A Consistent Stochastic Model of the Term Structure of Interest Rates
for Multiple Tenors
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abstract
Explicitly taking into account the risk incurred when borrowing at a shorter
tenor versus lending at a longer tenor ("roll-over risk"), we construct a
stochastic model framework for the term structure of interest rates in which a
frequency basis (i.e. a spread applied to one leg of a swap to exchange one
floating interest rate for another of a different tenor in the same currency)
arises endogenously. This rollover risk consists of two components, a credit
risk component due to the possibility of being downgraded and thus facing a
higher credit spread when attempting to roll over short-term borrowing, and a
component reflecting the (systemic) possibility of being unable to roll over
short-term borrowing at the reference rate (e.g., LIBOR) due to an absence of
liquidity in the market. The modelling framework is of "reduced form" in the
sense that (similar to the credit risk literature) the source of credit risk is
not modelled (nor is the source of liquidity risk). However, the framework has
more structure than the literature seeking to simply model a different term
structure of interest rates for each tenor frequency, since relationships
between rates for all tenor frequencies are established based on the modelled
roll-over risk. We proceed to consider a specific case within this framework,
where the dynamics of interest rate and roll-over risk are driven by a
multifactor Cox/Ingersoll/Ross-type process, show how such model can be
calibrated to market data, and used for relative pricing of interest rate
derivatives, including bespoke tenor frequencies not liquidly traded in the
market.
