We test a theory that provides a simple and robust linkage between the market prices of credit default swaps (CDS) and far out-of-the-money equity American put options on the same reference company. The linkage is established under a general class of stock price dynamics. We assume that the stock price stays above a barrier B>0 before default but drops below a lower barrier A at default and stays blow A thereafter. We further assume that investors can take a static position in at least two American put options with the same expiry date and struck within this default corridor [A,B]. We show that a vertical spread of such options scaled by the spread between the two strikes replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the existence of the default corridor, this simple replicating strategy is robust to the details of pre- and post-default stock price dynamics, interest rate movements, and default risk fluctuations. We use the American put spread to infer risk-neutral default probabilities and compare them to those estimated from the CDS spreads. Collecting CDS and American stock options data on several companies, we identify strong co-movements between the risk-neutral default probabilities inferred from the two markets. We also find that deviations between the two estimates predict future movements in both markets. In particular, the cross-market deviations predict future returns on the American put spread that synthesizes the credit insurance contract.
{"title":"Simple Robust Linkages between CDS and Equity Options","authors":"P. Carr, Liuren Wu","doi":"10.2139/ssrn.1107986","DOIUrl":"https://doi.org/10.2139/ssrn.1107986","url":null,"abstract":"We test a theory that provides a simple and robust linkage between the market prices of credit default swaps (CDS) and far out-of-the-money equity American put options on the same reference company. The linkage is established under a general class of stock price dynamics. We assume that the stock price stays above a barrier B>0 before default but drops below a lower barrier A at default and stays blow A thereafter. We further assume that investors can take a static position in at least two American put options with the same expiry date and struck within this default corridor [A,B]. We show that a vertical spread of such options scaled by the spread between the two strikes replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the existence of the default corridor, this simple replicating strategy is robust to the details of pre- and post-default stock price dynamics, interest rate movements, and default risk fluctuations. We use the American put spread to infer risk-neutral default probabilities and compare them to those estimated from the CDS spreads. Collecting CDS and American stock options data on several companies, we identify strong co-movements between the risk-neutral default probabilities inferred from the two markets. We also find that deviations between the two estimates predict future movements in both markets. In particular, the cross-market deviations predict future returns on the American put spread that synthesizes the credit insurance contract.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115440877","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 propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.
{"title":"Variance Risk Premia","authors":"Liuren Wu, P. Carr","doi":"10.2139/ssrn.577222","DOIUrl":"https://doi.org/10.2139/ssrn.577222","url":null,"abstract":"We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126465138","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 estimate the market prices of economic risks from the stock market, while overcoming the challenges faced by existing studies. First, we use two dynamic factors, one real and the other nominal, to summarize the systematic information and to suppress the noise in a large array of economic indicators. Second, in linking systematic economic risks to stock returns, we carefully separate the cash flow effect from the pricing kernel effect. We first estimate the economic risk exposures for each individual stock, and then investigate how the expected return on each stock varies with its economic risk exposures. The different risk exposure estimates for different stocks capture the cash flow effect. How the expected stock return varies with the economic risk exposure reveals how the market prices the economic risks. Our estimation shows that the market charges a positive price for the real output growth risk, but a negative price for the inflation risk.
{"title":"Market Pricing of Economic Risks and Stock Returns","authors":"Liuren Wu, Yi Tang","doi":"10.2139/ssrn.1018661","DOIUrl":"https://doi.org/10.2139/ssrn.1018661","url":null,"abstract":"We estimate the market prices of economic risks from the stock market, while overcoming the challenges faced by existing studies. First, we use two dynamic factors, one real and the other nominal, to summarize the systematic information and to suppress the noise in a large array of economic indicators. Second, in linking systematic economic risks to stock returns, we carefully separate the cash flow effect from the pricing kernel effect. We first estimate the economic risk exposures for each individual stock, and then investigate how the expected return on each stock varies with its economic risk exposures. The different risk exposure estimates for different stocks capture the cash flow effect. How the expected stock return varies with the economic risk exposure reveals how the market prices the economic risks. Our estimation shows that the market charges a positive price for the real output growth risk, but a negative price for the inflation risk.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126716624","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 investigates asset pricing in a three-period overlapping generations (OLG) model economy where each generation lives as young, middle-aged and old. There is one perishable consumption good in the economy and two types of traded securities in the capital market: a bond and a share of equity. Implications for asset pricing and security returns of an increasing risk aversion are explored by allowing each agent's coefficient of relative risk aversion to vary with his age; the middle-aged consumer has a higher aversion to risk than the young and the old consumers are more risk averse than the middle-aged ones. Our model produces high equity premium without requiring very large levels of consumer risk aversion; a result more consistent with the U.S. data. We further modify our model to reflect the U.S. demographic trend of an increasing share of older age group. This new specification generates an even higher equity premium and a lower risk-free rate of return with an added desirable result of a lower standard deviation for the risk premium.
{"title":"Higher Risk Aversion in Older Agents: Its Asset Pricing Implications","authors":"Amadeu DaSilva, C. Giannikos","doi":"10.2139/ssrn.955958","DOIUrl":"https://doi.org/10.2139/ssrn.955958","url":null,"abstract":"This paper investigates asset pricing in a three-period overlapping generations (OLG) model economy where each generation lives as young, middle-aged and old. There is one perishable consumption good in the economy and two types of traded securities in the capital market: a bond and a share of equity. Implications for asset pricing and security returns of an increasing risk aversion are explored by allowing each agent's coefficient of relative risk aversion to vary with his age; the middle-aged consumer has a higher aversion to risk than the young and the old consumers are more risk averse than the middle-aged ones. Our model produces high equity premium without requiring very large levels of consumer risk aversion; a result more consistent with the U.S. data. We further modify our model to reflect the U.S. demographic trend of an increasing share of older age group. This new specification generates an even higher equity premium and a lower risk-free rate of return with an added desirable result of a lower standard deviation for the risk premium.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133476924","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 intertemporal capital asset pricing model of Merton (1973) states that the expected excess return on an asset is proportional to the expected covariance of the excess return on this asset with the excess return on the market portfolio. The proportionality coefficient measures the average relative risk aversion of investors. When the investment opportunity is stochastic, the expected excess return is also proportional to the covariance of the excess return with the state variables that govern the state of the investment opportunity. The proportionality coefficients on these covariance terms measure the investors' average aversion to unfavorable shifts in these state variables. In this paper, we use GARCH-type models to estimate the conditional covariance of a wide array of industry and Fama-French size/book-to-market portfolios with the market portfolio and with the Fama-French size (SMB) and book-to-market (HML) risk factors. We then estimate the system of simultaneous equations that links the excess returns on these portfolios to the corresponding conditional covariances with the market portfolio and the common risk factors. We obtain a positive and highly significant estimate for the relative risk aversion coefficient. The coefficient is about three for the long sample from July 1926 to December 2002, and is around six for the more recent period from July 1963 to December 2002. Furthermore, the expected excess returns are negatively related to their conditional covariance with the Fama-French size risk factor, suggesting that an increase in the size factor predicts an unfavorable shift in the investment opportunity. However, we do not find any consistent loading on the covariance with the book-to-market risk factor. Our findings are robust to different ways of forming portfolios and estimating conditional covariances. Most of the existing literature estimates the intertemporal risk-return relation using one single series of the market portfolio return. We show that the estimates from a single return series have low statistical significance and large sample variation. Our key contribution here is to direct the attention of the literature to the cross-sectional consistency of the intertemporal asset pricing relation and the universal proportionality underlying the risk-return relation. By exploiting this universal relation, we obtain positive and highly significant estimates on the relative risk aversion coefficient. We also gain a better understanding on how different risk factors predict future movements in investment opportunities.
{"title":"Estimating the Intertemporal Capital Asset Pricing Model with Cross-Sectional Consistency","authors":"Turan G. Bali, Liuren Wu","doi":"10.2139/ssrn.683867","DOIUrl":"https://doi.org/10.2139/ssrn.683867","url":null,"abstract":"The intertemporal capital asset pricing model of Merton (1973) states that the expected excess return on an asset is proportional to the expected covariance of the excess return on this asset with the excess return on the market portfolio. The proportionality coefficient measures the average relative risk aversion of investors. When the investment opportunity is stochastic, the expected excess return is also proportional to the covariance of the excess return with the state variables that govern the state of the investment opportunity. The proportionality coefficients on these covariance terms measure the investors' average aversion to unfavorable shifts in these state variables. In this paper, we use GARCH-type models to estimate the conditional covariance of a wide array of industry and Fama-French size/book-to-market portfolios with the market portfolio and with the Fama-French size (SMB) and book-to-market (HML) risk factors. We then estimate the system of simultaneous equations that links the excess returns on these portfolios to the corresponding conditional covariances with the market portfolio and the common risk factors. We obtain a positive and highly significant estimate for the relative risk aversion coefficient. The coefficient is about three for the long sample from July 1926 to December 2002, and is around six for the more recent period from July 1963 to December 2002. Furthermore, the expected excess returns are negatively related to their conditional covariance with the Fama-French size risk factor, suggesting that an increase in the size factor predicts an unfavorable shift in the investment opportunity. However, we do not find any consistent loading on the covariance with the book-to-market risk factor. Our findings are robust to different ways of forming portfolios and estimating conditional covariances. Most of the existing literature estimates the intertemporal risk-return relation using one single series of the market portfolio return. We show that the estimates from a single return series have low statistical significance and large sample variation. Our key contribution here is to direct the attention of the literature to the cross-sectional consistency of the intertemporal asset pricing relation and the universal proportionality underlying the risk-return relation. By exploiting this universal relation, we obtain positive and highly significant estimates on the relative risk aversion coefficient. We also gain a better understanding on how different risk factors predict future movements in investment opportunities.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125205733","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 present a dynamic term structure model in which interest rates of all maturities are bounded from below at zero. Positivity and continuity, combined with no arbitrage, result in only one functional form for the term structure with three sources of risk. One dynamic factor controls the level of the interest rate and follows a special two-parameter square-root process under the risk-neutral measure. The two parameters of the process determine the other two sources of risk and act as two static factors. This model has no other parameters to estimate and hence bears no other risks.
{"title":"Taking Positive Interest Rates Seriously","authors":"Enlin Pan, Liuren Wu","doi":"10.2139/ssrn.585461","DOIUrl":"https://doi.org/10.2139/ssrn.585461","url":null,"abstract":"We present a dynamic term structure model in which interest rates of all maturities are bounded from below at zero. Positivity and continuity, combined with no arbitrage, result in only one functional form for the term structure with three sources of risk. One dynamic factor controls the level of the interest rate and follows a special two-parameter square-root process under the risk-neutral measure. The two parameters of the process determine the other two sources of risk and act as two static factors. This model has no other parameters to estimate and hence bears no other risks.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130782167","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 apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under appropriate measure change. We extend the traditional measure theory into the complex domain and define the measure change by a class of complex valued exponential martingales. We provide extensive examples to illustrate its applications and its link to existing models in the literature.
{"title":"Time-Changed Levy Process and Option Pricing","authors":"P. Carr, Liuren Wu","doi":"10.2139/ssrn.283999","DOIUrl":"https://doi.org/10.2139/ssrn.283999","url":null,"abstract":"We apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under appropriate measure change. We extend the traditional measure theory into the complex domain and define the measure change by a class of complex valued exponential martingales. We provide extensive examples to illustrate its applications and its link to existing models in the literature.","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128675118","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}
Pub Date : 1999-09-01DOI: 10.1016/S1044-0283(99)00013-7
L. Rodriguez, Terrence F. Martell, Gwendolyn P. Webb
{"title":"The Impact of Listing Latin American ADRs on the Risks and Returns of the Underlying Shares","authors":"L. Rodriguez, Terrence F. Martell, Gwendolyn P. Webb","doi":"10.1016/S1044-0283(99)00013-7","DOIUrl":"https://doi.org/10.1016/S1044-0283(99)00013-7","url":null,"abstract":"","PeriodicalId":433580,"journal":{"name":"Baruch: Finance (Topic)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124715587","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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