63 research outputs found
Shape invariant modelling pricing kernels and risk aversion
No full textPricing kernels play a major role in quantifying risk aversion and investors' preferences. Several empirical studies reported that pricing kernels exhibit a common pattern across dierent markets. Mostly visual inspection and occasionally numerically summarise are used to make comparison. With increasing amount of information updated every day, the empirical pricing kernels can be viewed as an object evolving over time. We propose a systematic modelling approach to describing the evolution of the empirical pricing kernels. The approach is based on shape invariant models. It captures the common features contained in the shape of the functions and at the same time characterises the variability between the pricing kernels based on a few interpretable parameters. The method is demonstrated with the European options and returns values of DAX index.pricing kernels, risk aversion, risk neutral density
Nonparametric Estimation of Risk-Neutral Densities
No full textThis chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a kernel smoother of the second derivative of call prices, while the second procedure applies kernel type smoothing in the implied volatility domain. In the conceptually different third approach we assume the existence of a stochastic discount factor (pricing kernel) which establishes the risk neutral density conditional on the physical measure of the underlying asset. Via direct series type estimation of the pricing kernel we can derive an estimate of the risk neutral density by solving a constrained optimization problem. The methods are compared using European call option prices. The focus of the presentation is on practical aspects such as appropriate choice of smoothing parameters in order to facilitate the application of the techniques.Risk neutral density, Pricing kernel, Kernel smoothing, Local polynomials, Series methods
Estimation of the signal subspace without estimation of the inverse covariance matrix
No full textLet a high-dimensional random vector X can be represented as a sum of two components - a signal S, which belongs to some low-dimensional subspace S, and a noise component N. This paper presents a new approach for estimating the subspace S based on the ideas of the Non-Gaussian Component Analysis. Our approach avoids the technical difficulties that usually exist in similar methods - it doesn’t require neither the estimation of the inverse covariance matrix of X nor the estimation of the covariance matrix of N.dimension reduction, non-Gaussian components, NGCA
Models for Heavy-tailed Asset Returns
No full textMany of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black- Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation
Liquidity and Capital Requirements and the Probability of Bank Failure
No full textUsing the model of Rochet and Vives (2004), this note shows that a prudential regulator can in general not mitigate a bank’s failure risk solely by means of liquidity requirements. However, their effectiveness can be restored if, in addition, minimum capital requirements are met. This provides a rationale for capital requirements beyond the commonly envoked reasoning that they are to be used to control the riskiness of banks’ asset portfolios.prudential regulation, liquidity requirements, minimum capital requirements, global games
Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes
No full textWe propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed on high frequencies, such as cumulated trading volumes or the time between potentially simultaneously occurring market events. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of liquid NYSE stocks, we show that the model captures both the dynamic and distribution properties of the data very well and is able to correctly predict future distributions.high-frequency data, point-mass mixture, multiplicative error model, excess zeros, semiparametric specification test, market microstructure
Dynamical systems forced by shot noise as a new paradigm in the interest rate modeling
No full textIn this paper we give a generalized model of the interest rates term structure including Nelson-Siegel and Svensson structure. For that we introduce a continuous m-factor exponential-polynomial form of forward interest rates and demonstrate its considerably better performance in a fitting of the zero-coupon curves in comparison with the well known Nelson-Siegel and Svensson ones. In the sequel we transform the model into a dynamic model for interest rates by designing a switching dynamical system of the considerably reduced dimension nforward interest rates, shot noise processes, switching dynamical systems, chaotic Brownian subordination, chaotic maps
Context Effects as Customer Reaction on Delisting of Brands
No full textThe delisting of brands is frequently used by retailers to strengthen their negotiating position with the manufacturers and suppliers of their product assortment. However, retailers and manufacturers have to consider the risk of potential reactions when customers are faced with a reduced or modified assortment and thus, different choice. In this paper, two studies are presented which investigate customers` switching behavior if a (sub-)brand is unavailable and key determinants of the resulting behavior are discussed. Various conditions are tested by taking into account context theory. The results reveal that customer responses depend significantly on the context. A real-life quasi-experiment suggests that manufacturers may encounter substantially larger losses than retailers. Managerial implications for both parties can be derived and recommendations for further research are developed.Consumer decisions, delisting, context effects, switching behavior, retailing, logistic regression
Parametric estimation of risk neutral density functions
No full textThis chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions determining the risk neutral distributions. We we shall differentiate between the direct and the indirect way. Following the direct way, parameter vectors are estimated which characterize the distributions from selected statistical families to model the risk neutral distributions. The idea of the indirect approach is to calibrate characteristic parameter vectors for stochastic models of the asset price processes, and then to extract the risk neutral density function via Fourier methods. For every of the reviewed methods the calculation of option prices under hypothetically true risk neutral distributions is a building block. We shall give explicit formula for call and put prices w.r.t. reviewed parametric statistical families used for direct estimation. Additionally, we shall introduce the Fast Fourier Transform method of call option pricing developed in [6]. It is intended to compare the reviewed estimation methods empirically
Asset Pricing and Portfolio Selection via Machine Learning
No full textThis thesis consists of three papers investigating stock returns forecasting, empirical asset pricing, and portfolio selection through the application of machine learning and quantitative methods. The first paper examines out-of-sample returns on 153 documented anomalies in equities, demonstrating that machine learning techniques, which aggregate these anomalies into a single mispricing signal, are profitable globally and effective even within a liquid universe of stocks. Notably, while past performance of quantitative strategies outside the U.S. does not reliably predict out-of-sample success within the U.S., U.S.-based evidence is broadly predictive of returns in international markets. The second paper introduces a novel method for predicting the full distribution of stock returns using a comprehensive set of 194 stock characteristics and market variables. This approach, free from restrictive model assumptions, leverages a two-stage quantile neural network with spline interpolation to explore non-Gaussian, heavy-tailed data and their non-linear interactions. The results indicate that this method outperforms traditional models in terms of out-of-sample losses and provides valuable alternative empirical estimates for mean estimation and forecasting across a wide range of U.S. and international..
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