In this talk I am going to introduce a new model for pricing of corporate bonds which is a modification of the classical model of Merton. In Merton's model, a corporate bond is a contingent claim on the assets of a firm. A geometric Brownian motion models the value of the firm's assets which are assumed to be liquidly traded in the market. This assumption makes the pay-off replicable with the firm's assets and the money market account; and a pricing formula is easily obtained. In this new model we drop the liquidity assumption, and instead assume that there is an asset in the market which is correlated with the firm's value, and all portfolios can be constructed using solely this asset and the money market account. We formulate the price of the corporate bond as the price of the optimal replicating portfolio * exp(- k * replication error), where k is a positive constant. The interpretation is that the investor accepts the price of the optimal replicating portfolio as a benchmark, however, 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.
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