Marcos Escobar - Academia.edu (original) (raw)

Papers by Marcos Escobar

Research paper thumbnail of The application of mathematical and statistical methods in industry

ABSTRACT Chemometrics has been defined as “The discipline that uses mathematical and statistical ... more ABSTRACT Chemometrics has been defined as “The discipline that uses mathematical and statistical methods for selection or design of optimal experimental conditions, and to provide relevant information from chemical data”. This is an area of intense activity, with ample applications in the chemical, energy, and process industry, and in environmental studies. The fast progress in its applications has received impulse from the advances in electronics and computers, which have made possible the acquisition, transmission and processing of data with great efficiency. This paper explains the advantages provided by coupling chemometrics with process analytical chemistry (PAT). Some examples are presented of the use of chemometric methods for material characterization, detection of deviations, process optimization, and instrumental data interpretation.

Research paper thumbnail of Oxidation of natural graphite in the laboratory and comparison with the synthetic graphite oxide, by means of thermal and spectroscopic techniques

Revista Tecnica De La Facultad De Ingenieria Universidad Del Zulia, 2009

With the aim of establishing the probable natural formation of graphite oxide (GO) during the wea... more With the aim of establishing the probable natural formation of graphite oxide (GO) during the weathering and transport of this mineral, a highly crystalline graphite sample isolated from a Sierra Nevada Formation graphitic schist (Precambrian Age) collected at the State of Trujillo, was subject to controlled oxidation in an oven (T~90°C) with a wet oxygen atmosphere through 25, 50 and 75 days of oxidation. This experimental design simuling weathering is equivalent to the natural alteration for the period of 8, 16 and 24 years, approximately. In addition, graphite oxide (GO) was synthesized by treatment with acid KMnO4. All samples and GO were characterized by means of XRD, Raman spectroscopy, thermogravimetric analysis and Fourier Transformed infrared spectroscopy. Oxydized samples exhibit a decrease in the crystallinity index and in the crystal thickness, reduction of the Raman signals corresponding to the ordered structure, displacements in the highest temperature towards lower values in thermogravimetry, and appearance of C -O strenght vibration in infrared spectroscopy. Such results indicate that a modification takes place in the graphite crystallinity, due to the expansion and incorporation of oxygen. The extent of the alteration do not reached the stage of GO formation.

Research paper thumbnail of A Note on the Distribution of Multivariate Brownian Extrema

International Journal of Stochastic Analysis, 2014

Research paper thumbnail of Pricing two-asset Barrier Options under Stochastic Correlation via Perturbation

ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular ba... more ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular barrier options. In this work we price two-asset path-dependent derivatives by means of perturbation theory in the context of a bi-dimensional asset model with stochastic correlation and volatilities. To our best knowledge, this is the first attempt at pricing barriers with stochastic correlation. It turns out that the leading term of the approximation corresponds to a constant covariance Black-Scholes type price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Research paper thumbnail of Stochastic covariance and dimension reduction in the pricing of basket options

Review of Derivatives Research, 2016

ABSTRACT This paper presents a tailor-made method for dimension reduction aimed at approximating ... more ABSTRACT This paper presents a tailor-made method for dimension reduction aimed at approximating the price of basket options in the context of stochastic volatility and correlation. The method is built on a modification to the Principal Component Stochastic Volatility (PCSV) model, a stochastic covariance model that accounts for most stylized facts in prices. The method to reduce dimension is first derived theoretically. Afterwards the results are applied to a multivariate lognormal context, a special case of the PCSV model. Finally empirical results for the application of the method to the general PCSV model are illustrated.

Research paper thumbnail of An Intensity-Based Approach for Modeling Hedge Fung Equity

Proceedings of the 3rd International Conference on Risk Management Global E Business, Oct 1, 2009

Research paper thumbnail of Portfolio Choice with Stochastic Interest Rates and Learning About Stock Return Predictability

Ssrn Electronic Journal, Nov 19, 2014

ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest r... more ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest rates are stochastic and stock returns are predictable with observed and unobserved factors. The stock risk premium is taken to be an affine function of the predictive variables and the stock return volatility is assumed to depend on the observed factor. The latent factor is estimated based on the observations. It is shown that the stock return predictability can significantly impact the optimal bond portfolio. The welfare loss from ignoring learning can be considerable.

Research paper thumbnail of A General Structural Approach For Credit Modeling Under Stochastic Volatility

Journal of Financial Transformation, 2011

ABSTRACT This paper assumes a structural credit model with underlying stochastic volatility combi... more ABSTRACT This paper assumes a structural credit model with underlying stochastic volatility combining the Black/Cox approach with the Heston model. We model the equity of a company as a barrier call option on its assets. The assets are assumed to follow a stochastic volatility process; this implies an equity model with most documented stylized facts incorporated. We derive the price of this option under a general framework where the barrier and strike are different from each other, allowing for richer financial applications. The expression for the probability of default under this framework is also provided. As the calibration of this model gets much more complex, we present an iterative fitting algorithm with which we are able to nicely estimate the parameters of the model, and we show via simulation the consistency of the estimator. We also study the sensitivity of the model parameters to the difference between the barrier and strike price.

Research paper thumbnail of Distribución De Compuestos Organosulfurados Tiofénicos en Algunos Carbones Venezolanos

Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different local... more Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different localities in Venezuelan coalfields was studied in order to establish if they could be used as geochemical peat accumulation environment markers, as well as the possibility of using these to establish organic matter maturity in coals. Typical coal organic geochemistry analyses were carried out, including proximate, ultimate and

Research paper thumbnail of Distribución De Compuestos Organosulfurados Tiofénicos en Algunos Carbones Venezolanos

Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different local... more Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different localities in Venezuelan coalfields was studied in order to establish if they could be used as geochemical peat accumulation environment markers, as well as the possibility of using these to establish organic matter maturity in coals. Typical coal organic geochemistry analyses were carried out, including proximate, ultimate and total sulphur analysis, mean vitrinite reflectance %Rm, yield extraction and bitumen fractionation. Saturates and aromatics fractions were analyzed by gas chromatography using FID and FPD detection, respectively. Results indicate that coals range between high volatile bituminous and anthracite. It was found that the degree of maturation of the studied coals was early catagenesis, except the Cerro Saroche coals that are in metagenesis. The sedimentary paleoenvironments were inferred as fresh or low saline water with slightly reducing conditions not free of oxygen. Organ...

Research paper thumbnail of A General Structural Approach For Credit Modeling Under Stochastic Volatility

This paper assumes a structural credit model with underlying stochastic volatility combining the ... more This paper assumes a structural credit model with underlying stochastic volatility combining the Black/Cox approach with the Heston model. We model the equity of a company as a barrier call option on its assets. The assets are assumed to follow a stochastic volatility process; this implies an equity model with most documented stylized facts incorporated. We derive the price of this option under a general framework where the barrier and strike are different from each other, allowing for richer financial applications. The expression for the probability of default under this framework is also provided. As the calibration of this model gets much more complex, we present an iterative fitting algorithm with which we are able to nicely estimate the parameters of the model, and we show via simulation the consistency of the estimator. We also study the sensitivity of the model parameters to the difference between the barrier and strike price.

Research paper thumbnail of Portfolio Optimization in Affine Models With Markov Switching

International Journal of Theoretical and Applied Finance, 2015

We consider a stochastic factor financial model where the asset price process and the process for... more We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this aim we apply Merton's approach, as we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains we first derive the HJB equations, which in our case correspond to a system of coupled non-linear PDEs. Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic factor. In the presence of leverage we propose a separable ansatz, which leads to explicit solutions in this case as well. General verification results are also proved. The results are illustrated for the special case of a Markov modulated Heston model.

Research paper thumbnail of Pricing Two-Asset Barrier Options Under Stochastic Correlation via Perturbation

International Journal of Theoretical and Applied Finance, 2015

ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular ba... more ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular barrier options. In this work we price two-asset path-dependent derivatives by means of perturbation theory in the context of a bi-dimensional asset model with stochastic correlation and volatilities. To our best knowledge, this is the first attempt at pricing barriers with stochastic correlation. It turns out that the leading term of the approximation corresponds to a constant covariance Black-Scholes type price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Research paper thumbnail of Single and Double Black-Cox for Pricing Risky Debt and Equity with Reorganization

In this paper we add a Black and Cox (1976) approach for debt and equity valuation to the common ... more In this paper we add a Black and Cox (1976) approach for debt and equity valuation to the common practice of reorganization leading to a more realistic setting. We introduce first passage models in order to allow for both reorganization as well as liquidation before maturity time. This paper considers two types of settings. The first one is a first-passage approach for reorganization together with a Merton approach for default, while the second setting uses first-passage models for both reorganization and default. A comparison among the models proposed with Merton (1974) and Black and Cox (1976) approaches is provided.

Research paper thumbnail of Collateralized Structured Products

In this paper multidimensional structured products with a collateral triggered by a default of th... more In this paper multidimensional structured products with a collateral triggered by a default of the issuing company are studied. In the last decade, the volume of trades in structured products has increased tremendously. Particularly after the subprime and financial crisis with the default by Lehman Brothers, the issue of default risk gained relevance worldwide. Since the early work of Black and Cox [1976], the default risk of a corporation is known to be a barrier-type product. Here, we present closed form solutions for arbitrary collateralized structured products (CSP) in the framework of n assets and two barriers, one representing default and the second a market-related option.

Research paper thumbnail of Estimation of Stochastic Covariance Models using a Continuum of Moment Conditions

We describe the implementation of a parameter estimation method suitable for models commonly used... more We describe the implementation of a parameter estimation method suitable for models commonly used in quantitative finance. The Continuum - Generalized Method of Moments (CGMM) is a Generalized Method of Moments (GMM) type of methodology that applies a continuum of moment conditions to achieve efficiency. Instead of the transition density, the more commonly available conditional characteristic function is used for estimation. We apply CGMM to two stochastic covariance models, the Wishart Affine Stochastic Correlation (WASC) model and the Principal Components Stochastic Volatility (PCSV) model. This illustrates the power of CGMM as stochastic covariance models are generally hard to estimate. The estimation method is implemented in Matlab.

Research paper thumbnail of On the Characteristic Function and Estimation of a Stochastic Covariance Model

In this paper we study, validate and simplify various relevant characteristic functions associate... more In this paper we study, validate and simplify various relevant characteristic functions associated to the Principal Component Stochastic Volatility model (PCSV, see [11]). These functions are later utilized in the estimation of relevant bivariate financial time series within the method known as Continuum Generalized Method of Moments (CGMM, see [7]). A simplified but still practical version of the PCSV model, called Partial-PCSV is proposed and empirically assessed on real data. In order to evaluate the resulting estimates, we perform a Monte Carlo study to quantify the estimation error and we perform a procedure that assesses the power of the models to capture time series features which are important to practitioners.

Research paper thumbnail of Multidimensional Structural Credit Modeling under Stochastic Volatility

ISRN Probability and Statistics, 2013

ABSTRACT This paper presents a structural credit model with underlying stochastic volatility, a C... more ABSTRACT This paper presents a structural credit model with underlying stochastic volatility, a CIR process, combining the Black/Cox framework with the Heston Model. We allow to calibrate a Heston Model for a non-observable process as underlying of the Black/Cox Model. A closed-form solution for the price of a down-and-out call option on the assets with the debt as barrier and strike price is derived using the concept of optional sampling. Furthermore, estimators are derived with the Method of Moments for Hidden Markov Chains. As an application in Statistical Finance, the default probabilities of Merrill Lynch are examined during the financial crisis.

Research paper thumbnail of Stochastic Correlation and Volatility Mean-reversion – Empirical Motivation and Derivatives Pricing via Perturbation Theory

Applied Mathematical Finance, 2014

ABSTRACT The dependence structure is crucial when modeling several assets simultaneously. We show... more ABSTRACT The dependence structure is crucial when modeling several assets simultaneously. We show for a real-data example that the correlation structure between assets is not constant over time but rather changes stochastically, and we propose a multidimensional asset model which fits the patterns found in the empirical data. The model is applied to price multi-asset derivatives by means of perturbation theory. It turns out that the leading term of the approximation corresponds to the Black-Scholes derivative price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Research paper thumbnail of Portfolio Choice with Stochastic Interest Rates and Learning About Stock Return Predictability

SSRN Electronic Journal, 2000

ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest r... more ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest rates are stochastic and stock returns are predictable with observed and unobserved factors. The stock risk premium is taken to be an affine function of the predictive variables and the stock return volatility is assumed to depend on the observed factor. The latent factor is estimated based on the observations. It is shown that the stock return predictability can significantly impact the optimal bond portfolio. The welfare loss from ignoring learning can be considerable.

Research paper thumbnail of The application of mathematical and statistical methods in industry

ABSTRACT Chemometrics has been defined as “The discipline that uses mathematical and statistical ... more ABSTRACT Chemometrics has been defined as “The discipline that uses mathematical and statistical methods for selection or design of optimal experimental conditions, and to provide relevant information from chemical data”. This is an area of intense activity, with ample applications in the chemical, energy, and process industry, and in environmental studies. The fast progress in its applications has received impulse from the advances in electronics and computers, which have made possible the acquisition, transmission and processing of data with great efficiency. This paper explains the advantages provided by coupling chemometrics with process analytical chemistry (PAT). Some examples are presented of the use of chemometric methods for material characterization, detection of deviations, process optimization, and instrumental data interpretation.

Research paper thumbnail of Oxidation of natural graphite in the laboratory and comparison with the synthetic graphite oxide, by means of thermal and spectroscopic techniques

Revista Tecnica De La Facultad De Ingenieria Universidad Del Zulia, 2009

With the aim of establishing the probable natural formation of graphite oxide (GO) during the wea... more With the aim of establishing the probable natural formation of graphite oxide (GO) during the weathering and transport of this mineral, a highly crystalline graphite sample isolated from a Sierra Nevada Formation graphitic schist (Precambrian Age) collected at the State of Trujillo, was subject to controlled oxidation in an oven (T~90°C) with a wet oxygen atmosphere through 25, 50 and 75 days of oxidation. This experimental design simuling weathering is equivalent to the natural alteration for the period of 8, 16 and 24 years, approximately. In addition, graphite oxide (GO) was synthesized by treatment with acid KMnO4. All samples and GO were characterized by means of XRD, Raman spectroscopy, thermogravimetric analysis and Fourier Transformed infrared spectroscopy. Oxydized samples exhibit a decrease in the crystallinity index and in the crystal thickness, reduction of the Raman signals corresponding to the ordered structure, displacements in the highest temperature towards lower values in thermogravimetry, and appearance of C -O strenght vibration in infrared spectroscopy. Such results indicate that a modification takes place in the graphite crystallinity, due to the expansion and incorporation of oxygen. The extent of the alteration do not reached the stage of GO formation.

Research paper thumbnail of A Note on the Distribution of Multivariate Brownian Extrema

International Journal of Stochastic Analysis, 2014

Research paper thumbnail of Pricing two-asset Barrier Options under Stochastic Correlation via Perturbation

ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular ba... more ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular barrier options. In this work we price two-asset path-dependent derivatives by means of perturbation theory in the context of a bi-dimensional asset model with stochastic correlation and volatilities. To our best knowledge, this is the first attempt at pricing barriers with stochastic correlation. It turns out that the leading term of the approximation corresponds to a constant covariance Black-Scholes type price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Research paper thumbnail of Stochastic covariance and dimension reduction in the pricing of basket options

Review of Derivatives Research, 2016

ABSTRACT This paper presents a tailor-made method for dimension reduction aimed at approximating ... more ABSTRACT This paper presents a tailor-made method for dimension reduction aimed at approximating the price of basket options in the context of stochastic volatility and correlation. The method is built on a modification to the Principal Component Stochastic Volatility (PCSV) model, a stochastic covariance model that accounts for most stylized facts in prices. The method to reduce dimension is first derived theoretically. Afterwards the results are applied to a multivariate lognormal context, a special case of the PCSV model. Finally empirical results for the application of the method to the general PCSV model are illustrated.

Research paper thumbnail of An Intensity-Based Approach for Modeling Hedge Fung Equity

Proceedings of the 3rd International Conference on Risk Management Global E Business, Oct 1, 2009

Research paper thumbnail of Portfolio Choice with Stochastic Interest Rates and Learning About Stock Return Predictability

Ssrn Electronic Journal, Nov 19, 2014

ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest r... more ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest rates are stochastic and stock returns are predictable with observed and unobserved factors. The stock risk premium is taken to be an affine function of the predictive variables and the stock return volatility is assumed to depend on the observed factor. The latent factor is estimated based on the observations. It is shown that the stock return predictability can significantly impact the optimal bond portfolio. The welfare loss from ignoring learning can be considerable.

Research paper thumbnail of A General Structural Approach For Credit Modeling Under Stochastic Volatility

Journal of Financial Transformation, 2011

ABSTRACT This paper assumes a structural credit model with underlying stochastic volatility combi... more ABSTRACT This paper assumes a structural credit model with underlying stochastic volatility combining the Black/Cox approach with the Heston model. We model the equity of a company as a barrier call option on its assets. The assets are assumed to follow a stochastic volatility process; this implies an equity model with most documented stylized facts incorporated. We derive the price of this option under a general framework where the barrier and strike are different from each other, allowing for richer financial applications. The expression for the probability of default under this framework is also provided. As the calibration of this model gets much more complex, we present an iterative fitting algorithm with which we are able to nicely estimate the parameters of the model, and we show via simulation the consistency of the estimator. We also study the sensitivity of the model parameters to the difference between the barrier and strike price.

Research paper thumbnail of Distribución De Compuestos Organosulfurados Tiofénicos en Algunos Carbones Venezolanos

Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different local... more Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different localities in Venezuelan coalfields was studied in order to establish if they could be used as geochemical peat accumulation environment markers, as well as the possibility of using these to establish organic matter maturity in coals. Typical coal organic geochemistry analyses were carried out, including proximate, ultimate and

Research paper thumbnail of Distribución De Compuestos Organosulfurados Tiofénicos en Algunos Carbones Venezolanos

Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different local... more Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four different localities in Venezuelan coalfields was studied in order to establish if they could be used as geochemical peat accumulation environment markers, as well as the possibility of using these to establish organic matter maturity in coals. Typical coal organic geochemistry analyses were carried out, including proximate, ultimate and total sulphur analysis, mean vitrinite reflectance %Rm, yield extraction and bitumen fractionation. Saturates and aromatics fractions were analyzed by gas chromatography using FID and FPD detection, respectively. Results indicate that coals range between high volatile bituminous and anthracite. It was found that the degree of maturation of the studied coals was early catagenesis, except the Cerro Saroche coals that are in metagenesis. The sedimentary paleoenvironments were inferred as fresh or low saline water with slightly reducing conditions not free of oxygen. Organ...

Research paper thumbnail of A General Structural Approach For Credit Modeling Under Stochastic Volatility

This paper assumes a structural credit model with underlying stochastic volatility combining the ... more This paper assumes a structural credit model with underlying stochastic volatility combining the Black/Cox approach with the Heston model. We model the equity of a company as a barrier call option on its assets. The assets are assumed to follow a stochastic volatility process; this implies an equity model with most documented stylized facts incorporated. We derive the price of this option under a general framework where the barrier and strike are different from each other, allowing for richer financial applications. The expression for the probability of default under this framework is also provided. As the calibration of this model gets much more complex, we present an iterative fitting algorithm with which we are able to nicely estimate the parameters of the model, and we show via simulation the consistency of the estimator. We also study the sensitivity of the model parameters to the difference between the barrier and strike price.

Research paper thumbnail of Portfolio Optimization in Affine Models With Markov Switching

International Journal of Theoretical and Applied Finance, 2015

We consider a stochastic factor financial model where the asset price process and the process for... more We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon and derive optimal dynamic investment strategies that maximize the investor's expected utility from terminal wealth. To this aim we apply Merton's approach, as we are dealing with an incomplete market. Based on the semimartingale characterization of Markov chains we first derive the HJB equations, which in our case correspond to a system of coupled non-linear PDEs. Exploiting the affine structure of the model, we derive simple expressions for the solution in the case with no leverage, i.e. no correlation between the Brownian motions driving the asset price and the stochastic factor. In the presence of leverage we propose a separable ansatz, which leads to explicit solutions in this case as well. General verification results are also proved. The results are illustrated for the special case of a Markov modulated Heston model.

Research paper thumbnail of Pricing Two-Asset Barrier Options Under Stochastic Correlation via Perturbation

International Journal of Theoretical and Applied Finance, 2015

ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular ba... more ABSTRACT The correlation structure is crucial when pricing multi-asset products, in particular barrier options. In this work we price two-asset path-dependent derivatives by means of perturbation theory in the context of a bi-dimensional asset model with stochastic correlation and volatilities. To our best knowledge, this is the first attempt at pricing barriers with stochastic correlation. It turns out that the leading term of the approximation corresponds to a constant covariance Black-Scholes type price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Research paper thumbnail of Single and Double Black-Cox for Pricing Risky Debt and Equity with Reorganization

In this paper we add a Black and Cox (1976) approach for debt and equity valuation to the common ... more In this paper we add a Black and Cox (1976) approach for debt and equity valuation to the common practice of reorganization leading to a more realistic setting. We introduce first passage models in order to allow for both reorganization as well as liquidation before maturity time. This paper considers two types of settings. The first one is a first-passage approach for reorganization together with a Merton approach for default, while the second setting uses first-passage models for both reorganization and default. A comparison among the models proposed with Merton (1974) and Black and Cox (1976) approaches is provided.

Research paper thumbnail of Collateralized Structured Products

In this paper multidimensional structured products with a collateral triggered by a default of th... more In this paper multidimensional structured products with a collateral triggered by a default of the issuing company are studied. In the last decade, the volume of trades in structured products has increased tremendously. Particularly after the subprime and financial crisis with the default by Lehman Brothers, the issue of default risk gained relevance worldwide. Since the early work of Black and Cox [1976], the default risk of a corporation is known to be a barrier-type product. Here, we present closed form solutions for arbitrary collateralized structured products (CSP) in the framework of n assets and two barriers, one representing default and the second a market-related option.

Research paper thumbnail of Estimation of Stochastic Covariance Models using a Continuum of Moment Conditions

We describe the implementation of a parameter estimation method suitable for models commonly used... more We describe the implementation of a parameter estimation method suitable for models commonly used in quantitative finance. The Continuum - Generalized Method of Moments (CGMM) is a Generalized Method of Moments (GMM) type of methodology that applies a continuum of moment conditions to achieve efficiency. Instead of the transition density, the more commonly available conditional characteristic function is used for estimation. We apply CGMM to two stochastic covariance models, the Wishart Affine Stochastic Correlation (WASC) model and the Principal Components Stochastic Volatility (PCSV) model. This illustrates the power of CGMM as stochastic covariance models are generally hard to estimate. The estimation method is implemented in Matlab.

Research paper thumbnail of On the Characteristic Function and Estimation of a Stochastic Covariance Model

In this paper we study, validate and simplify various relevant characteristic functions associate... more In this paper we study, validate and simplify various relevant characteristic functions associated to the Principal Component Stochastic Volatility model (PCSV, see [11]). These functions are later utilized in the estimation of relevant bivariate financial time series within the method known as Continuum Generalized Method of Moments (CGMM, see [7]). A simplified but still practical version of the PCSV model, called Partial-PCSV is proposed and empirically assessed on real data. In order to evaluate the resulting estimates, we perform a Monte Carlo study to quantify the estimation error and we perform a procedure that assesses the power of the models to capture time series features which are important to practitioners.

Research paper thumbnail of Multidimensional Structural Credit Modeling under Stochastic Volatility

ISRN Probability and Statistics, 2013

ABSTRACT This paper presents a structural credit model with underlying stochastic volatility, a C... more ABSTRACT This paper presents a structural credit model with underlying stochastic volatility, a CIR process, combining the Black/Cox framework with the Heston Model. We allow to calibrate a Heston Model for a non-observable process as underlying of the Black/Cox Model. A closed-form solution for the price of a down-and-out call option on the assets with the debt as barrier and strike price is derived using the concept of optional sampling. Furthermore, estimators are derived with the Method of Moments for Hidden Markov Chains. As an application in Statistical Finance, the default probabilities of Merrill Lynch are examined during the financial crisis.

Research paper thumbnail of Stochastic Correlation and Volatility Mean-reversion – Empirical Motivation and Derivatives Pricing via Perturbation Theory

Applied Mathematical Finance, 2014

ABSTRACT The dependence structure is crucial when modeling several assets simultaneously. We show... more ABSTRACT The dependence structure is crucial when modeling several assets simultaneously. We show for a real-data example that the correlation structure between assets is not constant over time but rather changes stochastically, and we propose a multidimensional asset model which fits the patterns found in the empirical data. The model is applied to price multi-asset derivatives by means of perturbation theory. It turns out that the leading term of the approximation corresponds to the Black-Scholes derivative price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations.

Research paper thumbnail of Portfolio Choice with Stochastic Interest Rates and Learning About Stock Return Predictability

SSRN Electronic Journal, 2000

ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest r... more ABSTRACT The problem of optimal wealth allocation is solved under the assumptions that interest rates are stochastic and stock returns are predictable with observed and unobserved factors. The stock risk premium is taken to be an affine function of the predictive variables and the stock return volatility is assumed to depend on the observed factor. The latent factor is estimated based on the observations. It is shown that the stock return predictability can significantly impact the optimal bond portfolio. The welfare loss from ignoring learning can be considerable.