Volatility of Housing

The aim of the project is to develop a theoretical framework where homelessness arises due to various economic and social factors that vary over time. The ultimate goal is i) to understand whether homelessness spells, entrances and exits could be predicted and if so what information is necessary; and ii) to design and evaluate a homelessness prevention programme in a changing and uncertain environment. Examples of the questions we want to answer are: Should it be made easier for people to borrow money so that they can get out of homelessness, or will such borrowing allow people to over-consume today and so fall into homelessness tomorrow? Should precautionary savings be encouraged so that people have cushions to withstand future shocks, or will savings just delay entry into homelessness? What interventions will affect the probability of becoming homeless and how will they affect behaviour? How will interventions affect incentives to save and to consume before homelessness prevention programmes kick in?

The rise and fall of piecework–timework wage differentials: market volatility, labor heterogeneity, and output pricing

Based on detailed payroll data of blue collar male and female labor in Britain’s engineering and metal working industrial sectors between the mid-1920s and mid-1960s, we provide empirical evidence in respect of several central themes in the piecework-timework wage literature. The period covers part of the heyday of pieceworking as well as the start of its post-war decline. We show the importance of relative piece rate flexibility during the Great Depression as well as during the build up to WWII and during the war itself. We account for the very significant decline in the differentials after the war. Labor market topics include piecework pay in respect of compensating differentials, labor heterogeneity, and the transaction costs of pricing piecework output.

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.

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.

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.

Focal dystonia and the Sensory-Motor Integrative Loop for Enacting (SMILE).

Performing accurate movements requires preparation, execution, and monitoring mechanisms. The first two are coded by the motor system, the latter by the sensory system. To provide an adaptive neural basis to overt behaviors, motor and sensory information has to be properly integrated in a reciprocal feedback loop. Abnormalities in this sensory-motor loop are involved in movement disorders such as focal dystonia, a hyperkinetic alteration affecting only a specific body part and characterized by sensory and motor deficits in the absence of basic motor impairments. Despite the fundamental impact of sensory-motor integration mechanisms on daily life, the general principles of healthy and pathological anatomic-functional organization of sensory-motor integration remain to be clarified. Based on the available data from experimental psychology, neurophysiology, and neuroimaging, we propose a bio-computational model of sensory-motor integration: the Sensory-Motor Integrative Loop for Enacting (SMILE). Aiming at direct therapeutic implementations and with the final target of implementing novel intervention protocols for motor rehabilitation, our main goal is to provide the information necessary for further validating the SMILE model. By translating neuroscientific hypotheses into empirical investigations and clinically relevant questions, the prediction based on the SMILE model can be further extended to other pathological conditions characterized by impaired sensory-motor integration.