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

Papers by Marcos Escobar

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

This report proposes a method to price spread options on stochastically correlated underlying ass... more This report proposes a method to price spread options on stochastically correlated underlying assets. Therefore it provides a more realistic approach towards correlation structure. We generalize a constant correlation tree model developed by Hull extend it by the notion of stochastic correlation. The resulting tree model is recombining and easy to implement. Moreover, the numerical convergence of our model is very fast.

Economic Modelling, 2009

In this paper we propose two first-passage-time approaches for pricing debt and equity when the f... more In this paper we propose two first-passage-time approaches for pricing debt and equity when the firm is able to restructure its debt as an alternative to liquidation. In contrast to other first passage models that account for reorganization, our approaches allow the firm to restructure its debt by changing its maturity and/or its face value. The first approach developed consists of a first-passage model for reorganization together with a Merton approach for default, while the second approach uses first-passage models for both reorganization and default. We also provide a comparison of the proposed approaches with the Merton (Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, and Black and Cox (Black, F. and Cox, J.C., 1976, Valuing corporate securities: Some effects of bond indenture provisions. Journal of Finance, 31, 351-367.) models.

Quantitative Finance, 2010

In this report, we propose a method to price Collateralized debt obligations (CDO) within

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.

The Journal of Alternative Investments, 2006

Partial di¤erential equations proved to be a fundamental tool as the derivatives market developed... more Partial di¤erential equations proved to be a fundamental tool as the derivatives market developed in the seventies. As markets continue into more sophisticated territory, such as credit trading, di¤erential equations continue to play an important role, with the added quali…er that the equations that arise are now much more complex. This paper presents a broad overview into the credit markets, and discusses a partial di¤erential equation that arises in that context.

International Journal of Services Sciences, 2008

In this paper we present a historical account of the evolution of mathematics and risk management... more In this paper we present a historical account of the evolution of mathematics and risk management over the last 20 years. In it, we will focus primarily on present credit market developments and we give an account of some new credit derivatives: collateralised fund obligations.

In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS... more In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS). These financial products are path dependent options where the underlying typically is a hedge fund portfolio. We describe and explain the functionality of CLSs, showing a closed form expression for the price of a CLS on a hedge fund assuming a Geometric Brownian Motion, discrete rebalancing for the hedge fund investment as well as stochastic interest rates. The risk of default before the next rebalancing date leads to a liquidity premium for the CLS which increases with the volatility of the underlying hedge fund portfolio and the leverage of the strategy. An increasing rebalancing period first leads to a higher liquidity premium, however, as the rebalancing period is extended further the liquidity premium begins to shrink again.

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2009

In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS... more In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS). These financial products are path dependent options where the underlying typically is a hedge fund portfolio. We describe and explain the functionality of CLSs, showing a closed form expression for the price of a CLS on a hedge fund assuming a Geometric Brownian Motion, discrete rebalancing for the hedge fund investment as well as stochastic interest rates. The risk of default before the next rebalancing date leads to a liquidity premium for the CLS which increases with the volatility of the underlying hedge fund portfolio and the leverage of the strategy. An increasing rebalancing period first leads to a higher liquidity premium, however, as the rebalancing period is extended further the liquidity premium begins to shrink again. La funcionalidad de las estrategias de apalancamiento constante (CLS) es investigada en este artículo. Estos productos financieros son opciones depedendientes del camino, donde los típicos subyacentes son Hedge Funds. En particular se encuentra una fórmula cerrada para el precio de liquidez de este derivado en el contexto de procesos brownianos geométricos con reajuste discreto de la cartera y tasa de interés estocástica. El riesgo de bancarrota antes de un reajuste conlleva a un precio de liquidez para el CLS, el cual es proporcional a la volatilidad del activo subyacente y al apalancamiento de la estrategia. Un incremento en el periodo entre reajustes implica un incremento inicial en el precio, sin embargo, el precio disminuye para largos periodos de reajuste.

Organic Geochemistry, 1995

Organic Geochemistry, 2011

The organic geochemistry of samples from 11 oil seeps was studied. The samples were collected fro... more The organic geochemistry of samples from 11 oil seeps was studied. The samples were collected from the Cachirí area, Carboniferous Region of Tulé (Lake Maracaibo Basin, Venezuela), associated with the Tigre Fault. Biomarkers (hopanes, steranes, n-alkanes, acyclic isoprenoids, and aromatic steroids) were analyzed using gas chromatography-mass spectrometry (GC-MS). These hydrocarbon rich fluids have undergone biodegradation (2-6 on the Peters and Moldowan scale), showing both the partial loss of n-alkanes and the microbial degradation of isoprenoids and steranes. These oil seeps were generated from a mature calcareous source rock that was deposited in a marine paleoenvironment under reducing conditions. Moreover, these seeps are likely derived from the Cretaceous La Luna Formation that reached a level of maturity near the peak of oil generation in the study area. The nature of the studied oil seeps, together with the oil generation models reported for this rock unit in the study area, suggests that these oils are a mixture of an initially heavy, altered oil and a second migrated light crude oil resulting from two generation pulses from the La Luna Formation. Evidence for the presence of light oil trapped in the study area should prompt re-exploration in the northwestern coast of Lake Maracaibo in shallow reservoirs, previously discarded because they usually demonstrated a lack of light oils.

Journal of South American Earth Sciences, 2001

The concentration and distribution of 35 elements in 78 coal samples from the Ta Âchira State coa... more The concentration and distribution of 35 elements in 78 coal samples from the Ta Âchira State coal ®elds belonging to Los Cuervos Formation (Paleocene) of western Venezuela were obtained using atomic absorption spectrometry (AAS) and inductively coupled plasma atomic emission (ICP-AES). The aim of this work was to determine, through a multivariate statistical approach (factor analysis), if there is a correlation between the trace element content in coal beds and the provenance rocks at the time of peat deposition. Comparison with world averages and geometric means for trace element concentrations in coal-bed samples shows that B, Ba, La, V, Mn, Zn, and Pb are depleted. However, Ta Âchira coal samples show a perceptible enrichment in Bi, Sb, As, Cd, and Mo, and they are highly enriched in Ag and Co. Nicholl's plot suggests that only B and Co show a distinctive organic af®nity. Enriched elements (Ni, Ag, Cd, Mo, Co) are both statistically and genetically related, and we attribute their origin to a volcaniclastic Jurassic unit. Other statistical factors (Th±V±P and Ca±Mg±Mn) reveal a different provenance, indicating a felsic plutonic source and a sedimentary limestone, respectively. A fourth factor (K±Mo±Th±S) is composed mainly of clay minerals and authigenic sul®des. q

ABSTRACT Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four differ... more ABSTRACT 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. Organic matter precursor in all cases is associated principally to higher plant contribution. FPD chromatograms are characterized by a lack of signs of benzothiophene and their alkylhomologues; The dibenzothiophene and monosustituted alkyl isomers are enriched with regard to the isomers dy and trisustituted. Organosulphur compounds

H Ho or rt te en ns se e U Ul ll lr ri ic ch h 1 10 00 00 0 R Ra az zo on ne es s P Pa ar ra a ( ... more H Ho or rt te en ns se e U Ul ll lr ri ic ch h 1 10 00 00 0 R Ra az zo on ne es s P Pa ar ra a ( (n no o) ) e en na am mo or ra ar rs se e ~1 1~ H Ho or rt te en ns se e U Ul ll lr ri ic ch h 1 10 00 00 0 R Ra az zo on ne es s P Pa ar ra a ( (n no o) ) e en na am mo or ra ar rs se e ~5 5~

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

Scenario generation techniques for gaussian markets are very well understood, and are based on Mo... more Scenario generation techniques for gaussian markets are very well understood, and are based on Monte Carlo methodologies for multivariate normal variables determined by marginal means and covariance matrices. This paper presents an approach for the calibration and generation of nongaussian scenarios; it is first developed in the one-factor setting, and then extended multifactor situations. They are both based on extreme value theory.

This report proposes a method to price spread options on stochastically correlated underlying ass... more This report proposes a method to price spread options on stochastically correlated underlying assets. Therefore it provides a more realistic approach towards correlation structure. We generalize a constant correlation tree model developed by Hull extend it by the notion of stochastic correlation. The resulting tree model is recombining and easy to implement. Moreover, the numerical convergence of our model is very fast.

Economic Modelling, 2009

In this paper we propose two first-passage-time approaches for pricing debt and equity when the f... more In this paper we propose two first-passage-time approaches for pricing debt and equity when the firm is able to restructure its debt as an alternative to liquidation. In contrast to other first passage models that account for reorganization, our approaches allow the firm to restructure its debt by changing its maturity and/or its face value. The first approach developed consists of a first-passage model for reorganization together with a Merton approach for default, while the second approach uses first-passage models for both reorganization and default. We also provide a comparison of the proposed approaches with the Merton (Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, and Black and Cox (Black, F. and Cox, J.C., 1976, Valuing corporate securities: Some effects of bond indenture provisions. Journal of Finance, 31, 351-367.) models.

Quantitative Finance, 2010

In this report, we propose a method to price Collateralized debt obligations (CDO) within

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.

The Journal of Alternative Investments, 2006

Partial di¤erential equations proved to be a fundamental tool as the derivatives market developed... more Partial di¤erential equations proved to be a fundamental tool as the derivatives market developed in the seventies. As markets continue into more sophisticated territory, such as credit trading, di¤erential equations continue to play an important role, with the added quali…er that the equations that arise are now much more complex. This paper presents a broad overview into the credit markets, and discusses a partial di¤erential equation that arises in that context.

International Journal of Services Sciences, 2008

In this paper we present a historical account of the evolution of mathematics and risk management... more In this paper we present a historical account of the evolution of mathematics and risk management over the last 20 years. In it, we will focus primarily on present credit market developments and we give an account of some new credit derivatives: collateralised fund obligations.

In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS... more In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS). These financial products are path dependent options where the underlying typically is a hedge fund portfolio. We describe and explain the functionality of CLSs, showing a closed form expression for the price of a CLS on a hedge fund assuming a Geometric Brownian Motion, discrete rebalancing for the hedge fund investment as well as stochastic interest rates. The risk of default before the next rebalancing date leads to a liquidity premium for the CLS which increases with the volatility of the underlying hedge fund portfolio and the leverage of the strategy. An increasing rebalancing period first leads to a higher liquidity premium, however, as the rebalancing period is extended further the liquidity premium begins to shrink again.

Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2009

In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS... more In this paper we develop a formula for the Liquidity Premium of constant leverage strategies (CLS). These financial products are path dependent options where the underlying typically is a hedge fund portfolio. We describe and explain the functionality of CLSs, showing a closed form expression for the price of a CLS on a hedge fund assuming a Geometric Brownian Motion, discrete rebalancing for the hedge fund investment as well as stochastic interest rates. The risk of default before the next rebalancing date leads to a liquidity premium for the CLS which increases with the volatility of the underlying hedge fund portfolio and the leverage of the strategy. An increasing rebalancing period first leads to a higher liquidity premium, however, as the rebalancing period is extended further the liquidity premium begins to shrink again. La funcionalidad de las estrategias de apalancamiento constante (CLS) es investigada en este artículo. Estos productos financieros son opciones depedendientes del camino, donde los típicos subyacentes son Hedge Funds. En particular se encuentra una fórmula cerrada para el precio de liquidez de este derivado en el contexto de procesos brownianos geométricos con reajuste discreto de la cartera y tasa de interés estocástica. El riesgo de bancarrota antes de un reajuste conlleva a un precio de liquidez para el CLS, el cual es proporcional a la volatilidad del activo subyacente y al apalancamiento de la estrategia. Un incremento en el periodo entre reajustes implica un incremento inicial en el precio, sin embargo, el precio disminuye para largos periodos de reajuste.

Organic Geochemistry, 1995

Organic Geochemistry, 2011

The organic geochemistry of samples from 11 oil seeps was studied. The samples were collected fro... more The organic geochemistry of samples from 11 oil seeps was studied. The samples were collected from the Cachirí area, Carboniferous Region of Tulé (Lake Maracaibo Basin, Venezuela), associated with the Tigre Fault. Biomarkers (hopanes, steranes, n-alkanes, acyclic isoprenoids, and aromatic steroids) were analyzed using gas chromatography-mass spectrometry (GC-MS). These hydrocarbon rich fluids have undergone biodegradation (2-6 on the Peters and Moldowan scale), showing both the partial loss of n-alkanes and the microbial degradation of isoprenoids and steranes. These oil seeps were generated from a mature calcareous source rock that was deposited in a marine paleoenvironment under reducing conditions. Moreover, these seeps are likely derived from the Cretaceous La Luna Formation that reached a level of maturity near the peak of oil generation in the study area. The nature of the studied oil seeps, together with the oil generation models reported for this rock unit in the study area, suggests that these oils are a mixture of an initially heavy, altered oil and a second migrated light crude oil resulting from two generation pulses from the La Luna Formation. Evidence for the presence of light oil trapped in the study area should prompt re-exploration in the northwestern coast of Lake Maracaibo in shallow reservoirs, previously discarded because they usually demonstrated a lack of light oils.

Journal of South American Earth Sciences, 2001

The concentration and distribution of 35 elements in 78 coal samples from the Ta Âchira State coa... more The concentration and distribution of 35 elements in 78 coal samples from the Ta Âchira State coal ®elds belonging to Los Cuervos Formation (Paleocene) of western Venezuela were obtained using atomic absorption spectrometry (AAS) and inductively coupled plasma atomic emission (ICP-AES). The aim of this work was to determine, through a multivariate statistical approach (factor analysis), if there is a correlation between the trace element content in coal beds and the provenance rocks at the time of peat deposition. Comparison with world averages and geometric means for trace element concentrations in coal-bed samples shows that B, Ba, La, V, Mn, Zn, and Pb are depleted. However, Ta Âchira coal samples show a perceptible enrichment in Bi, Sb, As, Cd, and Mo, and they are highly enriched in Ag and Co. Nicholl's plot suggests that only B and Co show a distinctive organic af®nity. Enriched elements (Ni, Ag, Cd, Mo, Co) are both statistically and genetically related, and we attribute their origin to a volcaniclastic Jurassic unit. Other statistical factors (Th±V±P and Ca±Mg±Mn) reveal a different provenance, indicating a felsic plutonic source and a sedimentary limestone, respectively. A fourth factor (K±Mo±Th±S) is composed mainly of clay minerals and authigenic sul®des. q

ABSTRACT Some tiophenic organosulphur compounds (OSC) distribution in coal bitumen of four differ... more ABSTRACT 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. Organic matter precursor in all cases is associated principally to higher plant contribution. FPD chromatograms are characterized by a lack of signs of benzothiophene and their alkylhomologues; The dibenzothiophene and monosustituted alkyl isomers are enriched with regard to the isomers dy and trisustituted. Organosulphur compounds

H Ho or rt te en ns se e U Ul ll lr ri ic ch h 1 10 00 00 0 R Ra az zo on ne es s P Pa ar ra a ( ... more H Ho or rt te en ns se e U Ul ll lr ri ic ch h 1 10 00 00 0 R Ra az zo on ne es s P Pa ar ra a ( (n no o) ) e en na am mo or ra ar rs se e ~1 1~ H Ho or rt te en ns se e U Ul ll lr ri ic ch h 1 10 00 00 0 R Ra az zo on ne es s P Pa ar ra a ( (n no o) ) e en na am mo or ra ar rs se e ~5 5~