Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach

Simple analytical pricing formulae have been derived, by different authors and for several derivatives, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulas under the most general stochastic volatility specification of the Duffie and Kan (1996) model. Using Gaussian Arrow-Debreu state prices, first order stochastic volatility approximate pricing solutions will be derived only involving one integral with respect to the time-to-maturity of the contingent claim under valuation. Such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate.     

The Dynamics of the S&P 500 Implied Volatility Surface

This empirical study is motivated by the literature on “smile-consistent” arbitrage pricing with stochastic volatility. We investigate the number and shape of shocks that move implied volatility smiles and surfaces by applying Principal Components Analysis. Two components are identified under a variety of criteria. Subsequently, we develop a “Procrustes” type rotation in order to interpret the retained components. The results have implications for both option pricing and hedging and for the economics of option pricing. This revised version was published online in June 2006 with corrections to the Cover Date.     

New mobility service users' perceptions on electric vehicle adoption

The recent growth of new mobility services such as car-sharing (ZipCar, Car2Go) and ride-hailing (Uber, Lyft) has interesting implications for new vehicle technologies. We explore the users of the services and their relation to electric vehicles preferences by analyzing two large-scale mobility service surveys. A number of categories (car-share usage, ride-hail usage, commute mode, demographics, current vehicle attributes, environmental attitudes, technology attitudes, and life-stage information) are examined in order to determine the likelihood a respondent considers purchasing an electric vehicle in the future. Survey respondents explicitly expressed that exposure to ride-hailing did not increase their propensity for wanting to purchase an electric vehicle in the future. However, we run a full suite of cross-validation models and find that in addition to the typical factors used in modeling preferences, the use of new mobility services statistically increases the predictive power of our model to identify preferences for electric vehicles.     

A note on the efficiency of the binomial option pricing model

We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.