This paper develops a reduced form model of interest rate swap spreads. The model accommodates both the default risk inherent in swap contracts and the liquidity difference between the swap and Treasury markets. We use an extended Kalman filter approach to estimate the model parameters. The model fits the swap rates well. We then solve for the implied general collateral repo rates and use them to decompose the swap spreads into their default risk and liquidity components. This exercise shows that the default risk and liquidity components of swap spreads behave very differently: although default risk accounts for the largest share of the levels of swap spreads, the liquidity component is much more volatile. In addition, while the default risk component has been historically positive, the liquidity component was negative for much of the 1990s and has become positive since the financial market turmoils in 1998.

We examine the preference free pricing of options on assets following a GARCH process. We address market incompleteness by a stochastic dominance argument, which provides two bounds that nest all equilibrium option prices. We also consider the limit behavior of the bounds if trading becomes denser, tending to continuous time.

This paper proposes a reduced form discrete-time approach for pricing defaultable bonds incorporating stochastic risk free interest rates, default intensities and recovery rates. The model provides new insights about the term structure of defaultable bonds when the recovery rate is stochastic. We provide pricing formulas for risky bonds in the case of an economy with an affine state vector for three standard recovery assumptions: recovery of Treasury, recovery of face value and recovery of market value. Under the assumptions of recovery of Treasury and recovery of face value, we derive closed form expressions using the Laplace transform of the state vector. Under the assumption of recovery of market value, it is not possible to price risky bonds analytically but our approach allows for disentangling variations in recovery rates and hazard rates, unlike existing methods. The affine specification enables the model to accommodate a flexible correlation structure provided that the Laplace transform is known analytically. As an illustration, we discuss two specific econometric formulations for the state variables: the Gaussian AR(1) model and the Gamma Markov process, and we provide a numerical example.

The electricity market, which used to be tightly regulated and limited to few market players, has undergone structural changes during the last decade. In the newly organized power markets, the electricity contracts are both traded physically and financially. In contrast to other energy commodity markets, the power markets are unique by the fact they are subject to many constraints in the production and transmission capacities besides the fact that the electricity is a non storable commodity. Therefore, the electricty prices exhibits some particular patterns i.e. seasonality, high volatility and frequent spikes. A log-normal mean-reverting jump-diffusion model is proposed in this paper to describe the stochastic process followed by the electricity prices. We derive closed form solution to price derivative securities (i.e. European options and forward contracts). We consider the pricing of electricity swing options which are generally embedded in base load contracts. With this type of options, the power usage is allowed to shuffle between some lower and upper boudaries. In general, the holder of a swing option seeks to hedge the electricity price risk and also to some extent the risk in the load pattern. The swing option price is modeled through a stochastic dynamic programming and we propose an extension to Longstaff and Scwartz (2002) for solving the problem.