Abstract.A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitragefree model with such volatility specification. The construction is explicit for the lognormal LIBOR and swap "market models", the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and swap derivatives are discussed and appropriate practical models suggested for each.

This paper derives a closed-form solution for European options on pure discount bonds, assuming a mean-reverting Gaussian interest rate model as in Vasicek [8]. The formula is extended to European options on discount bond portfolios.

This paper develops the quadratic interest-rate model of Beaglehole and Tenney in detail. For the quadratic model as well as the multifactor Cox-Ingersoll-Ross square-root model, explicit pricing formulae in terms of one-dimensional integrals of elementary functions are given for bond options, bond exchange options, caps, options on bond futures and forward contracts, and futures delivery options. For the quadratic model, certain forward and transport equations are found that explicitly determine the dynamics of the term structure in terms of initial yield and volatility curves. These option-pricing formulae are thus determined in term of the initial curves. Some shortcomings of the model are identified. New formulae for some distributions and their truncated moments are also derived.principal value integral, noncentral chi-squared distribution, forward risk adjustment, forward and transport equations, yield curve calibration,

This paper derives a closed‐form solution for European options on pure discount bonds, assuming a mean‐reverting Gaussian interest rate model as in Vasicek [8]. The formula is extended to European options on discount bond portfolios.

This paper presents a new simulation methodology for quantitative risk analysis of large multi-currency portfolios. The model discretizes the multivariate distribution of market variables into a limited number of scenarios. This results in a high degree of computational e ciency when there are many sources of risk and numerical accuracy dictates a large Monte Carlo sample. Both market and credit risk are incorporated. The model has broad applications in ÿnancial risk management, including value at risk. Numerical examples are provided to illustrate some of its practical applications.