Stefano Galluccio

The Co-Initial Swap Market Model

In this paper, we introduce a novel approach to the pricing and the risk management of generic European style interest-rate derivatives. This new model has great flexibility and has the advantage of avoiding complex model calibration techniques typical of standard short-rate models. Dynamics is assigned on a set of co-initial forward swap rates, and arbitrage-free restrictions are determined in a normal and lognormal setup. Model implementation and calibration are discussed, and details of two example applications are also presented.

A new measure of cross-sectional risk and its empirical implications for portfolio risk management

Litterman, Scheinkman, and Weiss (1991) and Engle and Ng (1993) provide empirical evidence of a relation between yield curve shape and volatility. This study offers theoretical support for that finding in the general context of cross-sectional time series. We introduce a new risk measure quantifying the link between cross-sectional shape and market risk. A simple econometric procedure allows us to represent the risk experienced by cross-sections over a time period in terms of independent factors reproducing possible cross-sectional deformations. We compare our risk measure to the traditional cross-yield covariance according to their relative performance. Empirical investigation in the US interest rate market shows that 1) cross-shape risk factors outperform cross-yield risk factors (i.e., yield curve level, slope, and convexity) in explaining the market risk of yield curve dynamics; 2) hedging multiple liabilities against cross-shape risk delivers superior trading strategies compared to those stemming from cross-yield risk management.

Valuing American Options Using Fast Recursive Projections

We introduce a fast and widely applicable numerical pricing method that uses recursive projections. We characterize its convergence speed. We find that the early exercise boundary of an American call option on a discrete dividend paying stock is higher under the Merton and Heston models than under the Black-Scholes model, as opposed to the continuous dividend case. A large database of call options on stocks with quarterly dividends shows that adding stochastic volatility and jumps to the Black-Scholes benchmark reduces the amount foregone by call holders failing to optimally exercise by 25%. Transaction fees cannot fully explain the suboptimal behavior.

Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps

Appendice A provides the proof of Propositions 1 of the main paper. In Appendix B, we provide the analytic form of êj(y). In Appendix C, we characterize the space translation invariance property of the transition matrices and we describe how we take advantage of this property in the implementation of the algorithm. Appendix D compares the recursive projections method with recent numerical technique which can accommodate discrete dividends, assuming a Black-Scholes dynamics for the underlying security. These methods are the binomial tree and its improved version provided by Vellekoop and Nieuwenhuis (2006), and the simulation least square approach method of Longsta and Schwartz (2001). We also discuss the new duality approach method of Haugh and Kogan (2004), Rogers (2002), and Andersen and Broadie (2004). Appendix E gives a detailed description of the data and the of calibration procedure, as well as the results of the calibration with a breakdown per stock. Appendix F provides further evidence on the importance of a correct modelling of the dividend as a discrete cash ow when computing the early exercise boundary. In Appendix G we describe the relative advantages of recursive projections and ADI schemes in solving di erent pricing problems.

Early exercise decision in American options with dividends, stochastic volatility and jumps

Using a fast numerical technique, we investigate a large database of investor suboptimal nonexercise of short maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modelling of the discrete dividend is essential for a correct calculation of the early exercise boundary as confirmed by theoretical insights. Pricing with stochastic volatility and jumps instead of the Black-Scholes-Merton benchmark cuts by a quarter the amount lost by investors through suboptimal exercise. The remaining three quarters are largely unexplained by transaction fees and may be interpreted as an opportunity cost for the investors to monitor optimal exercise.

Dynamic Mis-Specification in Local-Stochastic Volatility Models

In the context of interest rate derivatives, we present two simple cases of replication error associated with common hedging strategies when agents have partial information about the real dynamics of the underlying asset. In particular, we derive an explicit expression for the hedging error due to model mis-specification in the following cases, i) the trader delta-hedges his option position in the Black and Scholes framework with stochastic implied volatilities, and ii) the trader uses a given local-stochastic volatility model to delta and vega hedge his/her option exposure but the real dynamics of the underlying follow a different local-stochastic volatility process.

On Model Selection and its Impact on the Hedging of Financial Derivatives

We consider the problem of model misspecification in hedging contingent claims written on assets whose prices follow generic stochastic volatility processes. We determine a generic formula for the total hedging error and perform numerical tests to quantitatively estimate the error in practical situations. We find that errors due to a bad representation of the actual dynamics are in general larger than those stemming from just a bad estimation of the actual model parameters. In particular, we examine the case of a trader that wrongly believes that asset and volatility are not correlated, and show that hedging errors can be non-negligible even for vanilla European options.