This paper discusses pricing methods, comments on matters of concern in market risk management, and analyzes market characteristics of convertible bonds.
Valuation of the conversion option is essential in analyzing the market price of a convertible bond. In this paper, we use a binomial tree pricing model to derive the implied volatility of the conversion option from the past price information (time-series data for individual issues) in the Japanese market. We then use this implied volatility data: (1) to employ a Monte Carlo simulation to measure market risk for a test portfolio of convertible bonds and analyze the factors in price fluctuation; and (2) to perform regression analyses that empirically verify the characteristics of the convertible bond market in Japan.
The implication for market risk management is to underscore the need to be aware of market price fluctuation caused by implied volatility fluctuation. We found that in markets such as Japan is experiencing at the present time, in which most issues have little linkage to share price movements, there is a particular need to be aware of implied volatility in risk management. Moreover, our analysis of market characteristics found that (1) there is a significant negative correlation between implied volatility and underlying equity price fluctuation; (2) implied volatility tends to move in such a way as to reduce divergence from the historical volatility of the underlying equity price; and (3) the use of convertible bonds to raise funds during the "bubble" period in Japan was not necessarily an advantageous form of financing for the issuers.
Keywords: Convertible bond; Implied volatility; Historical volatility; Market risk; Arbitrage; Issuing conditions
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.