Forward Versus Spot Interest Rate Models Of The Term Structure

Using daily caps and floors market prices throughout the years 1993 and 1994, we address the open question whether spot or forward interest-rate models of the term structure provide a better fit to market prices of options. In particular, we compare the Hull and White (1994), Pelsser (1996) and Black and Karasinski (1991) models with Gaussian, square root and proportional models as developed by Ritchken and Sankarasubramanian (1995). Interestingly, we find that all spot interest-rate models outperform their similar counterparts in the forward rate setting. Furthermore, we test a number of humped volatility models obtained as extensions of the above-mentioned models under both approaches, and due to Mercurio and Moraleda (1996a and 1996b) and Moraleda and Vorst (1996). The fit to market option prices is largely improved (around 30 percent) by all humped volatility models under the spot interest-rate setting. Things are different for forward interest-rate models since we find strictly decreasing volatility structures for all maturities. An exception are forward rate models with deterministic volatility functions, for which humped shapes in the volatility are typically found. The results in this paper are consistent with previous studies, although they partly disagree with results of Bliss and Ritchken (1996).