Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structure... more Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structures (especially beyond first-to-default) • When trying to diversify credit risk: Portfolio management and credit risk management • Letter of Credit backed debt, Credit Guarantees • Counterparty risk, especially in credit derivatives
Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structure... more Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structures (especially beyond first-to-default) • When trying to diversify credit risk: Portfolio management and credit risk management • Letter of Credit backed debt, Credit Guarantees • Counterparty risk, especially in credit derivatives
Derivative instruments, or simply derivatives, are contracts that essentially derive their value ... more Derivative instruments, or simply derivatives, are contracts that essentially derive their value from the behavior of cash market instruments such as stocks, stock indexes, bonds, currencies, and commodities that underlie the contract. There are three general categories of derivatives: (1) futures and forwards, (2) options, and (3) swaps. Derivatives are either traded on an exchange or in the over-the-counter (OTC) market. That is, there are exchange-traded derivatives and OTC derivatives. Exchange-traded derivatives are standardized contracts. An advantage of OTC derivatives over exchange-traded derivatives is that they offer asset managers customized solutions for their investment strategy. In fact, one of the keys to the success of OTC derivatives is the flexibility of the payoff structures that can be created. A key difference between exchange-traded and OTC derivatives is that the former are guaranteed by the exchange, while the latter are the obligation of the non-exchange entity that is the counterparty. Thus, the user of an OTC derivative is subject to credit risk or counterparty risk…
ABSTRACT Lévy processes have been successfully applied in the modeling of financial assets. Usefu... more ABSTRACT Lévy processes have been successfully applied in the modeling of financial assets. Useful information such as implied volatility, skewness, and risk-preferences can be derived from market option prices. In this paper, we advocate using Esscher conjugate Lévy processes to estimate risk-neutral and empirical densities. More specifically, we employ the exponential Meixner and NIG processes to calculate in closed form the pricing kernel in the equity market and then study the evolution of equity market behavior between 2002 and 2010. Our empirical analysis using S&P 500 options shows that the risk preferences of equity investors were signalling an anomaly in the market well before the subprime prime mortgage crisis (August 2007) and the crisis of confidence that followed, anticipating the downfall in equity markets in 2008, but then returning to normal levels in 2009.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in p... more Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
In this paper we extend the theory of option pricing to take into account and explain the empiric... more In this paper we extend the theory of option pricing to take into account and explain the empirical evidence for asset prices such as non-Gaussian returns, long-range dependence, volatility clustering, non-Gaussian copula dependence, as well as theoretical issues such as asymmetric information and the presence of limited arbitrage opportunities
Review of Quantitative Finance and Accounting, Aug 31, 2020
In this paper we revisit the equity premium puzzle reported in 1985 by Mehra and Prescott. We sho... more In this paper we revisit the equity premium puzzle reported in 1985 by Mehra and Prescott. We show that the large equity premium that they report can be explained by choosing a more appropriate distribution for the return data. We demonstrate that the high-risk aversion value observed by Mehra and Prescott may be attributable to the problem of fitting a proper distribution to the historical returns and partly caused by poorly fitting the tail of the return distribution. We describe a new distribution that better fits the return distribution and when used to describe historical returns can explain the large equity risk premium and thereby explains the puzzle.
In the paper, we consider the application of the theory of probability metrics in several areas i... more In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics can be used to describe continuity of risk measures. Finally, the methods of probability metrics theory are applied to the benchmark-tracking problem significantly extending the problem setting.
Frontiers in Applied Mathematics and Statistics, Nov 26, 2020
In complete markets there are risky assets and a riskless asset. It is assumed that the riskless ... more In complete markets there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument's return series can be potentially used as an early warning system for a market crash.
Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structure... more Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structures (especially beyond first-to-default) • When trying to diversify credit risk: Portfolio management and credit risk management • Letter of Credit backed debt, Credit Guarantees • Counterparty risk, especially in credit derivatives
Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structure... more Where is Default Correlation Relevant? • Portfolios of defaultable bonds, CDOs • basket structures (especially beyond first-to-default) • When trying to diversify credit risk: Portfolio management and credit risk management • Letter of Credit backed debt, Credit Guarantees • Counterparty risk, especially in credit derivatives
Derivative instruments, or simply derivatives, are contracts that essentially derive their value ... more Derivative instruments, or simply derivatives, are contracts that essentially derive their value from the behavior of cash market instruments such as stocks, stock indexes, bonds, currencies, and commodities that underlie the contract. There are three general categories of derivatives: (1) futures and forwards, (2) options, and (3) swaps. Derivatives are either traded on an exchange or in the over-the-counter (OTC) market. That is, there are exchange-traded derivatives and OTC derivatives. Exchange-traded derivatives are standardized contracts. An advantage of OTC derivatives over exchange-traded derivatives is that they offer asset managers customized solutions for their investment strategy. In fact, one of the keys to the success of OTC derivatives is the flexibility of the payoff structures that can be created. A key difference between exchange-traded and OTC derivatives is that the former are guaranteed by the exchange, while the latter are the obligation of the non-exchange entity that is the counterparty. Thus, the user of an OTC derivative is subject to credit risk or counterparty risk…
ABSTRACT Lévy processes have been successfully applied in the modeling of financial assets. Usefu... more ABSTRACT Lévy processes have been successfully applied in the modeling of financial assets. Useful information such as implied volatility, skewness, and risk-preferences can be derived from market option prices. In this paper, we advocate using Esscher conjugate Lévy processes to estimate risk-neutral and empirical densities. More specifically, we employ the exponential Meixner and NIG processes to calculate in closed form the pricing kernel in the equity market and then study the evolution of equity market behavior between 2002 and 2010. Our empirical analysis using S&P 500 options shows that the risk preferences of equity investors were signalling an anomaly in the market well before the subprime prime mortgage crisis (August 2007) and the crisis of confidence that followed, anticipating the downfall in equity markets in 2008, but then returning to normal levels in 2009.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in p... more Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
In this paper we extend the theory of option pricing to take into account and explain the empiric... more In this paper we extend the theory of option pricing to take into account and explain the empirical evidence for asset prices such as non-Gaussian returns, long-range dependence, volatility clustering, non-Gaussian copula dependence, as well as theoretical issues such as asymmetric information and the presence of limited arbitrage opportunities
Review of Quantitative Finance and Accounting, Aug 31, 2020
In this paper we revisit the equity premium puzzle reported in 1985 by Mehra and Prescott. We sho... more In this paper we revisit the equity premium puzzle reported in 1985 by Mehra and Prescott. We show that the large equity premium that they report can be explained by choosing a more appropriate distribution for the return data. We demonstrate that the high-risk aversion value observed by Mehra and Prescott may be attributable to the problem of fitting a proper distribution to the historical returns and partly caused by poorly fitting the tail of the return distribution. We describe a new distribution that better fits the return distribution and when used to describe historical returns can explain the large equity risk premium and thereby explains the puzzle.
In the paper, we consider the application of the theory of probability metrics in several areas i... more In the paper, we consider the application of the theory of probability metrics in several areas in the field of finance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics can be used to describe continuity of risk measures. Finally, the methods of probability metrics theory are applied to the benchmark-tracking problem significantly extending the problem setting.
Frontiers in Applied Mathematics and Statistics, Nov 26, 2020
In complete markets there are risky assets and a riskless asset. It is assumed that the riskless ... more In complete markets there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument's return series can be potentially used as an early warning system for a market crash.
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