We evaluate a two-factor Cox et al. (1985a,b) model using Euribor zero-coupon yields. We estimate this model using a state-space framework, where we sum a log-likelihood function of the state vector dynamics to a log-likelihood function of cross-section pricing errors. We introduce a likelihood-scaling weight in the joint log-likelihood function and show that there is a tradeoff in how one estimates a yield curve. Giving more weight to the cross-section of pricing errors improves the fitting and forecasting of Euribor yields, while giving more weight to the log-likelihood function of the state vector dynamics improves interest rate derivative pricing at the expense of the first. The common practice of giving the same weight to both measures serves neither purpose and helps to explain why the literature has so far found that the Cox et al. (1985a,b) model prices interest rate derivatives poorly. Our cap pricing exercise is able to price cap volatilities within the bid-ask spread bounds albeit at the cost of worsening the cross-section fit of the yield curve.
- Yield Curve,
- Term Structure,
- Affine Model,
- Interest Rate Derivatives,
Available at: http://works.bepress.com/lp_fichtner/1/