[Solutions are presented for prices on interest rate options in a two-factor version of the Cox-Ingersoll-Ross model of the term structure. Specific solutions are developed for caps on floating interest rates and for European options on discount bonds, coupon bonds, coupon bond futures, and Euro-dollar futures. The solutions for the options are expressed as multivariate integrals, and we show how to reduce the calculations to univariate numerical integrations, which can be calculated very quickly. The two-factor model provides more flexibility in fitting observed term structures, and the fixed parameters of the model can be set to capture the variability of the term structure over time.]

This paper provides closed form solutions for futures and European futures options on pure discount bonds under the Ornstein-Uhlenbeck (normal) process. A significant difference between Black's model (1976) and the model in this paper for futures options is discussed.

This paper corrects the bond option formula presented by R. Rabinovitch ((1989), Equation (10)). With just one state variable driving the economy, the formula should be the same as the ones presented by Jamshidian (1989) and Chaplin (1987).

Solutions are presented for prices on interest rate options in a two-factor version of the Cox–Ingersoll–Ross model of the term structure. Specific solutions are developed for caps on floating interest rates and for European options on discount bonds, coupon bonds, coupon bond futures, and Euro-dollar futures. The solutions for the options are expressed as multivariate integrals, and we show how to reduce the calculations to univariate numerical integrations, which can be calculated very quickly. The two-factor model provides more flexibility in fitting observed term structures, and the fixed parameters of the model can be set to capture the variability of the term structure over time.

Chen, Sean Chen, and Harry Sharma. We also benefited from discussions with our colleagues Ivan Brick, Oded Palmon, Emilio Venezian, and John Wald. We are particularly indebted to the anonymous referee and the editor, Paul Malatesta, for their valuable suggestions that greatly improve the paper. All errors are our own.

This paper examines the interaction between default risk and interest-rate risk in determining the term structure of credit default swap spreads at different industry sectors and credit-rating classes. The paper starts with a parsimonious three-factor interest-rate dynamic term structure and projects the credit spread at each industry sector and rating class to these interest-rate factors while also allowing the projection residual dynamics to depend on the level of the interest-rate factors. Estimation shows that credit risk exhibits intricate dynamic interactions with the interest-rate factors.

American options require numerical methods, namely lattice models, to provide accurate price estimates. The computations can become expensive when more than one state variable is involved. Analytical upper bounds can therefore provide a useful guideline for how high American values can reach. In this paper, we derive analytical (closed-form) upper bounds for American option prices under stochastic interest rates, stochastic volatility, and jumps where American option prices are difficult to compute with accuracy. In a stochastic volatility model (Heston (1993) and Scott (1997)) that has two random factors, we demonstrate that the upper bound only takes a very small fraction of the time that the American option needs to compute.

This paper extends the seminal Cox-Ross-Rubinstein ((1979), CRR hereafter) binomial model to multiple assets. It differs from previous models in that it is derived under the complete market environment specified by Duffie and Huang (1985) and He (1990). The complete market assumption requires the number of states to grow linearly with the number of assets. However, the number of correlations grows at a faster rate, causing the CRR model to be indirectly extendable. We solve such a problem by recognizing that the fast growing correlation number is matched by the number of the angles of the edges of a hypercube spanned by the risky assets. As a result, we derive a solution that allows the number of equations to equal the number of risky assets and the riskless bond. The resulting tree structure hence provides the same intuition of pricing and hedging contingent claims as that provided by the CRR model. Finally, the proposed model is not only as easy to implement as the one-dimensional CRR model but also it is more memory efficient than the existing multi-factor lattice models.