This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Levy process. The novelty of our approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, we present two models. In the first one, the default occurs at bond maturity if the firm's value falls below a predetermined barrier. In the second version, the company can bankrupt at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. Finally, with synchronous jumps, the firm's asset and state processes are no longer uncorrelated.
{"title":"A Structural Model for Credit Risk with Markov Modulated Lévy Processes and Synchronous Jumps","authors":"Donatien Hainaut, David B. Colwell","doi":"10.2139/ssrn.2211424","DOIUrl":"https://doi.org/10.2139/ssrn.2211424","url":null,"abstract":"This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Levy process. The novelty of our approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, we present two models. In the first one, the default occurs at bond maturity if the firm's value falls below a predetermined barrier. In the second version, the company can bankrupt at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. Finally, with synchronous jumps, the firm's asset and state processes are no longer uncorrelated.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130818247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper shows the most relevant value creation indicator in a competitive economic equilibrium framework. We analyze the relationship between the cost of capital and the competitive dynamics of the firm. Several related propositions on the most relevant value creation indicator under a dynamic competitive setting are developed to establish the theoretical framework of the research hypotheses. A sample of 80 U.S. firms in convergence to equilibrium and cross section data are used in the empirical analysis. Firstly, we compare the costs of capital estimated from the CAPM with those from the Discounted Residual Income Model (DRIM). Using the competitive advantage period “T” as the forecast period in the DRIM, we have considered it as an ex ante model that takes into account the competitive dynamics of the firm. Secondly, we tested the explanatory power of the marginal return to cost of capital ratio from the DRIM compared to that of the CAPM. Finally, we tested the explanatory power of the marginal return to cost of capital ratio compared to the marginal performance spread (the difference between the marginal return on capital and the cost of capital). The results of difference tests, Cox tests, and J tests of Davidson and MacKinnon (1981) show that the marginal return to cost of capital ratio from the DRIM is the most valuable indicator of value creation.
{"title":"The Most Relevant Value Creation Indicator Under Competitive Dynamics of the Firm","authors":"Chawki Mouelhi, J. Saint-Pierre","doi":"10.2139/ssrn.2266050","DOIUrl":"https://doi.org/10.2139/ssrn.2266050","url":null,"abstract":"This paper shows the most relevant value creation indicator in a competitive economic equilibrium framework. We analyze the relationship between the cost of capital and the competitive dynamics of the firm. Several related propositions on the most relevant value creation indicator under a dynamic competitive setting are developed to establish the theoretical framework of the research hypotheses. A sample of 80 U.S. firms in convergence to equilibrium and cross section data are used in the empirical analysis. Firstly, we compare the costs of capital estimated from the CAPM with those from the Discounted Residual Income Model (DRIM). Using the competitive advantage period “T” as the forecast period in the DRIM, we have considered it as an ex ante model that takes into account the competitive dynamics of the firm. Secondly, we tested the explanatory power of the marginal return to cost of capital ratio from the DRIM compared to that of the CAPM. Finally, we tested the explanatory power of the marginal return to cost of capital ratio compared to the marginal performance spread (the difference between the marginal return on capital and the cost of capital). The results of difference tests, Cox tests, and J tests of Davidson and MacKinnon (1981) show that the marginal return to cost of capital ratio from the DRIM is the most valuable indicator of value creation.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126363660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use an empirical model to categorize firms into portfolios based on operational risk. Using these portfolios, we show that a strategy of buying firms in the highest decile of operational risk and shorting firms in the lowest decile of operational risk earned a positive but insignificant risk-adjusted average return of 0.72% per month from 1990 to 2000. However, from 2001 to 2010, the same strategy earned a significantly negative risk-adjusted average return of −1.50% per month. This change occurred during a time characterized by an increasing number of high profile operational losses and regulatory changes surrounding operational risk.
{"title":"Operational Risk and Equity Prices","authors":"Michael Shafer, Yildiray Yildirim","doi":"10.2139/ssrn.1960245","DOIUrl":"https://doi.org/10.2139/ssrn.1960245","url":null,"abstract":"We use an empirical model to categorize firms into portfolios based on operational risk. Using these portfolios, we show that a strategy of buying firms in the highest decile of operational risk and shorting firms in the lowest decile of operational risk earned a positive but insignificant risk-adjusted average return of 0.72% per month from 1990 to 2000. However, from 2001 to 2010, the same strategy earned a significantly negative risk-adjusted average return of −1.50% per month. This change occurred during a time characterized by an increasing number of high profile operational losses and regulatory changes surrounding operational risk.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124752009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the dividend optimization problem for a company where surplus in the absence of dividend payments follows a Cramer–Lundberg process compounded by constant force of interest. The company controls the times and amounts of dividend payments subject to reserve constraints that dividends are not payable if the surplus is below b0 and that a dividend payment, if any, cannot reduce the surplus to a level below b0, and its objective is to maximize the expected total discounted dividends. We show how the optimality can be achieved under the constraints and construct an optimal strategy of a band type.
{"title":"Dividend Optimization under Reserve Constraints for the Cramér-Lundberg Model Compounded by Force of Interest","authors":"Jinxia Zhu, Fenge Chen","doi":"10.2139/ssrn.2243913","DOIUrl":"https://doi.org/10.2139/ssrn.2243913","url":null,"abstract":"We study the dividend optimization problem for a company where surplus in the absence of dividend payments follows a Cramer–Lundberg process compounded by constant force of interest. The company controls the times and amounts of dividend payments subject to reserve constraints that dividends are not payable if the surplus is below b0 and that a dividend payment, if any, cannot reduce the surplus to a level below b0, and its objective is to maximize the expected total discounted dividends. We show how the optimality can be achieved under the constraints and construct an optimal strategy of a band type.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121102508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A one-dimensional partial differential-difference equation (pdde) under forward measure is developed to value European option under jump-diffusion, stochastic interest rate and local volatility. The corresponding forward Kolmogorov partial differential-difference equation for transition probability density is a also developed to value the options for various strikes at a given maturity time.The mathematical formulation of those equations is verified numerically by comparing their finite difference computation results with those of the Monte Carlo simulations. For the Kolmogorov equation, an alternate numerical method called the redistribution method is also developed. The redistribution method is based on the moments of the transition probability density and avoids some of the difficulties of a finite difference method.
{"title":"European Option Under Jump-Diffusion and Stochastic Interest Rate","authors":"S. Subramaniam","doi":"10.2139/ssrn.2072614","DOIUrl":"https://doi.org/10.2139/ssrn.2072614","url":null,"abstract":"A one-dimensional partial differential-difference equation (pdde) under forward measure is developed to value European option under jump-diffusion, stochastic interest rate and local volatility. The corresponding forward Kolmogorov partial differential-difference equation for transition probability density is a also developed to value the options for various strikes at a given maturity time.The mathematical formulation of those equations is verified numerically by comparing their finite difference computation results with those of the Monte Carlo simulations. For the Kolmogorov equation, an alternate numerical method called the redistribution method is also developed. The redistribution method is based on the moments of the transition probability density and avoids some of the difficulties of a finite difference method.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131964227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a general continuous-time mathematical framework for solution of dynamic mean–variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean–variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme’s symmetry on trading behavior and fund performance.
{"title":"Investment Strategies and Compensation of a Mean-Variance Optimizing Fund Manager","authors":"G. Aivaliotis, Jan Palczewski","doi":"10.2139/ssrn.1859289","DOIUrl":"https://doi.org/10.2139/ssrn.1859289","url":null,"abstract":"This paper introduces a general continuous-time mathematical framework for solution of dynamic mean–variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean–variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme’s symmetry on trading behavior and fund performance.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128897115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a general approximation method for the solutions to second-order parabolic partial differential equations (PDEs) widely used in finance through an extension of L'eandre's approach(L'eandre (2006,2008)) and the Bismut identiy(e.g. chapter IX-7 of Malliavin (1997)) in Malliavin calculus. We show two types of its applications, new approximations of derivatives prices and short-time asymptotic expansions of the heat kernel. In particular, we provide new approximation formulas for plain-vanilla and barrier option prices under stochastic volatility models. We also derive short-time asymptotic expansions of the heat kernel under general time-homogenous local volatility and local-stochastic volatility models in finance which include Heston (Heston (1993)) and (ƒE-)SABR models (Hagan et.al. (2002), Labordere (2008)) as special cases. Some numerical examples are shown.
{"title":"On Approximation of the Solutions to Partial Differential Equations in Finance","authors":"Akihiko Takahashi, T. Yamada","doi":"10.2139/ssrn.1915024","DOIUrl":"https://doi.org/10.2139/ssrn.1915024","url":null,"abstract":"This paper proposes a general approximation method for the solutions to second-order parabolic partial differential equations (PDEs) widely used in finance through an extension of L'eandre's approach(L'eandre (2006,2008)) and the Bismut identiy(e.g. chapter IX-7 of Malliavin (1997)) in Malliavin calculus. We show two types of its applications, new approximations of derivatives prices and short-time asymptotic expansions of the heat kernel. In particular, we provide new approximation formulas for plain-vanilla and barrier option prices under stochastic volatility models. We also derive short-time asymptotic expansions of the heat kernel under general time-homogenous local volatility and local-stochastic volatility models in finance which include Heston (Heston (1993)) and (ƒE-)SABR models (Hagan et.al. (2002), Labordere (2008)) as special cases. Some numerical examples are shown.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124572706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The theory of mean-variance based portfolio selection is a cornerstone of modern asset management. It rests on the assumption that rational investors choose among risky assets purely on the basis of expected return and risk, with risk measured as variance. The aim of this paper is to provide a foundation to such assumption in a general context of decision under uncertainty.
{"title":"Second Order Frechet Differential of Quasiconcave Monotone Normalized Functionals","authors":"Y. Shirai","doi":"10.2139/ssrn.2361563","DOIUrl":"https://doi.org/10.2139/ssrn.2361563","url":null,"abstract":"The theory of mean-variance based portfolio selection is a cornerstone of modern asset management. It rests on the assumption that rational investors choose among risky assets purely on the basis of expected return and risk, with risk measured as variance. The aim of this paper is to provide a foundation to such assumption in a general context of decision under uncertainty.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121320040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Investors face the challenge of understanding changes in risk. Did a recent increase in risk come from turnover into more aggressive positions, a spike in market volatility, or a loss of diversification? Which of the investor’s positions drove the change? Which parts of the market became more risky? A related issue is understanding differences among risk models. Do such differences indicate a weakness of one of the models, or do they provide insight into the evolving structure of the markets? The delta-sigma attribution framework addresses these issues by relating a change in risk to the underlying portfolio and market variables driving the change.
{"title":"Delta-Sigma Attribution: Understanding Differences in Risk","authors":"Peter Shepard","doi":"10.2139/ssrn.1915331","DOIUrl":"https://doi.org/10.2139/ssrn.1915331","url":null,"abstract":"Investors face the challenge of understanding changes in risk. Did a recent increase in risk come from turnover into more aggressive positions, a spike in market volatility, or a loss of diversification? Which of the investor’s positions drove the change? Which parts of the market became more risky? A related issue is understanding differences among risk models. Do such differences indicate a weakness of one of the models, or do they provide insight into the evolving structure of the markets? The delta-sigma attribution framework addresses these issues by relating a change in risk to the underlying portfolio and market variables driving the change.","PeriodicalId":129812,"journal":{"name":"Financial Engineering eJournal","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115406172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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