A closed formula for illiquid corporate bonds and an application to the European market

How to price illiquid corporate bonds when their prices are not available for several days in the marketplace, but other bonds of the same issuer trade frequently? This situation appears to be quite common in the fixed income market: it is rather usual to find issuers that, besides liquid benchmark bonds, issue some other debt instruments that either are placed to a small number of investors in private placements or have a limited issue size. To answer to this question we propose an option approach for pricing bond illiquidity that is reminiscent of the celebrated work of Longstaff (1995) on the non-marketability of some non-dividend-paying shares in IPOs. Our approach models interest rate and credit risks via a convenient reduced-form approach. We deduce a simple closed formula for illiquid corporate coupon bond prices when liquid bonds with similar characteristics (e.g. maturity) are present in the market for the same issuer. The key model parameter is the time-to-liquidate a position, i.e. the time that an experienced bond trader takes to liquidate a given position on a corporate coupon bond. We show that illiquid bonds present an additional liquidity spread that depends on the time-to-liquidate aside from bond volatility. We provide a detailed application for two financial issuers in the European market.