Liuren Wu - Academia.edu (original) (raw)

Papers by Liuren Wu

Research paper thumbnail of Predicting Stock Return Variance in a Large Cross Section

SSRN Electronic Journal

The accuracy of variance prediction depends both on the validity of the specification and the acc... more The accuracy of variance prediction depends both on the validity of the specification and the accuracy of parameter estimation. Facing the unique challenges of predicting stock return variance in a large and varying universe, this paper proposes a conditional pooling approach that balances the need for reducing estimation errors while also allowing dynamics variation both cross-sectionally and over time. We start by specifying a cross-sectional forecasting relation at each date to better match the large and varying nature of the stock universe. We allow the relation to vary across names through conditionally weighted cross-sectional regressions. We show that the variance dynamics vary across different phases of a company's information cycle and we use the historical variance term structure shape as conditioning variables to capture the phase differences in the information cycles of different names. Furthermore, we use the aggregate market variance term structure shape to capture the market condition and allow the forecasting dynamics to vary with market conditions via conditionally weighted averaging of historical coefficient estimates. The proposed estimation procedure reduces estimation errors via two-dimensional pooling, while also accommodates dynamics variation across both dimensions. A historical analysis of nearly a century worth of the US stock market data highlights the importance of two-dimensional pooling in reducing estimation errors, while also identifies large time-series and cross-sectional variations in the stock return variance dynamics. Our conditional pooling approach captures the benefits of both worlds, and greatly enhances the out-of-sample variance forecasting performance against standard benchmarks.

Research paper thumbnail of Multifrequency Cascade Interest Rate Dynamics and Dimension-Invariant Term Structures

We develop a class of dynamic term structure models that acco mmodates arbitrarily many interest-... more We develop a class of dynamic term structure models that acco mmodates arbitrarily many interest-rate factors with very few parameters. The model builds on a casca de interest-rate dynamics that naturally ranks the factors by their rates of mean reversion, with each revolving around the next lower-frequency factor. The model further achieves dimension invariance by parameterizing the distributions of coefficients of the different frequency components. The net result is a cl ass of term structure models with merely five parameters regardless of the number of factors. Using a pane l of 15 LIBOR and swap rates, we estimate 15 models with one to 15 factors. The extensive estimation exer cis shows that the 15-factor model significantly outperforms the other lower-dimensional specifications. T he high-dimensional specification generates root mean squared pricing errors less than one basis point, thus m aking it an ideal candidate as a basis for forward rate curve stripping. The model also...

Research paper thumbnail of Targets, Predictability, and Performance

SSRN Electronic Journal, 2020

We study market-timing strategies on a given portfolio to achieve a particular risk or return tar... more We study market-timing strategies on a given portfolio to achieve a particular risk or return target. Targeting a constant risk level leads to increasing investment at better investment opportunities whereas targeting a constant expected return does the opposite. Theoretical and numerical analysis shows that, within the usual ranges of investment opportunities, risk targeting generates better unconditional performance than return targeting across a wide range of metrics. Empirical analysis with commonly constructed stock portfolios further highlights the practical infeasibility of return targeting due to the inherently low out-of-sample predicting power. By contrast, risk targeting tends to enhance unconditional stability and performance.

Research paper thumbnail of Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

SSRN Electronic Journal, 2004

This paper proposes a stylized model that reconciles several seemingly conflicting findings on fi... more This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Lévy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps, and also different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements, but the maximally allowable premium on downward index movements.

Research paper thumbnail of Anchoring Credit Default Swap Spreads to Firm Fundamentals

SSRN Electronic Journal, 2012

This paper examines the capability of firm fundamentals in explaining the cross-sectional variati... more This paper examines the capability of firm fundamentals in explaining the cross-sectional variation of credit default swap (CDS) spreads. We start with the Merton (1974) model, which combines two major credit risk determinants, financial leverage and stock return volatility, into a standardized distance-to-default measure. We convert the distance-to-default measure into a raw CDS valuation and map the raw CDS valuation to the market observation via a cross-sectional nonparametric regression, removing the average bias of the raw valuation at different risk levels. We also collect a long list of firm fundamental characteristics that are not included in the Merton-based valuation but have been shown to be informative about a firm's credit spread, and propose a Bayesian shrinkage method to combine the Merton-based valuation with the information from this long list of fundamental characteristics. Historical analysis on 579 U.S. non-financial public firms over six and a half years shows that a linear regression of the market CDS against the two Merton model inputs only explains 49% of the cross-sectional CDS variation on average. By contrast, the bias-corrected Merton-modelbased valuation raises the average explanatory power to 65%. Incorporating additional firm fundamental characteristics further increases the average explanatory power to 77% while also making the performance more uniform over time. Finally, deviations between market observations and fundamental-based valuations generate statistically and economically significant forecasts on future market movements in credit default swap spreads.

Research paper thumbnail of Centrality of the Supply Chain Network

SSRN Electronic Journal, 2015

Research paper thumbnail of The Potential Approach to Bond and Currency Pricing

SSRN Electronic Journal, 1999

In this paper, we begin the modeling of bond and currency prices from the modeling of the state-p... more In this paper, we begin the modeling of bond and currency prices from the modeling of the state-price density satisfying basic properties of a potential. We provide extensive examples and show their implications on bond and currency pricing. Most classic short rate models are special cases of this general approach. We also investigate the connection to the Heath, Jarrow, and Morton model. One advantage of the potential approach resides in its ease in simultaneously modeling the yield curves of many countries and their exchange rates. The properties of exchange rates under each example are derived and we illustrate their possibility in explaining the forward premium puzzle.

Research paper thumbnail of Taking Positive Interest Rates Seriously

SSRN Electronic Journal, 2003

We propose a dynamic term structure model where interest rates of all maturities are bounded from... more We propose a dynamic term structure model where interest rates of all maturities are bounded from below at zero. We show that positivity and continuity, combined with no arbitrage, impose such a tight restriction on the term structure that only one functional form is possible. Even more strikingly, the term structure is governed by exactly three sources of risk, only one of which is dynamic. This one dynamic source controls the level of the interest rate and follows a special twoparameter square root process under the risk-neutral measure. The two parameters of the process determine the other two sources of risk and can be regarded as two static factors. Thus, unlike traditional models, this has no other parameters to estimate and hence no other risks to bear. We cast the model into a state space framework and estimate the model on both U.S. Treasury yields and U.S. dollar swap rates. Despite its extreme simplicity, the model fits the term structures of both markets well. The pricing errors are mostly within a few basis points.

Research paper thumbnail of Dynamic Interactions Between Interest Rate, Credit, and Liquidity Risks: Theory and Evidence from the Term Structure of Credit Default Swap Spreads

SSRN Electronic Journal, 2005

Using a large data set on credit default swaps, we study how default risk interacts with interest... more Using a large data set on credit default swaps, we study how default risk interacts with interest-rate risk and liquidity risk to jointly determine the term structure of credit spreads. We classify the reference companies into two broad industry sectors, two broad credit rating classes, and two liquidity groups. We develop a class of dynamic term structure models that include (i) two benchmark interest-rate factors to capture the libor and swap rates term structure, (ii) two credit-risk factors to capture the credit swap spreads of high-liquidity group of each industry and rating class, and (iii) both an additional credit-risk factor and a liquidity-risk factor to capture the difference between the high-and low-liquidity groups. Estimation shows that companies in different industry and credit rating classes have different credit-risk dynamics. Nevertheless, in all cases, credit risks exhibit intricate dynamic interactions with the interestrate factors. Interest-rate factors both affect credit spreads simultaneously, and impact subsequent moves in the credit-risk factors. Within each industry and credit rating class, we also find that the average credit default swap spreads for the high-liquidity group are significantly higher than for the low-liquidity group. Estimation shows that the difference is driven by both credit risk and liquidity differences. The low-liquidity group has a lower default arrival rate and also a much heavier discounting induced by the liquidity risk.

Research paper thumbnail of Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions

SSRN Electronic Journal, 2011

Equity index volatility variation and its interaction with the index return can come from three d... more Equity index volatility variation and its interaction with the index return can come from three distinct channels. First, index volatility increases with the market's aggregate financial leverage. Second, positive shocks to systematic risk increase the cost of capital and reduce the valuation of future cash flows, generating a negative correlation between the index return and its volatility, regardless of financial leverage. Finally, large negative market disruptions show self-exciting behaviors. This article proposes a model that incorporates all three channels and examines their relative contribution to index option pricing and stock option pricing for different types of companies.

Research paper thumbnail of Variance Risk Premia

SSRN Electronic Journal, 2007

and Technology for comments and discussions. We assume full responsibility for any errors. We wel... more and Technology for comments and discussions. We assume full responsibility for any errors. We welcome comments, including references we have inadvertently missed.

Research paper thumbnail of Variance Risk Dynamics, Variance Risk Premia, and Optimal Variance Swap Investments

SSRN Electronic Journal, 2007

Research paper thumbnail of Price Discovery in the U.S. Stock Options Market

SSRN Electronic Journal, 2004

* We thank Automated Trading Desk, LLC for providing data and computing assistance. We thank Robe... more * We thank Automated Trading Desk, LLC for providing data and computing assistance. We thank Robert Battalio, Joel Hasbrouck, Charles Jones, Maureen O'Hara, Martin Resch, Dan Weaver, David Whitcomb, and seminar participants at the 2003 Western Finance Association and the 2003 European Finance Association for insightful comments. We also thank Eric Crampton for help on the data preprocessing, and Sandra Size Moore for copy editing. Part of the results in this paper were circulated in an earlier draft titled "Price Discovery in the Equity Options Market: An Integrated Analysis of Trades and Quotes."

Research paper thumbnail of Crash-O-Phobia: A Domestic Fear or A Worldwide Concern?

SSRN Electronic Journal, 2005

From an options data set on 12 major equity indexes around the world, we find that worldwide, opt... more From an options data set on 12 major equity indexes around the world, we find that worldwide, options on equity indexes exhibit strikingly similar behaviors that present challenges for option modeling. Along the moneyness dimension, implied volatilities underlying all major equity indexes exhibit a heavily skewed average pattern, implying that the out-of-the-money put options are more expensive than the corresponding out-of-the-money call options, and that the risk-neutral distribution for these index returns are heavily negatively skewed. Along the maturity dimension, the average implied volatility smirk does not flatten out as the option maturity increases from one month up to five years. Instead, the smirk steepens, indicating that the conditional return distribution becomes even more negatively skewed at longer horizons. Time series analysis of the implied volatility series indicates that the volatility processes are stationary under both the objective measure and the risk-neutral measure. The mean term structure of the implied volatility level is quite flat, and the standard deviation of the volatility level declines readily with increasing maturity. Finally, principal component analysis on the whole panel of data indicates that there exists one global factor governing the movement of the volatility level, but the variations in the shape of the implied volatility smirk are largely country-specific, even though the average shape of the volatility smirk is strikingly similar across different equity indexes.

Research paper thumbnail of Accounting for Biases in Black-Scholes

SSRN Electronic Journal, 2004

Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: i... more Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at-the-money options increases, on average, with maturity). We account for both using Gram-Charlier expansions to approximate the conditional distribution of the logarithm of the price of the underlying security. In this setting, volatility is approximately a quadratic function of moneyness, a result we use to infer skewness and kurtosis from volatility smiles. Evidence suggests that both kurtosis in currency prices and biases in Black-Scholes option prices decline with maturity.

Research paper thumbnail of Simple Robust Hedging with Nearby Contracts

SSRN Electronic Journal, 2011

Most existing hedging approaches are based on neutralizing risk exposures defined under a pre-spe... more Most existing hedging approaches are based on neutralizing risk exposures defined under a pre-specified model. This paper proposes a new, simple, and robust hedging approach based on the affinity of the derivative contracts. As a result, the strategy does not depend on assumptions on the underlying risk dynamics. Simulation analysis under commonly proposed security price dynamics shows that the hedging performance of our methodology based on a static position of three options compares favorably against the dynamic delta hedging strategy with daily rebalancing. A historical hedging exercise on S&P 500 index option further highlights the superior performance of our strategy.

Research paper thumbnail of Imports, Exports, Dollar Exposures, and Stock Returns

SSRN Electronic Journal, 2011

We measure the dollar risk exposure of US industries by regressing stock portfolio returns on eac... more We measure the dollar risk exposure of US industries by regressing stock portfolio returns on each industry against the returns on a broadly defined dollar index. The exposure estimates vary widely across different industries in both magnitudes and directions. We trace this large cross-sectional variation in dollar exposure to the industry's average import and export activities. We find that the dollar exposure increases with imports but decreases with exports. On average, dollar appreciation helps the stock performance of import-oriented companies but hurts the stock performance of export-oriented companies. Based on this finding, we propose a methodology to combine the information in imports, exports, and stock returns to enhance the identification of the dollar risk exposure for different industries, and we analyze how each industry's expected stock return varies with its dollar exposure. We identify a strongly negative risk premium for bearing positive exposures to the dollar, and we find that the risk premium moves with the business cycle and becomes more negative during recessions.

Research paper thumbnail of Variance Risk Premiums

Review of Financial Studies, 2008

We propose a direct and robust method for quantifying the variance risk premium on financial asse... more We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the risk-neutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks. (JEL G10, G12, G13) We thank Yacine Aït-Sahalia (the editor), an anonymous referee, and

Research paper thumbnail of A No-Arbitrage Analysis of Macroeconomic Determinants of the Credit Spread Term Structure

Management Science, 2008

From a large array of economic and financial data series, this paper identifies three fundamental... more From a large array of economic and financial data series, this paper identifies three fundamental risk dimensions underlying an economy: inflation, real output growth, and financial market volatility. Furthermore, through a no-arbitrage model, the paper links the dynamics and market pricing of the three risk dimensions to the term structure of U.S. Treasury yields and corporate bond credit spreads. Model estimation shows that positive inflation shocks increase Treasury yields and widen credit spreads on corporate bonds across all maturities and credit-rating classes. Positive real output growth shocks also increase Treasury yields, but they suppress the credit spreads at low credit-rating classes, thus generating negative correlations between interest rates and credit spreads. The financial market volatility factor has a small and transient effect on the Treasury yield curve, but it exerts a strongly positive and persistent effect on the credit spread term structure. The paper provi...

Research paper thumbnail of Uncovered interest-rate parity over the past two centuries

Journal of International Money and Finance, 2011

for helpful comments and suggestions. We welcome comments, including references to related papers... more for helpful comments and suggestions. We welcome comments, including references to related papers we have inadvertently overlooked.

Research paper thumbnail of Predicting Stock Return Variance in a Large Cross Section

SSRN Electronic Journal

The accuracy of variance prediction depends both on the validity of the specification and the acc... more The accuracy of variance prediction depends both on the validity of the specification and the accuracy of parameter estimation. Facing the unique challenges of predicting stock return variance in a large and varying universe, this paper proposes a conditional pooling approach that balances the need for reducing estimation errors while also allowing dynamics variation both cross-sectionally and over time. We start by specifying a cross-sectional forecasting relation at each date to better match the large and varying nature of the stock universe. We allow the relation to vary across names through conditionally weighted cross-sectional regressions. We show that the variance dynamics vary across different phases of a company's information cycle and we use the historical variance term structure shape as conditioning variables to capture the phase differences in the information cycles of different names. Furthermore, we use the aggregate market variance term structure shape to capture the market condition and allow the forecasting dynamics to vary with market conditions via conditionally weighted averaging of historical coefficient estimates. The proposed estimation procedure reduces estimation errors via two-dimensional pooling, while also accommodates dynamics variation across both dimensions. A historical analysis of nearly a century worth of the US stock market data highlights the importance of two-dimensional pooling in reducing estimation errors, while also identifies large time-series and cross-sectional variations in the stock return variance dynamics. Our conditional pooling approach captures the benefits of both worlds, and greatly enhances the out-of-sample variance forecasting performance against standard benchmarks.

Research paper thumbnail of Multifrequency Cascade Interest Rate Dynamics and Dimension-Invariant Term Structures

We develop a class of dynamic term structure models that acco mmodates arbitrarily many interest-... more We develop a class of dynamic term structure models that acco mmodates arbitrarily many interest-rate factors with very few parameters. The model builds on a casca de interest-rate dynamics that naturally ranks the factors by their rates of mean reversion, with each revolving around the next lower-frequency factor. The model further achieves dimension invariance by parameterizing the distributions of coefficients of the different frequency components. The net result is a cl ass of term structure models with merely five parameters regardless of the number of factors. Using a pane l of 15 LIBOR and swap rates, we estimate 15 models with one to 15 factors. The extensive estimation exer cis shows that the 15-factor model significantly outperforms the other lower-dimensional specifications. T he high-dimensional specification generates root mean squared pricing errors less than one basis point, thus m aking it an ideal candidate as a basis for forward rate curve stripping. The model also...

Research paper thumbnail of Targets, Predictability, and Performance

SSRN Electronic Journal, 2020

We study market-timing strategies on a given portfolio to achieve a particular risk or return tar... more We study market-timing strategies on a given portfolio to achieve a particular risk or return target. Targeting a constant risk level leads to increasing investment at better investment opportunities whereas targeting a constant expected return does the opposite. Theoretical and numerical analysis shows that, within the usual ranges of investment opportunities, risk targeting generates better unconditional performance than return targeting across a wide range of metrics. Empirical analysis with commonly constructed stock portfolios further highlights the practical infeasibility of return targeting due to the inherently low out-of-sample predicting power. By contrast, risk targeting tends to enhance unconditional stability and performance.

Research paper thumbnail of Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns

SSRN Electronic Journal, 2004

This paper proposes a stylized model that reconciles several seemingly conflicting findings on fi... more This paper proposes a stylized model that reconciles several seemingly conflicting findings on financial security returns and option prices. The model is based on a pure jump Lévy process, wherein the jump arrival rate obeys a power law dampened by an exponential function. The model allows for different degrees of dampening for positive and negative jumps, and also different pricing for upside and downside market risks. Calibration of the model to the S&P 500 index shows that the market charges only a moderate premium on upward index movements, but the maximally allowable premium on downward index movements.

Research paper thumbnail of Anchoring Credit Default Swap Spreads to Firm Fundamentals

SSRN Electronic Journal, 2012

This paper examines the capability of firm fundamentals in explaining the cross-sectional variati... more This paper examines the capability of firm fundamentals in explaining the cross-sectional variation of credit default swap (CDS) spreads. We start with the Merton (1974) model, which combines two major credit risk determinants, financial leverage and stock return volatility, into a standardized distance-to-default measure. We convert the distance-to-default measure into a raw CDS valuation and map the raw CDS valuation to the market observation via a cross-sectional nonparametric regression, removing the average bias of the raw valuation at different risk levels. We also collect a long list of firm fundamental characteristics that are not included in the Merton-based valuation but have been shown to be informative about a firm's credit spread, and propose a Bayesian shrinkage method to combine the Merton-based valuation with the information from this long list of fundamental characteristics. Historical analysis on 579 U.S. non-financial public firms over six and a half years shows that a linear regression of the market CDS against the two Merton model inputs only explains 49% of the cross-sectional CDS variation on average. By contrast, the bias-corrected Merton-modelbased valuation raises the average explanatory power to 65%. Incorporating additional firm fundamental characteristics further increases the average explanatory power to 77% while also making the performance more uniform over time. Finally, deviations between market observations and fundamental-based valuations generate statistically and economically significant forecasts on future market movements in credit default swap spreads.

Research paper thumbnail of Centrality of the Supply Chain Network

SSRN Electronic Journal, 2015

Research paper thumbnail of The Potential Approach to Bond and Currency Pricing

SSRN Electronic Journal, 1999

In this paper, we begin the modeling of bond and currency prices from the modeling of the state-p... more In this paper, we begin the modeling of bond and currency prices from the modeling of the state-price density satisfying basic properties of a potential. We provide extensive examples and show their implications on bond and currency pricing. Most classic short rate models are special cases of this general approach. We also investigate the connection to the Heath, Jarrow, and Morton model. One advantage of the potential approach resides in its ease in simultaneously modeling the yield curves of many countries and their exchange rates. The properties of exchange rates under each example are derived and we illustrate their possibility in explaining the forward premium puzzle.

Research paper thumbnail of Taking Positive Interest Rates Seriously

SSRN Electronic Journal, 2003

We propose a dynamic term structure model where interest rates of all maturities are bounded from... more We propose a dynamic term structure model where interest rates of all maturities are bounded from below at zero. We show that positivity and continuity, combined with no arbitrage, impose such a tight restriction on the term structure that only one functional form is possible. Even more strikingly, the term structure is governed by exactly three sources of risk, only one of which is dynamic. This one dynamic source controls the level of the interest rate and follows a special twoparameter square root process under the risk-neutral measure. The two parameters of the process determine the other two sources of risk and can be regarded as two static factors. Thus, unlike traditional models, this has no other parameters to estimate and hence no other risks to bear. We cast the model into a state space framework and estimate the model on both U.S. Treasury yields and U.S. dollar swap rates. Despite its extreme simplicity, the model fits the term structures of both markets well. The pricing errors are mostly within a few basis points.

Research paper thumbnail of Dynamic Interactions Between Interest Rate, Credit, and Liquidity Risks: Theory and Evidence from the Term Structure of Credit Default Swap Spreads

SSRN Electronic Journal, 2005

Using a large data set on credit default swaps, we study how default risk interacts with interest... more Using a large data set on credit default swaps, we study how default risk interacts with interest-rate risk and liquidity risk to jointly determine the term structure of credit spreads. We classify the reference companies into two broad industry sectors, two broad credit rating classes, and two liquidity groups. We develop a class of dynamic term structure models that include (i) two benchmark interest-rate factors to capture the libor and swap rates term structure, (ii) two credit-risk factors to capture the credit swap spreads of high-liquidity group of each industry and rating class, and (iii) both an additional credit-risk factor and a liquidity-risk factor to capture the difference between the high-and low-liquidity groups. Estimation shows that companies in different industry and credit rating classes have different credit-risk dynamics. Nevertheless, in all cases, credit risks exhibit intricate dynamic interactions with the interestrate factors. Interest-rate factors both affect credit spreads simultaneously, and impact subsequent moves in the credit-risk factors. Within each industry and credit rating class, we also find that the average credit default swap spreads for the high-liquidity group are significantly higher than for the low-liquidity group. Estimation shows that the difference is driven by both credit risk and liquidity differences. The low-liquidity group has a lower default arrival rate and also a much heavier discounting induced by the liquidity risk.

Research paper thumbnail of Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions

SSRN Electronic Journal, 2011

Equity index volatility variation and its interaction with the index return can come from three d... more Equity index volatility variation and its interaction with the index return can come from three distinct channels. First, index volatility increases with the market's aggregate financial leverage. Second, positive shocks to systematic risk increase the cost of capital and reduce the valuation of future cash flows, generating a negative correlation between the index return and its volatility, regardless of financial leverage. Finally, large negative market disruptions show self-exciting behaviors. This article proposes a model that incorporates all three channels and examines their relative contribution to index option pricing and stock option pricing for different types of companies.

Research paper thumbnail of Variance Risk Premia

SSRN Electronic Journal, 2007

and Technology for comments and discussions. We assume full responsibility for any errors. We wel... more and Technology for comments and discussions. We assume full responsibility for any errors. We welcome comments, including references we have inadvertently missed.

Research paper thumbnail of Variance Risk Dynamics, Variance Risk Premia, and Optimal Variance Swap Investments

SSRN Electronic Journal, 2007

Research paper thumbnail of Price Discovery in the U.S. Stock Options Market

SSRN Electronic Journal, 2004

* We thank Automated Trading Desk, LLC for providing data and computing assistance. We thank Robe... more * We thank Automated Trading Desk, LLC for providing data and computing assistance. We thank Robert Battalio, Joel Hasbrouck, Charles Jones, Maureen O'Hara, Martin Resch, Dan Weaver, David Whitcomb, and seminar participants at the 2003 Western Finance Association and the 2003 European Finance Association for insightful comments. We also thank Eric Crampton for help on the data preprocessing, and Sandra Size Moore for copy editing. Part of the results in this paper were circulated in an earlier draft titled "Price Discovery in the Equity Options Market: An Integrated Analysis of Trades and Quotes."

Research paper thumbnail of Crash-O-Phobia: A Domestic Fear or A Worldwide Concern?

SSRN Electronic Journal, 2005

From an options data set on 12 major equity indexes around the world, we find that worldwide, opt... more From an options data set on 12 major equity indexes around the world, we find that worldwide, options on equity indexes exhibit strikingly similar behaviors that present challenges for option modeling. Along the moneyness dimension, implied volatilities underlying all major equity indexes exhibit a heavily skewed average pattern, implying that the out-of-the-money put options are more expensive than the corresponding out-of-the-money call options, and that the risk-neutral distribution for these index returns are heavily negatively skewed. Along the maturity dimension, the average implied volatility smirk does not flatten out as the option maturity increases from one month up to five years. Instead, the smirk steepens, indicating that the conditional return distribution becomes even more negatively skewed at longer horizons. Time series analysis of the implied volatility series indicates that the volatility processes are stationary under both the objective measure and the risk-neutral measure. The mean term structure of the implied volatility level is quite flat, and the standard deviation of the volatility level declines readily with increasing maturity. Finally, principal component analysis on the whole panel of data indicates that there exists one global factor governing the movement of the volatility level, but the variations in the shape of the implied volatility smirk are largely country-specific, even though the average shape of the volatility smirk is strikingly similar across different equity indexes.

Research paper thumbnail of Accounting for Biases in Black-Scholes

SSRN Electronic Journal, 2004

Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: i... more Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at-the-money options increases, on average, with maturity). We account for both using Gram-Charlier expansions to approximate the conditional distribution of the logarithm of the price of the underlying security. In this setting, volatility is approximately a quadratic function of moneyness, a result we use to infer skewness and kurtosis from volatility smiles. Evidence suggests that both kurtosis in currency prices and biases in Black-Scholes option prices decline with maturity.

Research paper thumbnail of Simple Robust Hedging with Nearby Contracts

SSRN Electronic Journal, 2011

Most existing hedging approaches are based on neutralizing risk exposures defined under a pre-spe... more Most existing hedging approaches are based on neutralizing risk exposures defined under a pre-specified model. This paper proposes a new, simple, and robust hedging approach based on the affinity of the derivative contracts. As a result, the strategy does not depend on assumptions on the underlying risk dynamics. Simulation analysis under commonly proposed security price dynamics shows that the hedging performance of our methodology based on a static position of three options compares favorably against the dynamic delta hedging strategy with daily rebalancing. A historical hedging exercise on S&P 500 index option further highlights the superior performance of our strategy.

Research paper thumbnail of Imports, Exports, Dollar Exposures, and Stock Returns

SSRN Electronic Journal, 2011

We measure the dollar risk exposure of US industries by regressing stock portfolio returns on eac... more We measure the dollar risk exposure of US industries by regressing stock portfolio returns on each industry against the returns on a broadly defined dollar index. The exposure estimates vary widely across different industries in both magnitudes and directions. We trace this large cross-sectional variation in dollar exposure to the industry's average import and export activities. We find that the dollar exposure increases with imports but decreases with exports. On average, dollar appreciation helps the stock performance of import-oriented companies but hurts the stock performance of export-oriented companies. Based on this finding, we propose a methodology to combine the information in imports, exports, and stock returns to enhance the identification of the dollar risk exposure for different industries, and we analyze how each industry's expected stock return varies with its dollar exposure. We identify a strongly negative risk premium for bearing positive exposures to the dollar, and we find that the risk premium moves with the business cycle and becomes more negative during recessions.

Research paper thumbnail of Variance Risk Premiums

Review of Financial Studies, 2008

We propose a direct and robust method for quantifying the variance risk premium on financial asse... more We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the risk-neutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks. (JEL G10, G12, G13) We thank Yacine Aït-Sahalia (the editor), an anonymous referee, and

Research paper thumbnail of A No-Arbitrage Analysis of Macroeconomic Determinants of the Credit Spread Term Structure

Management Science, 2008

From a large array of economic and financial data series, this paper identifies three fundamental... more From a large array of economic and financial data series, this paper identifies three fundamental risk dimensions underlying an economy: inflation, real output growth, and financial market volatility. Furthermore, through a no-arbitrage model, the paper links the dynamics and market pricing of the three risk dimensions to the term structure of U.S. Treasury yields and corporate bond credit spreads. Model estimation shows that positive inflation shocks increase Treasury yields and widen credit spreads on corporate bonds across all maturities and credit-rating classes. Positive real output growth shocks also increase Treasury yields, but they suppress the credit spreads at low credit-rating classes, thus generating negative correlations between interest rates and credit spreads. The financial market volatility factor has a small and transient effect on the Treasury yield curve, but it exerts a strongly positive and persistent effect on the credit spread term structure. The paper provi...

Research paper thumbnail of Uncovered interest-rate parity over the past two centuries

Journal of International Money and Finance, 2011

for helpful comments and suggestions. We welcome comments, including references to related papers... more for helpful comments and suggestions. We welcome comments, including references to related papers we have inadvertently overlooked.