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...

We analyze the specifications of option pricing models based on time- changed Levy processes. We classify option pricing models based on the structure of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process...

Critics regarding the Black and Scholes model aren't new. The model was about of being labelled 'historic'. It is new now that the model has become an auto-nomous, unreflected item in international accounting standards and law allowing "creative" accounting. There is no economial relation...

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...

This paper provides an introduction to Monte Carlo algorithms for pricing American options written on multiple assets, with special emphasis on methods that can be applied in a multi-dimensional setting. Simulated paths can be used to estimate by nonparametric regression the continuation value...

After a brief review of option pricing theory, we introduce various methods proposed for extracting the statistical information implicit in options prices. Among the methods discussed are: lognormal Edgeworth expansions, cumulant expansions, Hermite polynomial expansions, nonparametric kernel...

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...