Pricing and Hedging Mandatory Convertible Bonds

Abstract

This article examines the pricing and hedging of mandatory convertible bonds on the U.S. market using daily market prices for a period of 498 trading days, resulting in a sample of more than 14,600 daily price observations. We explore the pricing and hedging performance based on a simple contingent claims model. On average, the pricing errors are lower than those found for standard convertible bonds. An analysis of the hedging performance of the model indicates that it is useful for hedging as, on average, the hedging errors observed are relatively small and mostly not systematic.Notes: This exhibit provides the basic characteristics of the mandatory convertibles in our sample. Maturity is the due date of the security (dd.mm.yyyy). The annual coupon is the percentage of the par value paid per year. The par value is the lower strike multiplied by the lower ratio or the upper strike price multiplied by the upper ratio. The upper ratio and the lower ratio are the conversion ratios that specify the number of shares the mandatory convertible is converted into depending on the final stock price. The upper and lower strike prices determine the offsetting option spread and the characteristic payoff profile of the mandatory convertibles.Notes: This exhibit provides some characteristics of our sample within the observed time window. The average time to maturity indicates where the securities are within their life cycle. The average four-year historical volatility describes the standard deviation of the continuously compounded returns of the underlying shares. The average dividend yield describes the average dividend divided by current stock price. Moody's median bond spread data give the credit spreads. The moneyness is defined as follows: moneyness ϭ 1 if the current stock price is between the lower and the upper strike prices; moneyness Ͻ1 if the current stock price is below the lower strike price; moneyness Ͼ1 if the current stock price is above the upper strike price. This subsection explores the driving factors for the pricing errors. First, we show a breakdown of the pricing error by moneyness of the option and, second, pricing errors are regressed against the factors that enter the valuation model. Robustness of the Model with Respect to Volatility*Denotes significance level of 1%. Notes: This exhibit shows pricing statistics for different rolling window lengths used for volatility estimation. As can be seen, the estimation window has a very limited impact on pricing errors. Std. dev. denotes the standard deviation of the pricing errors.Note: Assuming a linear dependence (the dashed line represent a linear trend), the pricing error decreases with the moneyness.Standard errors are adjusted for autocorrelation and heteroskedasticity according to Newey and West [1987]. Adj. R 2 denotes the value of the adjusted R 2 (coefficient of determination). In regressions (1) to (6), each regressor is estimated separately. In regressions (7) to (10), we omit the highly correlated regressors. Numbers in parentheses are t-values.

Simulation-based pricing of convertible bonds

“…Ammann and Seiz (2006) show that in the case of mandatory convertible bonds, pricing and hedging in closed-form is rather accurate. However, this is due to the simpler payoff structure of mandatory convertible bonds.…”

Analysis of Convertible Bond Value Based on Integration of Support Vector Machine and Copula Function

“…Tsiveriotis and Fernandes (1998), Duffie and Singleton (1999), and Takahashi et al (2001) expanded simplified structured model by adding default probability and recovery rate. Ammann and Seiz (2006) employed the modified Black-Scholes European option pricing model, and Yigitbasioglu and Alexander (2006) proposed that a nonlinear, multi-factor, reduced-form, equity-linked default model leads to a set of nonlinear partial differential complementarity equations governed by the volatility path. Chambers and Lu (2007) presented a binomial tree model for pricing convertible bonds, different from Das and Sundaram (2006) through differences in the specification of the correlation between interest rates and stock prices, and found that the correlation between the stock price and interest rate levels is especially important in the pricing of CBs of financial institutions.…”

Innovating Risk Management and Hedging Strategy for Convertible Bonds Using Support Vector Machine

“…Hari and Norman (2002) estimated these partial derivatives by regressing changes in CB's value against changes in the factors and simply offered a conceptual approach [3]. Manuel and Ralf (2006) employed the modified BlackScholes European option pricing model to take the delta and found that the hedging errors observed are relatively small and mostly not systematic [4]. Ali and Carol (2006) proposed that a non-linear multi-factor reduced-form equitylinked default model leads to a set of non-linear partial di erential complementarity equations governed by the volatility path.…”