Derivative pricing using multivariate affine generalized hyperbolic distributions

In this paper we use multivariate affine generalized hyperbolic (MAGH) distributions, introduced by Schmidt et al. (2006), to show how to price multidimensional derivatives when the underlying asset follows a MAGH distribution. We also illustrate the approach using market data from the BOVESPA (São Paulo Stock Exchange) and the exchange rate of the Brazilian Real vs. US Dollar to price some multidimensional derivatives.     

Nonparametric rank tests for event studies

Because stock prices are not normally distributed, the power of nonparametric rank tests dominate parametric tests in event study analyses of abnormal returns on a single day. However, problems arise in the application of nonparametric tests to multiple day analyses of cumulative abnormal returns (CARs) that have caused researchers to normally rely upon parametric tests. In an effort to overcome this shortfall, this paper proposes a generalized rank (GRANK) testing procedure that can be used on both single day and cumulative abnormal returns. Asymptotic distributions of the associated test statistics are derived, and their empirical properties are studied with simulations of CRSP returns. The results show that the proposed GRANK procedure outperforms previous rank tests of CARs and is robust to abnormal return serial correlation and event-induced volatility. Moreover, the GRANK procedure exhibits superior empirical power relative to popular parametric tests.     

Empirical evaluation of asset pricing models: Arbitrage and pricing errors in contingent claims

Hansen and Jagannathan (1997) have developed two measures of pricing errors for asset-pricing models: the maximum pricing error in all static portfolios of the test assets and the maximum pricing error in all contingent claims of the assets. In this paper, we develop simulation-based Bayesian inference for these measures. While the literature reports that the time-varying extensions substantially reduce pricing errors of classic models on the standard test assets, our analysis shows that the reduction is much smaller based on the second measure. Those time-varying models have large pricing errors on the contingent claims of the test assets because their stochastic discount factors are often negative and admit arbitrage opportunities.     

Multivariate option pricing with time varying volatility and correlations

In this paper we consider option pricing using multivariate models for asset returns. Specifically, we demonstrate the existence of an equivalent martingale measure, we characterize the risk neutral dynamics, and we provide a feasible way for pricing options in this framework. Our application confirms the importance of allowing for dynamic correlation, and it shows that accommodating correlation risk and modeling non-Gaussian features with multivariate mixtures of normals substantially changes the estimated option prices.     

Generalized parameter functions for option pricing

We extend the benchmark nonlinear deterministic volatility regression functions of Dumas et al. (1998) to provide a semi-parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models. Besides volatility, skewness and kurtosis of the asset return distribution can also be enhanced. Empirical results, using closing prices of the S&P 500 index call options (in one day ahead out-of-sample pricing tests), strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps. Moreover, it is found to be superior in various robustness tests. Our semi-parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters. The economic significance of the approach is tested in terms of hedging, where the evaluation and estimation loss functions are aligned.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.     

Variations in sovereign credit quality assessments across rating agencies

We investigate agency variation in credit quality assessment (Standard and Poor’s vs. Moody’s vs. Fitch) employing sovereign ratings data for 129 countries, spanning the period 1990–2006. While we find that the credit rating agencies often disagree about credit quality, it is usually confined to one or two notches on the finer scale. We find that several variables have varying importance in explaining ratings across agencies which leads us to conclude that material heterogeneity exists between them. Also, while watch and outlook procedures are generally strong predictors of rating changes relative to other public data, additional significant variables suggest that it might be possible to augment these agency data to provide better forecasts of future rating changes.     

Daily pricing of emerging market sovereign CDS before and during the global financial crisis

In this paper, we study the determinants of daily spreads for emerging market sovereign credit default swaps (CDSs) over the period April 2002–December 2011. Using GARCH models, we find, first, that daily CDS spreads for emerging market sovereigns are more related to global and regional risk premia than to country-specific risk factors. This result is particularly evident during the second subsample (August 2007–December 2011), where neither macroeconomic variables nor country ratings significantly explain CDS spread changes. Second, measures of US bond, equity, and CDX High Yield returns, as well as emerging market credit returns, are the most dominant drivers of CDS spread changes. Finally, our analysis suggests that CDS spreads are more strongly influenced by international spillover effects during periods of market stress than during normal times.     

Cashflow news,the value premium and an asset pricing view on European stock market integration

The decomposition of national CAPM market betas of European countries’ value and growth portfolio returns into cashflow and discount rate news driven components reveals that i) high average returns on value portfolios are associated with disproportionately high sensitivity to national cashflow news which corroborates recent evidence for the U.S. and ii) two-beta variants of national CAPMs capture the cross-sectional dispersion in European stock returns. The latter finding is suggestive of relatively well integrated stock markets among the core European countries and reflects basic asset pricing theory. One (national) discount factor should price any (international) asset.     

Numerical evaluation of multivariate contingent claims

We develop a numerical approximation method for valuing multivariatecontingent claims. The approach is based on an n-dimensionalextension of the lattice binomial method. Closed-form solutionsfor the jump probabilities and the jump amplitudes are obtained.The accuracy of the method is illustrated in the case of Europeanoptions when there are three underlying assets.     

The Samuelson hypothesis in futures markets: An analysis using intraday data

This paper considers the Samuelson hypothesis, which argues that the futures price volatility increases as the futures contract approaches its expiration. Utilizing intraday data from 20 futures markets in six futures exchanges, we find strong support for the Samuelson hypothesis in agricultural futures. However, the Samuelson hypothesis does not hold for other futures contracts. We also provide supporting evidence that the ‘negative covariance’ hypothesis is the key factor for the empirical support of the Samuelson hypothesis. In addition, our findings remain largely unaltered even after we control for seasonality and liquidity effects.     

A semiparametric conditional capital asset pricing model

This paper proposes using a functional coefficient regression technique to estimate time-varying betas and alpha in the conditional capital asset pricing model (CAPM). Functional coefficient representation relaxes the strict assumptions regarding the structure of betas and alpha by combining the predictors into an index. Appropriate index variables are selected by applying the smoothly clipped absolute deviation penalty. In such a way, estimation and variable selection can be done simultaneously. Based on the empirical studies, the proposed model performs better than the alternatives in explaining asset returns and we find no strong evidence to reject the conditional CAPM.     

Liquidity distribution in the limit order book on the stock exchange of Thailand

The liquidity distribution, or the shape of the limit order book, influences trading behavior and choice of order submission by public liquidity suppliers. The present study seeks to discover whether liquidity providers are concerned about being picked off by informed traders, and whether they are less willing to supply liquidity at the market or demand higher price spreads. The results show that liquidity at the market is a small portion of total liquidity, and that firm size, minimum tick size, volatility, and trading volume play significant roles in determining the liquidity distribution within an order book.     

Nonparametric correlation models for portfolio allocation

This article proposes time-varying nonparametric and semiparametric estimators of the conditional cross-correlation matrix in the context of portfolio allocation. Simulations results show that the nonparametric and semiparametric models are best in DGPs with substantial variability or structural breaks in correlations. Only when correlations are constant does the parametric DCC model deliver the best outcome. The methodologies are illustrated by evaluating two interesting portfolios. The first portfolio consists of the equity sector SPDRs and the S&P 500, while the second one contains major currencies. Results show the nonparametric model generally dominates the others when evaluating in-sample. However, the semiparametric model is best for out-of-sample analysis.     

Stock market momentum, business conditions, and GARCH option pricing models

This paper examines the forecasting performance of GARCH option pricing models from a market momentum perspective, and the possible impacts of financial crises and business conditions are also examined. The empirical results demonstrate that market momentum impacts the forecasting performance of GARCH option pricing models. The EGARCH model performs better under downward market momentum, while the standard GARCH performs better under upward market momentum. In addition, parsimonious models generally outperform richly parameterized ones. The above findings are robust to financial crises, and the results further demonstrate that business conditions influence the forecasting performance of GARCH option pricing models.     

Volatility spillovers and the effect of news announcements

We examine the effect of US and European news announcements on the spillover of volatility across US and European stock markets. Using synchronously observed international implied volatility indices at a daily frequency, we find significant spillovers of implied volatility between US and European markets as well as within European markets. We observe a stark contrast in the effect of scheduled versus unscheduled news releases. Scheduled (unscheduled) news releases resolve (create) information uncertainty, leading to a decrease (increase) in implied volatility. Nevertheless, news announcements do not fully explain the volatility spillovers, although they do affect the magnitude of volatility spillovers. Our results are robust to extreme market events such as the recent financial crisis and provide evidence of volatility contagion across markets.     

Belief updating, debt pricing and financial decisions under asymmetric information

This paper studies debt holders’ belief updating, valuation of corporate debt, and equity owners’ financing decisions during financial distress under asymmetric information. This is done within a continuous-time framework, where the relevant state variable is assumed to follow an Arithmetic Brownian motion (ABM). ABM can take negative values and has very realistic feature compared with Geometric Brownian motion (GBM). Using Chapter 11 of U.S. Bankruptcy Code as a costly screening device, we can characterize which firm will choose private workouts (in the form of strategic debt service) and which will choose to file for the Chapter 11 Bankruptcy procedure (in the form of debt-equity swap) when the firm is in financial distress. Using arguments similar to equilibrium refinements, we give a clear picture of how debt holders’ beliefs about the firm’s types are updated according to the state variable and the firm’s default behavior, and describe optimal strategies of both parties under those beliefs. We also provide an approximate solution to the debt pricing problem under asymmetric information.     

VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation

This study integrates CBOE VIX Term Structure and VIX futures to simplify VIX option pricing in multifactor models. Exponential and hump volatility functions with one- to three-factor models of the VIX evolution are used to examine their pricing for VIX options across strikes and maturities. The results show that using exponential volatility functions presents an effective choice as pricing models for VIX calls, whereas hump volatility functions provide efficient out-of-sample valuation for most VIX puts, in particular with deep in-the-money and deep out-of-the-money. Pricing errors for calls can be further reduced with a two-factor model.     

Pricing and hedging contingent claims using variance and higher order moment swaps

This paper suggests perfect hedging strategies of contingent claims under stochastic volatility and random jumps of the underlying asset price. This is done by enlarging the market with appropriate swaps whose pay-offs depend on higher order sample moments of the asset price process. Using European options and variance swaps, as well as barrier options written on the S&P 500 index, the paper provides clear cut evidence that hedging strategies employing variance and higher order moment swaps considerably improves upon the performance of traditional delta hedging strategies. Inclusion of the third-order moment swap improves upon the performance of variance swap-based strategies to hedge against random jumps. This result is more profound for short-term out-of-the money put options.     

A general closed-form spread option pricing formula

We propose a new accurate method for pricing European spread options by extending the lower bound approximation of Bjerksund and Stensland (2011) beyond the classical Black–Scholes framework. This is possible via a procedure requiring a univariate Fourier inversion. In addition, we are also able to obtain a new tight upper bound. Our method provides also an exact closed form solution via Fourier inversion of the exchange option price, generalizing the Margrabe (1978) formula. The method is applicable to models in which the joint characteristic function of the underlying assets forming the spread is known analytically. We test the performance of these new pricing algorithms performing numerical experiments on different stochastic dynamic models.