Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Making development simple. The genetic deterministic hypothesis for economic development

This paper discusses the dangers inherent in allempting to simplify something as complex as development. It does this by exploring the Lynn and Vanhanen theory of deterministic development which asserts that varying levels of economic development seen between countries can be explained by differences in 'national intelligence' (national IQ). Assuming that intelligence is genetically determined, and as different races have been shown to have different IQ, then they argue that economic development (measured as GDP/capita) is largely a function of race and interventions to address imbalances can only have a limited impact. The paper presents the Lynne and Vanhanen case and critically discusses the data and analyses (linear regression) upon which it is based. It also extends the cause-effect basis of Lynne and Vanhanen's theory for economic development into human development by using the Human Development Index (HDI). It is argued that while there is nothing mathematically incorrect with their calculations, there are concerns over the data they employ. Even more fundamentally it is argued that statistically significant correlations between the various components of the HDI and national IQ can occur via a host of cause-effect pathways, and hence the genetic determinism theory is far from proven. The paper ends by discussing the dangers involved in the use of over-simplistic measures of development as a means of exploring cause-effect relationships. While the creators of development indices such as the HDI have good intentions, simplistic indices can encourage simplistic explanations of under-development. (c) 2005 Elsevier B.V. All rights reserved.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Futures basis, inventory and commodity price volatility: an empirical analysis

We employ a large dataset of physical inventory data on 21 different commodities for the period 1993–2011 to empirically analyze the behavior of commodity prices and their volatility as predicted by the theory of storage. We examine two main issues. First, we analyze the relationship between inventory and the shape of the forward curve. Low (high) inventory is associated with forward curves in backwardation (contango), as the theory of storage predicts. Second, we show that price volatility is a decreasing function of inventory for the majority of commodities in our sample. This effect is more pronounced in backwardated markets. Our findings are robust with respect to alternative inventory measures and over the recent commodity price boom.

Reality check for volatility models

Asset allocation decisions and value at risk calculations rely strongly on volatility estimates. Volatility measures such as rolling window, EWMA, GARCH and stochastic volatility are used in practice. GARCH and EWMA type models that incorporate the dynamic structure of volatility and are capable of forecasting future behavior of risk should perform better than constant, rolling window volatility models. For the same asset the model that is the ‘best’ according to some criterion can change from period to period. We use the reality check test∗ to verify if one model out-performs others over a class of re-sampled time-series data. The test is based on re-sampling the data using stationary bootstrapping. For each re-sample we check the ‘best’ model according to two criteria and analyze the distribution of the performance statistics. We compare constant volatility, EWMA and GARCH models using a quadratic utility function and a risk management measurement as comparison criteria. No model consistently out-performs the benchmark.

Radio-wave propagation model for UHF band in different climatic conditions with dyadic green’s function

This article proposes a deterministic radio propagation model using dyadic Green's function to predict the value of the electric field. Dyadic is offered as an efficient mathematical tool which has symbolic simplicity and robustness, as well as taking account of the anisotropy of the medium. The proposed model is an important contribution for the UHF band because it considers climatic conditions by changing the constants of the medium. Most models and recommendations that include an approach for climatic conditions, are designed for satellite links, mainly Ku and Ka bands. The results obtained by simulation are compared and validated with data from a Digital Television Station measurement campaigns conducted in the Belém city in Amazon region during two seasons. The proposed model was able to provide satisfactory results by differentiating between the curves for dry and wet soil and these corroborate the measured data, (the RMS errors are between 2-5 dB in the case under study).

Improvements in the sensibility of MSA-GA tool using COFFEE objective function

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Forward implied volatility expansions in LSV models

In this work we address the problem of finding formulas for efficient and reliable analytical approximation for the calculation of forward implied volatility in LSV models, a problem which is reduced to the calculation of option prices as an expansion of the price of the same financial asset in a Black-Scholes dynamic. Our approach involves an expansion of the differential operator, whose solution represents the price in local stochastic volatility dynamics. Further calculations then allow to obtain an expansion of the implied volatility without the aid of any special function or expensive from the computational point of view, in order to obtain explicit formulas fast to calculate but also as accurate as possible.

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Price discovery and volatility spillovers in index futures markets: Some evidence from Mexico

This paper investigates the hypotheses that the recently established Mexican stock index futures market effectively serves the price discovery function, and that the introduction of futures trading has provoked volatility in the underlying spot market. We test both hypotheses simultaneously with daily data from Mexico in the context of a modified EGARCH model that also incorporates possible cointegration between the futures and spot markets. The evidence supports both hypotheses, suggesting that the futures market in Mexico is a useful price discovery vehicle, although futures trading has also been a source of instability for the spot market. Several managerial implications are derived and discussed. (C) 2004 Elsevier B.V. All rights reserved.

Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Stochastic volatility and the goodness-of-fit of the Heston model

Recently, Drǎgulescu and Yakovenko proposed an analytical formula for computing the probability density function of stock log returns, based on the Heston model, which they tested empirically. Their research design inadvertently favourably biased the fit of the data to the Heston model, thus overstating their empirical results. Furthermore, Drǎgulescu and Yakovenko did not perform any goodness-of-fit statistical tests. This study employs a research design that facilitates statistical tests of the goodness-of-fit of the Heston model to empirical returns. Robustness checks are also performed. In brief, the Heston model outperformed the Gaussian model only at high frequencies and even so does not provide a statistically acceptable fit to the data. The Gaussian model performed (marginally) better at medium and low frequencies, at which points the extra parameters of the Heston model have adverse impacts on the test statistics. © 2005 Taylor & Francis Group Ltd.

Productivity change using growth accounting and frontier-based approaches:evidence from a Monte Carlo analysis

This study presents some quantitative evidence from a number of simulation experiments on the accuracy of the productivitygrowth estimates derived from growthaccounting (GA) and frontier-based methods (namely data envelopment analysis-, corrected ordinary least squares-, and stochastic frontier analysis-based malmquist indices) under various conditions. These include the presence of technical inefficiency, measurement error, misspecification of the production function (for the GA and parametric approaches) and increased input and price volatility from one period to the next. The study finds that the frontier-based methods usually outperform GA, but the overall performance varies by experiment. Parametric approaches generally perform best when there is no functional form misspecification, but their accuracy greatly diminishes otherwise. The results also show that the deterministic approaches perform adequately even under conditions of (modest) measurement error and when measurement error becomes larger, the accuracy of all approaches (including stochastic approaches) deteriorates rapidly, to the point that their estimates could be considered unreliable for policy purposes.

Accommodating energy price volatility in life cycle cost analysis of asphalt pavements

Energy price is related to more than half of the total life cycle cost of asphalt pavements. Furthermore, the fluctuation related to price of energy has been much higher than the general inflation and interest rate. This makes the energy price inflation an important variable that should be addressed when performing life cycle cost (LCC) studies re- garding asphalt pavements. The present value of future costs is highly sensitive to the selected discount rate. Therefore, the choice of the discount rate is the most critical element in LCC analysis during the life time of a project. The objective of the paper is to present a discount rate for asphalt pavement projects as a function of interest rate, general inflation and energy price inflation. The discount rate is defined based on the portion of the energy related costs during the life time of the pavement. Consequently, it can reflect the financial risks related to the energy price in asphalt pavement projects. It is suggested that a discount rate sensitivity analysis for asphalt pavements in Sweden should range between –20 and 30%.

An autoregressive conditional filtering process to remove intraday seasonal volatility and its application to testing the noisy rational expectations model

We develop a new autoregressive conditional process to capture both the changes and the persistency of the intraday seasonal (U-shape) pattern of volatility in essay 1. Unlike other procedures, this approach allows for the intraday volatility pattern to change over time without the filtering process injecting a spurious pattern of noise into the filtered series. We show that prior deterministic filtering procedures are special cases of the autoregressive conditional filtering process presented here. Lagrange multiplier tests prove that the stochastic seasonal variance component is statistically significant. Specification tests using the correlogram and cross-spectral analyses prove the reliability of the autoregressive conditional filtering process. In essay 2 we develop a new methodology to decompose return variance in order to examine the informativeness embedded in the return series. The variance is decomposed into the information arrival component and the noise factor component. This decomposition methodology differs from previous studies in that both the informational variance and the noise variance are time-varying. Furthermore, the covariance of the informational component and the noisy component is no longer restricted to be zero. The resultant measure of price informativeness is defined as the informational variance divided by the total variance of the returns. The noisy rational expectations model predicts that uninformed traders react to price changes more than informed traders, since uninformed traders cannot distinguish between price changes caused by information arrivals and price changes caused by noise. This hypothesis is tested in essay 3 using intraday data with the intraday seasonal volatility component removed, as based on the procedure in the first essay. The resultant seasonally adjusted variance series is decomposed into components caused by unexpected information arrivals and by noise in order to examine informativeness.