion is carried out alongside a recombining binomial tree. Whereas in the reduced-form approach, the optimization problem is formulated and solved with the help of the theory of doubly reflected backward stochastic differential equations. In practice, it is often a difficult problem to calibrate a given model to the available data. Determining the volatility of the firm's value process or stock price process is not a trivial problem. We therefore assume that the volatility of the firm's value process/stock price process lies between two extreme values, and combine it with the results on game option in incomplete market to derive certain pricing bounds for callable and convertible bonds. The maximizing strategy of the bondholder and the choice of the most pessimistic pricing measure from his perspective determine the lower bound of the no-arbitrage price. Whereas the minimizing strategy of the issuer and the most pessimistic expectation from his aspect construct the upper bound of the no-arbitrage price. Numerically, to make the computation tractable a constant interest rate is assumed. The pricing bounds can be calculated with recursion alongside a recombining trinomial tree or with the finite-difference method

Pricing Inflation-Indexed Convertible Bonds with Credit Risk

In Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. The valuation model of inflation-indexed (or equivalently foreign-currency) convertible bonds derived in this paper considers two sources of uncertainty allowing both the underlying stock and the consumer-price-index to be stochastic and incorporates credit risk in the analysis. We approximate the pricing equations by using a Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate the sensitivity of the theoretical values with respect to the characteristics of the issuer, the economic environment and the security’s characteristics (number of principal payments). Moreover, we demonstrate the usefulness and the limitations of the pricing model by using inflation-indexed and foreign-currency linked convertibles traded on the Tel- Aviv stock exchange

Pricing inflation-indexed convertible bonds with credit

Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. The valuation model of inflation-indexed (or equivalently foreign-currency) convertible bonds derived in this paper considers two sources of uncertainty allowing both the underlying stock and the consumer-price-index to be stochastic and incorporates credit risk in the analysis. We approximate the pricing equations by using a Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate the sensitivity of the theoretical values with respect to the characteristics of the issuer, the economic environment and the security’s characteristics (number of principal payments). Moreover, we demonstrate the usefulness and the limitations of the pricing model by using inflation-indexed and foreign currency linked convertibles traded on the Tel- Aviv stock exchange

Aspects and Dynamics of Contingent Convertible Bonds. Pricing Norwegian CoCo Issuances With Equity Derivative Approach

Contingent convertible bonds have emerged as a going-concern loss-absorbing instrument in response to the last financial crisis. These hybrids, commenced by the new Basel III regulation, might be able to substitute the prevailing subordinated debt instruments that failed to effectively absorb losses during the last crisis. Issuing CoCos present an effective way to provide automatic recapitalizing for banks in times with financial distress, by forcing conversion to shares or automatic write-down when certain triggers are breached. Consequently, the instrument enhances robustness of the banking sector if constructed properly. This thesis presents the structure and promising pricing methods of CoCos with Core Equity Tier 1 trigger, in which equity derivatives pricing method is found to be the most suitable. As the dynamics and structure of the instrument are complex, finding the appropriate trigger is not straightforward. Most of the existing models, including equity derivatives, imply high co-movement between Core Equity Tier 1 and stock prices in order to find the trigger level. However, as the historical correlation prove to be insignificant, there is need for new research in this field. This thesis develop an modest attempt at finding the stock price trigger level based on an analytical approach using scenario CAPM β values. To test the analytical method in an equity derivatives approach, CoCo issuances by DNB in 2015 and 2016 are examined. The data is retrieved from TITLON financial database and company filings, whereas simple data handling is performed in Microsoft Excel. All computations are done in the statistical programming software R. The codes are available upon request. According to the best estimate, the price of both DNB CoCos are undervalued. As underpricing is apparent, the thesis points to several factors that may explain the discrepancy between theoretical and observed prices. These consists mainly of (1) mispricing caused by the model, and (2) mispricing due to market participants’ perception of CoCos dynamics. Keywords: Contingent convertible bonds, Basel III, capital structure, regulatory capital, equity derivative

Convertible bond underpricing in the french market : an empirical study

The pricing of convertible bonds is a fairly unstudied field of asset pricing due to the instruments’ complex nature and its niche character. The aim of this dissertation is to compute model implied prices for convertible bonds and compare it to their market value in order to determine whether the market truly underprices convertible bonds, a financial theory that has been discussed broadly in the academic community. As a pricing model I applied a Monte Carlo simulation for stock prices and determined the optimal exercise strategy through the Least-Squares method. With this methodology I priced 34 convertible bonds in the French market and obtained an average underpricing of 4.17%, which reduces to 2.72% when excluding outliers. The results align with previous conducted studies of the French market but are in contrast with some other empirical results in the United States, but due to the substantial difference in convertible bond markets worldwide a direct comparison is not appropriate. Although the finding supports the general claim of convertible bond underpricing and encourages investors to engage in hedging strategies, the lack of substantial research in the European market calls for further empirical studies and improvements of the work presented.A valorização de obrigações convertíveis é um campo muito pouco estudado da valorização de ativos devido à complexidade dos instrumentos e ao seu carácter de nicho. O objetivo desta dissertação é calcular os preços implícitos de obrigações convertíveis e compará-los com o seu valor de mercado a fim de determinar se o seu mercado está realmente subvalorizado, um fenómeno frequentemente descrito por outros autores. Como modelo de preços, apliquei uma simulação Monte-Carlo para os preços das ações e determinei a estratégia ótima de exercício através do método de Least-Squares. Com esta metodologia, fixei o preço de 34 obrigações convertíveis no mercado francês e obtive uma subvalorização média de 4,17%, que reduz para 2,72% ao excluir os outliers. Os resultados estão em linha com estudos anteriores realizados no mercado francês, mas contrastam com outros resultados empíricos nos Estados Unidos; no entanto, devido à diferença substancial nos mercados de obrigações convertíveis em todo o mundo, uma comparação direta não é apropriada. Embora a conclusão apoie a alegação geral de subvalorização de obrigações convertíveis e encoraje os investidores a adotar estratégias de cobertura, a falta de investigação substancial no mercado europeu requer mais estudos empíricos e melhorias do trabalho apresentado

Methods of pricing convertible bonds

Includes abstract.Includes bibliographical references (leaves 112-115).The aim of this dissertation was to build a basic understanding of hybrid securities with a focus on convertible bonds. We look at various methods to price these complex instruments and learn of the many subtleties they exhibit when traded in the market