In the context of arbitrage-free modelling of financial derivatives, we introduce a novel calibration technique for models in the affine- quadratic class for the purpose of contingent claims pricing and risk- management. In particular, we aim at calibrating a stochastic volatility jump diffusion...

For option whose striking price equals the forward price of the underlying asset, the Black-Scholes pricing formula can be approximated in closed-form. A interesting result is that the derived equation is not only very simple in structure but also that it can be immediately inverted to obtain an...

The security dynamics described by the Black-Scholes equation with price-dependent variance can be approximated as a damped discrete-time hopping process on a recombining binomial tree. In a previous working paper, such a nonuniform tree was explicitly constructed in terms of the continuous-time...

Interest-rate derivative models governed by parabolic partial differential equations (PDEs) are studied with discrete-time recombining binomial trees. For the Buehler-Kaesler discount-bond model, the expiration value of the bond is a limit point of tree sites. Representative calculations give a...

A valuation model is presented for options on stocks for which Black- Scholes arbitrage does not entirely eliminate risk. The price dynamics of a portfolio of options and the underlying security is quantified by requiring that the excess reward-to-risk ratio of the portfolio be identical to that...

We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts...

We develop a simple robust test for the presence of continuous and discontinuous (jump) com­ponents in the price of an asset underlying an option. Our test examines the prices of at­the­money and out­of­the­money options as the option maturity approaches zero. We show that these prices...

We derive discrete markov chain approximations for continuous state equilibrium term structure models. The states and transition probabilities of the markov chain are chosen effciently according to a quadrature rule as in Tauchen and Hussey (1991). Quadrature provides a simple yet method which...

As is well known, the classic Black­Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non­normal return innovations. Second,...

A generalized Black-Scholes formula is presented for the case when the volatility part of the percentage changes in a stock price obeys a mean reverting Ornstein-Uhlenbeck process. When the parameter of the Ornstein-Uhlenbeck process converges to zero the generalized formula converges to the...