Title: A closed formula for illiquid corporate bonds and an application to the European market,
Abstract: 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.
The option approach we propose for pricing bonds' illiquidity is reminiscent
of the celebrated work of Longstaff (1995) on the non-marketability of some
non-dividend-paying shares in IPOs. This approach describes a quite common
situation in the fixed income market: it is rather usual to find issuers that,
besides liquid benchmark bonds, issue some other bonds that either are placed
to a small number of investors in private placements or have a limited issue
size.
The model considers interest rate and credit spread term structures and their
dynamics. We show that illiquid bonds present an additional liquidity spread
that depends on the time-to-liquidate aside from credit and interest rate
parameters. We provide a detailed application for two issuers in the European
market.