B-spline techniques for volatility modeling

This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines obtained by including basis functions with infinite support. We first come back to the application of shape-constrained B-splines to the estimation of conditional expectations, not merely from a scatter plot but also from the given marginal distributions. An application is the Monte Carlo calibration of stochastic local volatility models by Markov projection. Then we present a new technique for the calibration of an implied volatility surface to sparse option data. We use a B-spline parameterization of the Radon-Nikodym derivative of the underlying's risk-neutral probability density with respect to a roughly calibrated base model. We show that this method provides smooth arbitrage-free implied volatility surfaces. Finally, we sketch a Galerkin method with B-spline finite elements to the solution of the partial differential equation satisfied by the Radon-Nikodym derivative.Comment: 25 page

Dynamic Semiparametric Factor Models in Risk Neutral Density Estimation

Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most prominent dimension reduction technique - functional principal components analysis - however, does not model time dependences embedded in functional data. In this paper we use dynamic semiparametric factor models (DSFM) to reduce dimensionality and analyse the dynamic structure of unknown random functions by means of inference based on their lower dimensional representation. We apply DSFM to estimate the dynamic structure of risk neutral densities implied by prices of option on the DAX stock index.dynamic factor models, dimension reduction, risk neutral density

Empirical Pricing Kernels and Investor Preferences

This paper analyzes empirical market utility functions and pricing kernels derived from the DAX and DAX option data for three market regimes. A consistent parametric framework of stochastic volatility is used. All empirical market utility functions show a region of risk proclivity that is reproduced by adopting the hypothesis of heterogeneous individual investors whose utility functions have a switching point between bullish and bearish attitudes. The inverse problem of finding the distribution of individual switching points is formulated in the space of stock returns by discretization as a quadratic optimization problem. The resulting distributions vary over time and correspond to different market regimes.Utility function, Pricing Kernel, Behavioral Finance, Risk Aversion, Risk Proclivity, Heston model.

Pricing and Inference with Mixtures of Conditionally Normal Processes.

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.Derivative Pricing ; Stochastic Discount Factor ; Implied Volatility, Mixture of Normal Distributions ; Mixture of Conditionally Normal Processes ; Nonparametric Kernel Estimation ; Mixed-Normal GARCH Processes ; Switching Regime Models.

Effect of baseline meteorological data selection on hydrological modelling of climate change scenarios

This study evaluates how differences in hydrological model parameterisation resulting from the choice of gridded global precipitation data sets and reference evapotranspiration (ETo) equations affects simulated climate change impacts, using the north western Himalayan Beas river catchment as a case study. Six combinations of baseline precipitation data (the Tropical Rainfall Measuring Mission (TRMM) and the Asian Precipitation – Highly Resolved Observational Data Integration Towards Evaluation of Water Resources (APHRODITE)) and Reference Evapotranspiration equations of differing complexity and data requirements (Penman-Monteith, Hargreaves –Samani and Priestley – Taylor) were used in the calibration of the HySim model. Although the six validated hydrological models had similar historical model performance (Nash–Sutcliffe model efficiency coefficient (NSE) from 0.64-0.70), impact response surfaces derived using a scenario neutral approach demonstrated significant deviations in the models’ responses to changes in future annual precipitation and temperature. For example, the change in Q10 varies between -6.5 % to -11.5% in the driest and coolest climate change simulation and +79% to +118% in the wettest and hottest climate change simulation among the six models. The results demonstrate that the baseline meteorological data choices made in model construction significantly condition the magnitude of simulated hydrological impacts of climate change, with important implications for impact study design.NER

Monetary policy analysis with potentially misspecified models

This paper proposes a novel method for conducting policy analysis with potentially misspecified dynamic stochastic general equilibrium (DSGE) models and applies it to a New Keynesian DSGE model along the lines of Christiano, Eichenbaum, and Evans (JPE 2005 and Smets and Wouters (JEEA 2003). Specifically, we are studying the effects of coefficient changes in interest-rate feedback rules on the volatility of output growth, inflation, and nominal rates. The paper illustrates the sensitivity of the results to assumptions on the policy invariance of model misspecifications. JEL Classification: C32Bayesian Analysis, DSGE Models, Model Misspecification