Revisiting Shiller’s excess volatility hypothesis

One of the cornerstone of financial anomalies is that there exists money making opportunities. Shiller’s excess volatility theory is re-investigated from the perspective of a trading strategy where the present value is computed using a series of simple econometric models to forecast the present value. The results show that the excess volatility may not be exploited given the data available until time t. However, when learning is introduced empirically, the simple trading strategy may offer profits, but which are likely to disappear once transaction costs are considered.

Volatility smile extrapolation with an artificial neural network

I use a multi-layer feedforward perceptron, with backpropagation learning implemented via stochastic gradient descent, to extrapolate the volatility smile of Euribor derivatives over low-strikes by training the network on parametric prices.

Inflation, political instability and stockmarket volatility in interwar Germany

What determined the volatility of asset prices in Germany between thewars? This paper argues that the influence of political factors has beenoverstated. The majority of events increasing political uncertainty hadlittle or no effect on the value of German assets and the volatility ofreturns on them. Instead, it was inflation (and the fear of it) that islargely responsible for most of the variability in asset returns.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Monetary policy and exchange rate volatility in a small open economy

We lay out a small open economy version of the Calvo sticky price model, and show how the equilibrium dynamics can be reduced to simple representation in domestic inflation and the output gap. We use the resulting framework to analyze the macroeconomic implications of three alternative rule-based policy regimes for the small open economy: domestic inflation and CPI-based Taylor rules, and an exchange rate peg. We show that a key difference amongthese regimes lies in the relative amount of exchange rate volatility that they entail. We also discuss a special case for which domestic inflation targeting constitutes the optimal policy, and where a simple second order approximation to the utility of the representative consumer can be derived and used to evaluate the welfare losses associated with the suboptimal rules.

A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

The Implied Book and the Narrative Text. On a Blind Spot in Narratological Theory - from a Media Studies Perspective

The article is concerned with the formal definition of a largely unnoticed factor in narrative structure. Based on the assumptions that (1) the semantics of a written text depend, among other factors, directly on its visual alignment in space, that (2) the formal structure of a text has to meet that of its spatial presentation and that (3) these assumptions hold true also for narrative texts (which, however, in modern times typically conceal their spatial dimensions by a low-key linear layout), it is argued that, how ever low-key, the expected material shape of a given narrative determines the configuration of its plot by its author. The ,implied book' thus denotes an author's historically assumable, not necessarily conscious idea of how his text, which is still in the process of creation, will be dimensionally presented and under these circumstances visually absorbed. Assuming that an author's knowledge of this later (potentially) substantiated material form influences the composition, the implied book is to be understood as a text-genetically determined, structuring moment of the text. Historically reconstructed, it thus serves the methodical analysis of structural characteristics of a completed text.