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

The Valuation of Inflation-Indexed and FX Convertible Bonds

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. In this paper we extend the convertible pricing models of Tsiveriotis and Fernandes (1998) and McConnell and Schwartz (1986) to the case of indexation of the promised payments of the convertible to a general price index or to the price of foreign exchange. The theoretical framework derived in this paper considers two sources of uncertainty: both the underlying stock price and the consumer-price-index (or equivalently foreign-currency) are stochastic, and incorporate credit risk in the analysis. The extensions of two models enable to establish upper and lower bounds for the price of the indexed convertible. We approximate the pricing equations by using Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate and compare the models with respect to the characteristics of the issuer, the economic environment and the security’s characteristics. Moreover, we demonstrate the usefulnes and the limitations of the pricing model by using convertible traded on the Tel- Aviv stock exchange.Convertible Bonds, Credit Spread, Pricing, Inflation, Foreign- Exchange

An empirical comparison of convertible bond valuation models

This paper empirically compares three convertible bond valuation models. We use an innovative approach where all model parameters are estimated by the Marquardt algorithm using a subsample of convertible bond prices. The model parameters are then used for out-of-sample forecasts of convertible bond prices. The mean absolute deviation is 1.86% for the Ayache-Forsyth-Vetzal model, 1.94% for the Tsiveriotis-Fernandes model, and 3.73% for the Brennan-Schwartz model. For this and other measures of fit, the Ayache-Forsyth-Vetzal and Tsiveriotis-Fernandes models outperform the Brennan-Schwartz model

Pricing Convertible Bonds with Interest Rate, Equity, Credit and FX Risk

Convertible bonds are hybrid securities whose pricing relies on a set of complex inter-dependencies due to the sensitivity to interest rate risk, underlying (equity) risk, FX risk, and credit risk, and due to the convertible bond’s early exercise American feature. We present a two factor model of interest rate and equity risk that is implemented using the Crank-Nicholson technique on the discretized pricing equation with projective successive over-relaxation. This paper extends a methodology proposed in the literature (TF[98]) to deal with credit risk in a self- consistent way, and proposes a new methodology to deal with FX sensitive cross-currency convertibles. A technique for extracting the price of vanilla options struck on a synthetic asset, the foreign equity in domestic currency, is employed to obtain the implied volatility for these options. These implied volatilities are then used to obtain the local volatility for use in the numerical routine. The model is designed to deal with most of the usual contractual features such as coupons, dividends, continuous and/or Bermudan call and put clauses. We suggest that credit spread adjustments in the boundary conditions can be made, to account for the negative correlation between spreads and equity. Detailed description of the numerical methods and the discretization schemes, together with their accuracy, are provided.cross-currency convertibles, credit spread, interest rate risk, American feature, local volatility, Crank-Nicholson.

Simulation-Based Pricing of Convertible Bonds

We propose and empirically study a pricing model for convertible bonds based on Monte Carlo simulation. The method uses parametric representations of the early exercise decisions and consists of two stages. Pricing convertible bonds with the proposed Monte Carlo approach allows us to better capture both the dynamics of the underlying state variables and the rich set of real-world convertible bond specifications. Furthermore, using the simulation model proposed, we present an empirical pricing study of the US market, using 32 convertible bonds and 69 months of daily market prices. Our results do not confirm the evidence of previous studies that market prices of convertible bonds are on average lower than prices generated by a theoretical model. Similarly, our study is not supportive of a strong positive relationship between moneyness and mean pricing error, as argued in the literature.Convertible bonds, Pricing, American Options, Monte Carlo simulation

Convertible Bonds: Default Risk and Uncertain Volatility

Within a default intensity approach we discuss the optimal exercise of the callable and convertible bonds. Pricing bounds for convertible bonds are derived in an uncertain volatility model, i.e. when the volatility of the stock price process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk

Pricing Convertible Bonds with Interest Rate, Equity, Credit and FX Risk

Convertible bonds are hybrid securities whose pricing relies on a set of complex inter-dependencies due to the sensitivity to interest rate risk, underlying (equity) risk, FX risk, and credit risk, and due to the convertible bond’s early exercise American feature. We present a two factor model of interest rate and equity risk that is implemented using the Crank-Nicholson technique on the discretized pricing equation with projective successive over-relaxation. This paper extends a methodology proposed in the literature (TF[98]) to deal with credit risk in a self-consistent way, and proposes a new methodology to deal with FX sensitive cross-currency convertibles. A technique for extracting the price of vanilla options struck on a synthetic asset, the foreign equity in domestic currency, is employed to obtain the implied volatility for these options. These implied volatilities are then used to obtain the local volatility for use in the numerical routine. The model is designed to deal with most of the usual contractual features such as coupons, dividends, continuous and/or Bermudan call and put clauses. We suggest that credit spread adjustments in the boundary conditions can be made, to account for the negative correlation between spreads and equity. Detailed description of the numerical methods and the discretization schemes, together with their accuracy, are provided. cross-currency convertibles, credit spread, interest rate risk. American feature, local volatility, Crank-Nicholson

The Convertible Arbitrage Strategy Analyzed

This paper analyzes convertible bond arbitrage on the Canadian market for the period 1998 to 2004.Convertible bond arbitrage is the combination of a long position in convertible bonds and a short position in the underlying stocks. Convertible arbitrage has been one of the most successful strategies of hedge funds.This paper shows that the convertible arbitrage strategy has considerable effects on capital markets.First, there is a downward pressure on cumulative average abnormal returns of the underlying stocks between the announcement and the issuance dates of convertible bonds.Second, short sales of the underlying equity around the issuance dates strongly increase for equity-like convertibles. Third, convertible bonds are underpriced at the issuance dates.All effects are stronger for equity-like than for debt-like convertible bonds.Finally, we find that over a one-year period following the issue, equity-like convertibles earn a return that is more than 23 percentage points higher than the return of debt-like convertibles.In the last years of our sample, convertible arbitrage returns have strongly decreased.This seems to be related to a shift from equity-like to debt-like convertibles by the issuing companies.convertible arbitrage;short sales;underpricing;convertible bonds;abnormal returns

Fixed-income instrument pricing.

In this article we discuss the fundamentals of pricing of the popular financial instruments. The basic point of our approach is to extend the present value benchmark concept. The present value valuation approach plays the similar role as The Newton Laws in the Classic Mechanics. Thus our primary goal is to present a new outlook on valuation of the debt securities and its derivatives. We also, demonstrate why the present value is not a complete method of pricing either securities or derivatives. Then, as illustration we present a valuation of the floating rate, callable and convertible bonds. Next we discuss major drawbacks of the risk neutral interpretation of the derivatives pricing. At the end of the article we discuss interest rate swap and derivative valuation of some classes of the fixed income securities.Bond; coupon bond; present value; floating rate bond; convertible; callable bond; interest rate swap; options valuation; risk neutral probabilities; interest rate derivatives