Simulation-Based Pricing of Convertible Bonds

Abstract

We propose and empirically investigate 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.

A simple and precise method for pricing convertible bond with credit risk

“…Our empirical evidence does not support a systematic underpricing hypothesis. A similar conclusion is reached by Ammann et al (2008) who use a Monte-Carlo simulation approach. Moreover, market participants almost always calibrate their models to the observed market prices using implied convertible volatilities.…”

“…Similarly, Brennan and Schwartz (1980) conclude that the effect of a stochastic interest rate on convertible bond prices is so small that it can be neglected. Furthermore, Ammann et al (2008) notice that the overall pricing benefit of incorporating stochastic interest rates would be very limited and would not justify the additional computational costs. For these reasons, most practical convertible models in the market do not take stochastic interest rate into account.…”

The pricing of convertible bonds within the Tsiveriotis and Fernandes framework with exogenous credit spread: Empirical analysis

“…Existing research includes the papers of King, 19 Carayannopoulos, 20 Carayannopoulos and Kalimipalli, 21 Buchan, 22 Ammann et al 23,24 and Alex and Chan. 25 A drawback of these studies is in the very limited number of instruments analysed and the short studied history of convertibles: King 19 performs his tests for 103 American convertible bonds for two calendar days, Buchan 22 analyses pricing models for only one day, Carayannopoulus 20 investigates 30 American bonds for 12 days, Ammann et al 23 examine 21 French convertibles for a 1.5-year history (from February 1999 until August 2000).…”

Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

“…Furthermore, Ammann, Kind, and Wilde (2008) notice that the overall pricing benefit of incorporating stochastic interest rates would be very limited and would not justify the additional computational costs. For these reasons, most practical convertible models in the market do not take stochastic interest rate into account.…”