Enrique ter Horst

Stochastic volatility models including open, close, high and low prices

Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility models that uses opening and closing prices along with the minimum and maximum prices within a trading period to infer the dynamics underlying the volatility process of asset prices and compare it with similar models presented previously in the literature. The paper also discusses sequential Monte Carlo algorithms to fit this class of models and illustrates its features using both a simulation study and real data.

The Black Market for Dollars in Venezuela

In February 2003, the Venezuelan government imposed a strict capital controls policy to stem the outflow of dollars. We describe the mechanics and structure of the resulting black market and analyze the comparative performance of alternative models in explaining and forecasting the black market premium. Robustly significant determinants of the premium include the lagged premium, the official real exchange rate, the implied returns from arbitrage, and the oil price. Our preferred model exhibits outstanding out-of-sample forecasting performance, with an average prediction error of -0.9 percent, and an error standard deviation of 7.8 percent, during the ten-month period until July 2009. We provide evidence that the exogenous change of the black market swap vehicle to government bonds in 2007 induced a significant shift in the relative importance of the determinants of the premium, causing shocks to become significantly more persistent, the coefficient on the implied returns from arbitrage to double, and rendering the beneficial effect of oil price increases insignificant.

A Bayesian Beta Markov Random Field Calibration of the Term Structure of Implied Risk Neutral Densities

We build on Fackler and King (1990) and propose a general calibration model for implied risk neutral densities. Our model allows for the joint calibration of a set of densities at different maturities and dates. The model is a Bayesian dynamic beta Markov random field which allows for possible time dependence between densities with the same maturity and for dependence across maturities at the same point in time. The assumptions on the prior distribution allow us to compound the needs of model flexibility, parameter parsimony and information pooling across densities.

A Relationship between the Ordinary Maximum Entropy Method and the Method of Maximum Entropy in the Mean

There are two entropy-based methods to deal with linear inverse problems, which we shall call the ordinary method of maximum entropy (OME) and the method of maximum entropy in the mean (MEM). Not only doesMEM use OME as a stepping stone, it also allows for greater generality. First, because it allows to include convex constraints in a natural way, and second, because it allows to incorporate and to estimate (additive) measurement errors from the data. Here we shall see both methods in action in a specific example. We shall solve the discretized version of the problem by two variants of MEM and directly with OME. We shall see that OME is actually a particular instance of MEM, when the reference measure is a Poisson Measure.

MEASURING EXPECTATIONS IN OPTIONS MARKETS: AN APPLICATION TO THE S&P500 INDEX

Extracting market expectations has always been an important issue when making national policies and investment decisions in financial markets. In options markets, the most popular way has been to extract implied volatilities to assess the future variability of the underlying asset with the use of the Black–Scholes formula. In this manuscript, we propose a novel way to extract the whole time varying distribution of the market implied asset price from option prices. We use a Bayesian non-parametric method that makes use of the Sethuraman representation for Dirichlet processes to take into account the evolution of distributions in time. As an illustration, we present an analysis of options on the S&P500 index.

Recovering Decay Rates from Noisy Measurements with Maximum Entropy in the Mean

We present a new method, based on the method of maximum entropy in the mean, which builds upon the standard method of maximum entropy, to improve the parametric estimation of a decay rate when the measurements are corrupted by large level of noise and, more importantly, when the number of measurements is small. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We show how to obtain an estimator with the noise filtered out, and using simulated data, we compare the performance of our method with the Bayesian and maximum likelihood approaches.

Customer behavior in electronic commerce: a Bayesian approach

Online shopping has increasingly replaced traditional retail shopping, as a large number of consumers have adopted it on a global scale. However, while it is well established in developed countries, e-commerce is still at an early stage in emerging markets, hence there is a need to unveil which factors contributes to its adoption. The main objective of this study is to integrate the theory of planned behavior, the theory of reasoned action, and the technology acceptance model using a Bayesian approach to determine the key predictors of online purchase intention among internet users in Colombia. The results demonstrate the pertinence of the theory of reasoned action and technology acceptance model, models to explain online purchase intention, confirming that the intention to purchase online is mostly determined by the attitudes to e-commerce which, in turn, are explained by perceived usefulness, perceived ease of use, and the subjective norm related to online shopping.

Timing Foreign Exchange Markets

To improve short-horizon exchange rate forecasts, we employ foreign exchange market risk factors as fundamentals, and Bayesian treed Gaussian process (BTGP) models to handle non-linear, time-varying relationships between these fundamentals and exchange rates. Forecasts from the BTGP model conditional on the carry and dollar factors dominate random walk forecasts on accuracy and economic criteria in the Meese-Rogoff setting. Superior market timing ability for large moves, more than directional accuracy, drives the BTGP’s success. We explain how, through a model averaging Monte Carlo scheme, the BTGP is able to simultaneously exploit smoothness and rough breaks in between-variable dynamics. Either feature in isolation is unable to consistently outperform benchmarks throughout the full span of time in our forecasting exercises. Trading strategies based on ex ante BTGP forecasts deliver the highest out-of-sample risk-adjusted returns for the median currency, as well as for both predictable, traded risk factors.

Risk Neutral Measure Determination from Price Ranges: Single Period Market Models

Risk neutral measures are defined such that the basic random assets in a portfolio are martingales. Hence, when the market model is complete, valuation of other financial instruments is a relatively straightforward task when those basic random assets constitute their underlying asset. To determine the risk neutral measure, it is assumed that the current prices of the basic assets are known exactly. However, oftentimes all we know about the current price, or that of a derivative having it as underlying, is a bid-ask range. The question then arises as to how to determine the risk neutral measure from that information. We may want to determine risk neutral measures from that information to use it, for example, to price other derivatives on the same asset. In this paper we propose an extended version of the maximum entropy method to carry out that task. This approach provides a novel solution to this problem, which is computationally simple and fast.

Heard It Through the Grapevine! How Peer-to-Peer Interaction Affects Customer Experience and Word-of-Mouth Intention in Different Service Environments: A Bayesian Approach

The study of customer experience (CX) has become a prominent topic in marketing research lately because of the evolution of the customer/company relationship. The total number of touch points where this interaction can take place has increased significantly due to the total number of channels and media outlets now available to customers, further increasing the complexity of the customer journey. As a consequence, the level of control companies yield over the experience provided to customers decreased resulting in a more intricate process of creation, management and delivery of experiences to customers. The present research contributes to marketing research in four main ways. First, it investigates the relationship between peer-to-peer interaction, peace-of-mind, and service outcome quality with the customer experience construct. Second, we examine the role peer-to-peer (PTP) interaction plays as a social/external/independent touch point in accordance with Lemon and Verhoef (2016), where interpersonal communication among customers occurs through WOM. PTP interaction is particularly important within the retail context. The present study introduces the novel approach of utilizing an innovative and less common analysis methodology based on Bayesian modeling that offers several advantages over traditional methods such as SEM in terms of how it approaches sample size and homogeneity, potential missing data and specification of research.