Are credit spreads too low or too high? A hybrid barrier option approach for financial distress

Based on the works of Brockman, P. and Turtle, H. J. (2003) and Giesecke, K. (2004), we propose in this study a hybrid barrier option model to explain observed credit spreads. It is free of problems with the structural model, which underprescribed credit spreads for investment grade corporate bonds and overprescribed the high‐yield issues. Unlike the standard barrier option approach, our hybrid model does not imply, for high‐yield issues with firms under financial stress, a reduction of credit spreads while firm value actually falls. Our empirical analysis supports that when credit spreads are quoted abnormally higher or rising faster than expected, unexpected changes tend to persist. Otherwise a significant and prompt reversion to long‐term equilibrium takes place. This asymmetric pricing phenomenon is validated with a method introduced by Enders, W. and Granger, C. W. J. (1998) and Enders, W. and Siklos, P. L. (2001). The pricing asymmetry could not have been produced by a structural model employing only standard option. But it is consistent with a hybrid barrier option model. Our model characterizes the valuation of debt under financial stress and the asymmetric price pattern better than both the classical structural and the standard barrier option approaches. It can be extended to the study of individual CDS for its better liquidity than individual corporate bonds. This study provides helpful implications especially for the medium and high‐yield issues in pricing as well as portfolio diversification. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:1161–1189, 2009     

Effects of rollover strategies and information stability on the performance measures in options markets: An examination of the KOSPI 200 index options market

One of the most widely used option valuation models among practitioners is the ad hoc Black–Scholes (AHBS) model. The main contribution of this study is methodological. We carefully consider two rollover strategies (nearest‐to‐next strategy and next‐to‐next) used in the AHBS model to investigate their effect on pricing errors. We suggest a new rollover strategy, next‐to‐next strategy, and demonstrate that our rollover strategy produces more consistent estimates between in‐sample market and model option prices. Probably even more important is that our new rollover strategy makes more accurate out‐of‐sample forecasts for 1‐day or 1‐week ahead prices. Prior literature has documented some anomalies associated with the use of AHBS model, for example, an overfitting problem. A secondary contribution is that our new rollover strategy does not suffer from this overfitting critique. Third, this study uses the mean square error for out‐of‐sample pricing and price changes to determine how the options investors are influenced by moneyness. The results indicate that underpricing (or overpricing) by the AHBS model for the near‐the‐money category is more likely to be maintained for the next several trading days but that such a phenomenon is disappeared for the deep out‐of‐the‐money category. Finally, we suggest the ratio of the number of option contracts to differences in strike prices available for trading between the current day and the previous day(s) as a good categorizing factor for options, such as moneyness. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

The performance of VIX option pricing models: Empirical evidence beyond simulation

We examine the pricing performance of VIX option models. Such models possess a wide‐range of underlying characteristics regarding the behavior of both the S&P500 index and the underlying VIX. Our tests employ three representative models for VIX options: Whaley ( 1993 ), Grunbichler and Longstaff ( 1996 ), Carr and Lee ( 2007 ), Lin and Chang ( 2009 ), who test four stochastic volatility models, as well as to previous simulation results of VIX option models. We find that no model has small pricing errors over the entire range of strike prices and times to expiration. In particular, out‐of‐the‐money VIX options are difficult to price, with Grunbichler and Longstaff's mean‐reverting model producing the smallest dollar errors in this category. Whaley's Black‐like option model produces the best results for in‐the‐money VIX options. However, the Whaley model does under/overprice out‐of‐the‐money call/put VIX options, which is opposite the behavior of stock index option pricing models. VIX options exhibit a volatility skew opposite the skew of index options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark31:251–281, 2011     

A Better Model? An Empirical Investigation of the Fama–French Five‐factor Model in Australia

Recently, Fama and French ( 2015a ) propose a five‐factor model by adding profitability and investment factors to their three‐factor model. This model outperforms the three‐factor model previously proposed by Fama and French ( 1993 ). Using an extensive sample over the 1982–2013 period, we investigate the performance of the five‐factor model in pricing Australian equities. We find that the five‐factor model is able to explain more asset pricing anomalies than a range of competing asset pricing models, which supports the superiority of the five‐factor model. We also find that despite the results documented by Fama and French ( 2015a ), the book‐to‐market factor retains its explanatory power in the presence of the investment and profitability factors. Our results are robust to alternative factor definitions and the formation of test assets. The study provides a strong out‐of‐sample test of the model, adding to the comparative evidence across international equity markets.     

MARKETS FOR INFLATION‐INDEXED BONDS AS MECHANISMS FOR EFFICIENT MONETARY POLICY

We consider a continuous‐time framework featuring a central bank, private agents, and a financial market. The central bank's objective is to maximize a functional, which measures the classical trade‐off between output and inflation over time plus income from the sales of inflation‐indexed bonds minus payments for the liabilities that the inflation‐indexed bonds produce at maturity. Private agents are assumed to have adaptive expectations. The financial market is modeled in continuous‐time Black–Scholes–Merton style and financial agents are averse against inflation risk, attaching an inflation risk premium to nominal bonds. Following this route, we explain demand for inflation‐indexed securities on the financial market from a no‐arbitrage assumption and derive pricing formulas for inflation‐linked bonds and calls, which lead to a supply‐demand equilibrium. Furthermore, we study the consequences that the sales of inflation‐indexed securities have on the observed inflation rate and price level. Similar to the study of Walsh, we find that the inflationary bias is significantly reduced, and hence that markets for inflation‐indexed bonds provide a mechanism to reduce inflationary bias and increase central bank's credibility.     

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.     

VIX option pricing

Substantial progress has been made in developing more realistic option pricing models for S&P 500 index (SPX) options. Empirically, however, it is not known whether and by how much each generalization of SPX price dynamics improves VIX option pricing. This article fills this gap by first deriving a VIX option model that reconciles the most general price processes of the SPX in the literature. The relative empirical performance of several models of distinct interest is examined. Our results show that state‐dependent price jumps and volatility jumps are important for pricing VIX options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:523–543, 2009     

The Chinese warrant bubble: A fundamental analysis

We investigate the information content in Chinese warrant prices based on an option pricing framework that incorporates short‐selling and margin‐trading constraints in the underlying stock market. We show that Chinese warrant prices can be explained under this pricing framework. On the basis of this new model, we develop a price deviation measure to quantify stock market investors' unobserved demand for short selling or margin trading due to market constraints. We find that warrant‐price deviations are driven by underlying stock valuation to a great extent. Chinese warrant prices, save for the time around expiration dates, are better characterized as derivatives than as pure bubbles.     

Hedging under model misspecification: All risk factors are equal,but some are more equal than others …

It is often difficult to distinguish among different option pricing models that consider stochastic volatility and/or jumps based on a cross‐section of European option prices. This can result in model misspecification. We analyze the hedging error induced by model misspecification and show that it can be economically significant in the cases of a delta hedge, a minimum‐variance hedge, and a delta‐vega hedge. Furthermore, we explain the surprisingly good performance of a simple ad‐hoc Black‐Scholes hedge. We compare realized hedging errors (an incorrect hedge model is applied) and anticipated hedging errors (the hedge model is the true one) and find that there are substantial differences between the two distributions, particularly depending on whether stochastic volatility is included in the hedge model. Therefore, hedging errors can be useful for identifying model misspecification. Furthermore, model risk has severe implications for risk measurement and can lead to a significant misestimation, specifically underestimation, of the risk to which a hedged position is exposed. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Lévy betas: Static hedging with index futures

This study considers calibration to forward‐looking betas by extracting information on equity and index options from prices using Lévy models. The resulting calibrated betas are called Lévy betas. The objective of the proposed approach is to capture market expectations for future betas through option prices, as betas estimated from historical data may fail to reflect structural change in the market. By assuming a continuous‐time capital asset pricing model (CAPM) with Lévy processes, we derive an analytical solution to index and stock options, thus permitting the betas to be implied from observed option prices. One application of Lévy betas is to construct a static hedging strategy using index futures. Employing Hong Kong equity and index option data from September 16, 2008 to October 15, 2009, we show empirically that the Lévy betas during the sub‐prime mortgage crisis period were much more volatile than those during the recovery period. We also find evidence to suggest that the Lévy betas improve static hedging performance relative to historical betas and the forward‐looking betas implied by a stochastic volatility model.     

A term structure model for dividends and interest rates

Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method for option pricing. In a calibration exercise we show that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 Index dividend futures and dividend options, and Euro Stoxx 50 Index options.     

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.     

Are Derivative Warrants Overpriced?

This study investigates the pricing efficiency of Hang Seng Index (HSI) derivative warrants in Hong Kong. Different from similar research, the study examines the pricing efficiency of index warrants by comparing their implied volatilities (IV) with realized volatility (RV). Although prior studies find that warrants are more expensive than the corresponding options, they are not necessarily overpriced in the conventional sense—that is, relative to the RV. This approach allows the study to test the pricing efficiency of warrants via a test of their information content. Moreover, unlike studies that focus on data at market close, the study uses a large sample of highly synchronous intraday, firm, bid–ask quote data to avoid possible distortions arising from intraday variations in liquidity and pricing in the instruments. The data also helps eliminate the potential nonsynchronous price problem that may affect the test results. Consistent with the results from previous studies, we find that warrants are often more expensive than options. This result is attributed to the inability of non‐issuers to sell short, and the high participation rate of unsophisticated investors in the warrants market. However, regression analysis shows that IVs from ATM and OTM warrants provide unbiased volatility forecasts, and that IVs from ATM options do not subsume the information content of ATM warrants. ATM warrant prices are in line with the RV and are efficiently priced. Simulation results show that writing warrants is more profitable than writing options, and that the overpricing is directly related to the volatility premium.     

A generalization of the Barone‐Adesi and Whaley approach for the analytic approximation of American options

This article introduces a general quadratic approximation scheme for pricing American options based on stochastic volatility and double jump processes. This quadratic approximation scheme is a generalization of the Barone‐Adesi and Whaley approach and nests several option models. Numerical results show that this quadratic approximation scheme is efficient and useful in pricing American options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:478–493, 2009     

A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models

Recently, Duan (1995) proposed a GARCH option pricing formula and a corresponding hedging formula. In a similar ARCH-type model for the underlying asset, Kallsen and Taqqu (1994) arrived at a hedging formula different from Duan's although they concur on the pricing formula. In this note, we explain this difference by pointing out that the formula developed by Kallsen and Taqqu corresponds to the usual concept of hedging in the context of ARCH-type models. We argue, however, that Duan's formula has some appeal and we propose a stochastic volatility model that ensures its validity. We conclude by a comparison of ARCH-type and stochastic volatility option pricing models.     

An expanded model for the valuation of employee stock options

The unique characteristics of employee stock options make straightforward applications of traditional option pricing models questionable. This study extends the standard pricing model to account for the dilution effect, the employees' exercise pattern, and the state‐dependent employee forfeiture rate. It also performs comparative analysis of popular existing models and the proposed models. Finally, the impacts of the above‐mentioned factors on the fair value of employee stock options are investigated. The results support the claim that our models reflect the reality better than existing models. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:713–735, 2009     

The Pricing Kernel Puzzle: A Real Phenomenon or a Statistical Artifact?

A large literature finds evidence that the pricing kernels estimated from option prices and historical returns are not monotonically decreasing in market returns. We show that the inevitable coalescence of contingencies, especially in the left‐tail, associated with estimating a distribution function may give rise to a nonmonotonic empirical pricing kernel even if the actual pricing kernel is monotonic. Hence, the observed nonmonotonicity of pricing kernels may be a statistical artifact rather than a real phenomenon. We argue that empirical work should explicitly correct for this effect by widening the option pricing bounds associated with monotonic pricing kernels.     

Comment on “A new simple square root option pricing model”

Câmara A. and Wang Y.‐H. ( 2010 ) introduce a simple square root option pricing model where the square root of the stock price is governed by a normal distribution. They show that their three‐parameter option pricing model can outperform the Black–Scholes option pricing model. We demonstrate that their assumption possesses an internal inconsistency in that the square root of the stock price can take on negative values. We generalize and revise their assumption so that the internal inconsistency can be avoided, and introduce a new square root option pricing model. The difference in option prices calculated from the two models may not be trivial. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Empirical tests of canonical nonparametric American option‐pricing methods

Alcock and Carmichael (2008, The Journal of Futures Markets, 28, 717–748) introduce a nonparametric method for pricing American‐style options, that is derived from the canonical valuation developed by Stutzer (1996, The Journal of Finance, 51, 1633–1652). Although the statistical properties of this nonparametric pricing methodology have been studied in a controlled simulation environment, no study has yet examined the empirical validity of this method. We introduce an extension to this method that incorporates information contained in a small number of observed option prices. We explore the applicability of both the original method and our extension using a large sample of OEX American index options traded on the S&P100 index. Although the Alcock and Carmichael method fails to outperform a traditional implied‐volatility‐based Black–Scholes valuation or a binomial tree approach, our extension generates significantly lower pricing errors and performs comparably well to the implied‐volatility Black–Scholes pricing, in particular for out‐of‐the‐money American put options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:509–532, 2010     

The economic significance of conditional skewness in index option markets

This study examines whether conditional skewness forecasts of the underlying asset returns can be used to trade profitably in the index options market. The results indicate that a more general skewness‐based option‐pricing model can generate better trading performance for strip and strap trades. The results show that conditional skewness model forecasts, when combined with forward‐looking option implied volatilities, can significantly improve the performance of skewness‐based trades but trading costs considerably weaken the profitability of index option strategies. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:378–406, 2010