Factors explaining movements in the implied volatility surface

This article explores the relationship of changes in the S&P 500 index implied volatility surface to economic state variables. Observable variables can explain some of the variation in implied volatility, with the majority of explanatory power from index returns. Although the contemporaneous return is most important for explaining changes in short dated volatility, the path of the index is important for explaining changes in long dated volatility. Other variables also display statistically significant relations to volatility changes. Shocks to the Nikkei 225, short‐term interest rates, and the corporate/government bond yield spread are correlated with small, systematic changes in implied volatility. The results suggest a multifactor model for market volatility, with factors other than index returns adding negligible explanatory ability. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:915–937, 2002     

Regime‐switching in stock index and Treasury futures returns and measures of stock market stress

We investigate bivariate regime‐switching in daily futures‐contract returns for the US stock index and ten‐year Treasury notes over the crisis‐rich 1997–2005 period. We allow the return means, volatilities, and correlation to all vary across regimes. We document a striking contrast between regimes, with a high‐stress regime that exhibits a much higher stock volatility, a much lower stock–bond correlation, and a higher mean bond return. The high‐stress regime is associated with higher average values of stock‐implied volatility, stock illiquidity, and stock and bond futures trading volume. The lagged implied volatility from equity‐index options is useful in modeling the time‐varying transition probabilities of the regime‐switching process. Our findings support the notions that: (1) stock market stress can have a material influence on Treasury bond pricing, and (2) the diversification benefits of combined stock–bond holdings tend to be greater during times with relatively high stock market stress. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:753–779, 2010     

Identifying the Factors that Affect Interest‐Rate Swap Spreads: Some Evidence from the United States and the United Kingdom

We assess the ability of the factors proposed in previous research to account for the stochastic evolution of the term structure of the U.S. and U.K. swap spreads. Using as factor proxies the level, volatility, and slope of the zero‐coupon government yield curve as well as the Treasury‐bill—London Interbank Offer Rate (LIBOR) spread and the corporate bond spread, we identify a procyclical behavior for the short‐maturity U.S. swap spreads and a countercyclical behavior for longer maturity U.S. swap spreads. Liquidity and corporate bond spreads are also significant, but their importance varies with maturity. The liquidity premium is more important for short‐maturity swap spreads, although the corporate bond spread affects long‐maturity swap spreads. For the United Kingdom, swap spreads are countercyclical across maturities. In addition, we find that shocks to the liquidity premium are more significant for long‐maturity swaps and that the links between corporate bond markets and swap markets are much stronger than in the United States. When we look at the links between U.S. and U.K. swap markets, we identify a significant influence of the U.S. factors on the U.K. swap spreads across maturities. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:737–768, 2001     

The Co‐Movement of Credit Default Swap Spreads,Equity Returns and Volatility: Evidence from Asia‐Pacific Markets

We provide a comprehensive analysis of the co‐movement of credit default swap (CDS), equity, and volatility markets in four Asia‐Pacific countries at firm and index level during the period 2007–2010. First, we examine lead–lag relationships between CDS spread changes, equity returns, and changes in volatility using a vector autoregressive model. At the firm level equity returns lead changes in CDS spreads and realized volatility. However, at the index level the intertemporal linkages between the three markets are less clear‐cut. Second, we apply the measures proposed by Diebold and Yilmaz (2014) to an analysis of volatility spillovers among the CDS, equities, and volatility asset classes. The results suggest that realized volatility (at firm level) and implied volatility (at index level) are the main transmitters of cross‐market volatility spillovers. Third, we analyze the impact of various structural factors and confirm the importance of realized volatility of equity returns as a determinant of CDS spreads.     

A UNIFIED FRAMEWORK FOR PRICING CREDIT AND EQUITY DERIVATIVES

We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid, or over‐the‐counter derivatives. We observe that our model matches the equity option implied volatility surface well since we properly account for the default risk in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque et al., which only accounts for stochastic volatility.     

Examining the Return–Volatility Relation for Foreign Exchange: Evidence from the Euro VIX

We compare the return–volatility relation for the euro currency to the equivalent relation for the equity market, examining the sign, symmetry, and strength of the relation. We employ the euro‐currency exchange‐traded fund (FXE) and its associated option implied volatility index (the EVZ), whereas previous studies only employ equities and/or realized volatility. The equity studies find a negative asymmetric return–volatility relation for implied volatility, with a strong relation when large market movements occur. We find that the euro return–volatility relation can possess either a positive or negative sign, is asymmetric, and has a weaker relation. Thus, the sign and strength of the euro relation differs from the equivalent equity relation. Our quantile regressions show that both the positive and negative contemporaneous returns of the euro result in increased volatility in the extreme quantiles of the conditional distribution, with the contemporaneous effect showing a stronger relation when the euro depreciates. We also find that the volume of the euro‐currency ETF options affects the return–volatility relation for the euro ETF. Overall, the results here expand the concept originally restricted to equities, with the surprising results that the return‐implied volatility relation is weaker and the asymmetric return sometimes is positive for the euro currency. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:74–92, 2014     

Are single stock futures used as an alternative during a short‐selling ban?

The response of the single stock futures (SSF) market to a short‐selling ban is investigated. The hypothesis is that traders use SSF as a substitute instrument for short‐selling. A significant increase in SSF trading activity is documented, accompanied by narrower spreads. SSF market volatility did not react during the ban, which suggests that the increased trading activity did not weaken SSF market quality. The quality of the underlying market during the ban period is also assessed, with the results suggesting that changes in SSF market activity had neither positive nor negative effects on the stocks’ liquidity, volatility, and volume.     

CREDIT SPREADS, OPTIMAL CAPITAL STRUCTURE, AND IMPLIED VOLATILITY WITH ENDOGENOUS DEFAULT AND JUMP RISK

We propose a two-sided jump model for credit risk by extending the Leland–Toft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) Jumps and endogenous default can produce a variety of non-zero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The two-sided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; although in general credit spreads and implied volatility tend to move in the same direction under exogenous default models, this may not be true in presence of endogenous default and jumps. Pricing formulae of credit default swaps and equity default swaps are also given. In terms of mathematical contribution, we give a proof of a version of the "smooth fitting" principle under the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model.     

Quantile Regression Analysis of the Asymmetric Return‐Volatility Relation

We use quantile regression to investigate the short‐term return‐volatility relation between stock index returns and changes in implied volatility index. Neither the leverage hypothesis nor the volatility feedback hypothesis effectively explains the asymmetric return‐volatility relation. Instead, behavioral explanations, such as the affect and representativeness heuristics, are supported by our results, particularly in the short‐term; the affect heuristic plays an important role. Moreover, in the context of an extreme volatility change distribution, the affect heuristic and time‐pressure dominate. Thus, we observe strong negative and asymmetric relations between each volatility index and its corresponding stock market index. The asymmetry increases monotonically from the median quantile to the uppermost quantile (i.e., 95%); therefore, ordinary least squares (OLS) regression underestimates this relation at upper quantiles. Additionally, the VIX presents the highest asymmetric return‐volatility relation, followed by the VSTOXX, VDAX, and VXN. Finally, the observed asymmetry is more pronounced with the new volatility index measure than with the old, at‐the‐money volatility index measure. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:235–265, 2013     

Vulnerable options,risky corporate bond,and credit spread

In the current literature, the focus of credit‐risk analysis has been either on the valuation of risky corporate bond and credit spread or on the valuation of vulnerable options, but never both in the same context. There are two main concerns with existing studies. First, corporate bonds and credit spreads are generally analyzed in a context where corporate debt is the only liability of the firm and a firm’s value follows a continuous stochastic process. This setup implies a zero short‐term spread, which is strongly rejected by empirical observations. The failure of generating non‐zero short‐term credit spreads may be attributed to the simplified assumption on corporate liabilities. Because a corporation generally has more than one type of liability, modeling multiple liabilities may help to incorporate discontinuity in a firm’s value and thereby lead to realistic credit term structures. Second, vulnerable options are generally valued under the assumption that a firm can fully pay off the option if the firm’s value is above the default barrier at the option’s maturity. Such an assumption is not realistic because a corporation can find itself in a solvent position at option’s maturity but with assets insufficient to pay off the option. The main contribution of this study is to address these concerns. The proposed framework extends the existing equity‐bond capital structure to an equity‐bond‐derivative setting and encompasses many existing models as special cases. The firm under study has two types of liabilities: a corporate bond and a short position in a call option. The risky corporate bond, credit spreads, and vulnerable options are analyzed and compared with their counterparts from previous models. Numerical results show that adding a derivative type of liability can lead to positive short‐term credit spreads and various shapes of credit‐spread term structures that were not possible in previous models. In addition, we found that vulnerable options need not always be worth less than their default‐free counterparts. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:301–327, 2001     

The impact of macroeconomic announcements on emerging market bonds

This paper examines how emerging market bonds react to macroeconomic announcements. Global bond spreads respond to rating actions and changes in U.S. interest rates rather than domestic data and policy announcements. All announcements affect market volatility. Macroeconomic data and policy announcements reduce uncertainty and stabilize spreads, while rating actions cause greater volatility. Results are robust to country-specific and panel analyses, assuming conditional variance and controlling for the surprise content of news. In subsamples, announcements matter less for countries with more transparent policies and higher credit ratings. In a crisis, rating actions become less important, and investors focus on simple and timely indicators.     

PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY

We solve in closed form a parsimonious extension of the Black–Scholes–Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets.     

Smiling less at LIFFE

This study investigates the structure of the implied volatility smile, using the prices of equity options traded on the LIFFE. First, the slope of the implied volatility curve is significantly negative for both individual stocks and index options, and the slope is less negative for longer‐term options. The implied volatility skew can be described by risk‐neutral skewness and kurtosis, with the former having the first‐order effect. Moreover, the implied volatility skew for individual stock options is less severe than for index options. Finally, the relationship between the real and risk‐neutral moments implied in option prices is significant. The results indicate that, for equity options traded on the LIFFE, the slope of the implied volatility skew is flatter than that on the Chicago Board of Exchange (CBOE). © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:57–81, 2008     

Updating the estimation of the supply of storage

An updated supply of storage is estimated to reflect recent developments in the literature. This study adds a measure of price variability, specifically implied volatility. It also adds a measure of the call‐option value to sell stocks before the end of the storage period, specifically a measure developed by Heaney (2002). The model is estimated for U.S. soybean stocks carried between crop years. A quadratic relationship is found between stocks to use ratio and implied volatility. A statistically significant, inverse, linear relationship is found between the storage‐cost–adjusted spread and the estimated call‐option value. This finding is consistent with the much debated idea that convenience yield is a return to storage that can offset losses from storage when intertemporal price spreads are negative. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:657–676, 2006     

The information content in implied idiosyncratic volatility and the cross‐section of stock returns: Evidence from the option markets

Current literature is inconclusive as to whether idiosyncratic risk influences future stock returns and the direction of the impact. Earlier studies are based on historical realized volatility. Implied volatilities from option prices represent the market's assessment of future risk and are likely a superior measure to historical realized volatility. Implied idiosyncratic volatilities on firms with traded options are used to examine the relationship between idiosyncratic volatility and future returns. A strong positive link was found between implied idiosyncratic risk and future returns. After considering the impact of implied idiosyncratic volatility, historical realized idiosyncratic volatility is unimportant. This performance is strongly tied to small size and high book‐to‐market equity firms. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 1013–1039, 2008     

INCORPORATING RISK AND AMBIGUITY AVERSION INTO A HYBRID MODEL OF DEFAULT

It is well known that purely structural models of default cannot explain short‐term credit spreads, while purely intensity‐based models lead to completely unpredictable default events. Here we introduce a hybrid model of default, in which a firm enters a “distressed” state once its nontradable credit worthiness index hits a critical level. The distressed firm then defaults upon the next arrival of a Poisson process. To value defaultable bonds and credit default swaps (CDSs), we introduce the concept of robust indifference pricing. This paradigm incorporates both risk aversion and model uncertainty. In robust indifference pricing, the optimization problem is modified to include optimizing over a set of candidate measures, in addition to optimizing over trading strategies, subject to a measure dependent penalty. Using our model and valuation framework, we derive analytical solutions for bond yields and CDS spreads, and find that while ambiguity aversion plays a similar role to risk aversion, it also has distinct effects. In particular, ambiguity aversion allows for significant short‐term spreads.     

The Chinese interbank repo market: An analysis of term premiums

Because of the lack of short‐term government bonds, the interbank repo market in China has been providing the best information about market‐driven short‐term interest rates since its inception. This article examines the behavior of the repo rates of various terms and their term premiums. The work in this article supplements the study by F. Longstaff (2000), which reports supportive evidence for the pure expectations hypothesis over the short range of the term structure with the use of repo data from the United States. It is found that the pure expectations hypothesis is statistically rejected, although the term premiums are economically small. It is shown that the short‐term repo rate, repo rate volatility, repo market liquidity, and repo rate spreads are all important in determining the term premiums. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:153–167, 2006     

Counter‐Credit‐Risk Yield Spreads: A Puzzle in China's Corporate Bond Market

In this paper, using China's risk‐free and corporate zero yields together with aggregate credit risk measures and various control variables from 2006 to 2013, we document a puzzle of counter‐credit‐risk corporate yield spreads. We interpret this puzzle as a symptom of the immaturity of China's credit bond market, which reveals a distorted pricing mechanism latent in the fundamental of this market. We also find interesting results about relationships between corporate yield spreads and interest rates and risk premia and the stock index, and these results are somewhat attributed to this puzzle.     

Determinants of Japanese Yen interest rate swap spreads: Evidence from a smooth transition vector autoregressive model

This study investigates the determinants of variations in the yield spreads between Japanese yen interest rate swaps and Japan government bonds for a period from 1997 to 2005. A smooth transition vector autoregressive (STVAR) model and generalized impulse response functions are used to analyze the impact of various economic shocks on swap spreads. The volatility based on a GARCH (generalized autoregressive conditional heteroskedasticity) model of the government bond rate is identified as the transition variable that controls the smooth transition from a high volatility regime to a low volatility regime. The break point of the regime shift occurs around the end of the Japanese banking crisis. The impact of economic shocks on swap spreads varies across the maturity of swap spreads as well as regimes. Overall, swap spreads are more responsive to the economic shocks in the high volatility regime. Moreover, a volatility shock has profound effects on shorter maturity spreads, whereas the term structure shock plays an important role in impacting longer maturity spreads. Results of this study also show noticeable differences between the nonlinear and linear impulse response functions. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:82–107, 2008     

Estimation Uncertainty and the Equity Premium*

This paper studies a dynamic equilibrium model of asset prices in a partially observable exchange economy. It shows that the precautionary savings motive in response to estimation uncertainty can dominate the risk aversion effect, resulting in the reduction of the equity premium over short horizons. This exacerbates the equity premium puzzle. Over longer holding horizons, however, estimation uncertainty does induce higher risk premiums on equity over risk‐free coupon bonds of matching maturities, as long‐term bond yields are lowered due to the precautionary savings effect.