A variation of Merton's corporate bond valuation model for firms with illiquid but observable assets

Abstract

We introduce a new model for pricing corporate bonds, which is a modification of the classical model of Merton. In this new model, we drop the liquidity assumption of the firm's asset value process, and assume that there is a liquidly tradeable asset in the market whose value is correlated with the firm's asset value, and all portfolios can be constructed using solely this asset and the money market account. We formulate the market price of the corporate bond as the product of the price of an optimal replicating portfolio and $\exp (-\kappa \times \text{replication error})$, where κ is a non-negative constant. The interpretation is that the representative investor uses the price of the optimal replicating portfolio as a benchmark and requests compensation for the non-hedgeable risk. We show that if the replication error is measured relative to the firm's value, the resulting formula is arbitrage free with mild restrictions on the parameters.

Keywords:

• Credit risk
• Merton's model
• Illiquidity
• Mean variance hedging
• Stochastic control

2000 Mathematics Subject Classifications:

• 60G55
• 60G60

Acknowledgements

We express our gratitude to several anonymous referees who read past versions of this manuscript and provided extensive suggestions and corrections.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Sezer is supported by a discovery grant from the Natural Sciences and Engineering Research Council of Canada.