Forward vs Spot Interest-Rate Models of the Term Structure: An Empirical Comparison

Posted: 9 Jan 1997

See all articles by Juan M. Moraleda

Juan M. Moraleda

Tinbergen Institute

Antoon Pelsser

Maastricht University; Netspar

Date Written: November 15, 1996


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).

JEL Classification: G13, E43

Suggested Citation

Moraleda, Juan M. and Pelsser, Antoon A. J., Forward vs Spot Interest-Rate Models of the Term Structure: An Empirical Comparison (November 15, 1996). Available at SSRN:

Juan M. Moraleda (Contact Author)

Tinbergen Institute

Burg. Oudlaan 50
Rotterdam, 3062 PA

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD

HOME PAGE: http://

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics