Affine fractional stochastic volatility models

By fractional integration of a square root volatility process, we propose in this paper a long memory extension of the Heston (Rev Financ Stud 6:327–343, 1993) option pricing model. Long memory in the volatility process allows us to explain some option pricing puzzles as steep volatility smiles in long term options and co-movements between implied and realized volatility. Moreover, we take advantage of the analytical tractability of affine diffusion models to clearly disentangle long term components and short term variations in the term structure of volatility smiles. In addition, we provide a recursive algorithm of discretization of fractional integrals in order to be able to implement a method of moments based estimation procedure from the high frequency observation of realized volatilities.     

Portfolio allocation using multivariate variance gamma models

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.     

Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models

In this paper, we show how to approximate Heath–Jarrow–Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite-dimensional state space. Moreover, we recover a closed-form representation of the forward price dynamics in the approximation models and derive the rate of convergence to the true dynamics uniformly over an interval of time to maturity under certain additional smoothness conditions. In the Markovian case, we can strengthen the convergence to be uniform over time as well. Our results are based on the construction of a convenient Riesz basis on the state space of the term structure dynamics.     

On the use of the Box–Cox transformation on conditional variance models

We investigate the effects of using the Box–Cox transformation on conditional variance specifications. By deriving its autocorrelation functions, we infer “rich” autocorrelation structures due to the existence of the specification parameter in this non-linear transformation. To illustrate transformation's effects on conditional variance models, we first generate its theoretical autocorrelation function and then investigate model's fit using real financial time-series data.     

Arithmetic variance swaps

Biases in standard variance swap rates (VSRs) can induce substantial deviations below market rates. Defining realized variance as the sum of squared price (not log-price) changes yields an ‘arithmetic’ variance swap with no such biases. Its fair value has advantages over the standard VSR: no discrete monitoring or jump biases; and the same value applies for any monitoring frequency, even irregular monitoring and to any underlying, including those taking zero or negative values. We derive the fair value for the arithmetic variance swap and compare it with the standard VSR by: analysing errors introduced by interpolation and integration techniques; numerical experiments for approximation accuracy; and using 23 years of FTSE 100 options data to explore the empirical properties of arithmetic variance (and higher moment) swaps. The FTSE 100 variance risk has a strong negative correlation with the implied third moment, which can be captured using a higher moment arithmetic swap.     

Affine Models for Credit Risk Analysis

Continuous-time affine models have been recently introducedin the theoretical financial literature on credit risk. Theyprovide a coherent modeling, rather easy to implement, but havenot yet encountered the expected success among practitionersand regulators. This is likely due to a lack of flexibilityof these models, which often implied poor fit, especially comparedto more ad hoc approaches proposed by the industry. The aimof this article is to explain that this lack of flexibilityis mainly due to the continuous-time assumption. We developa discrete-time affine analysis of credit risk, explain howdifferent types of factors can be introduced to capture separatelythe term structure of default correlation, default heterogeneity,correlation between default, and loss-given-default; we alsoexplain why the factor dynamics are less constrained in discretetime and are able to reproduce complicated cycle effects. Thesemodels are finally used to derive a credit-VaR and various decompositionsof the spreads for corporate bonds or first-to-default basket.     

Credit Derivatives in an Affine Framework

An efficient method for valuing credit derivatives based on three entities is developed in an affine framework. This includes interdependence of market and credit risk, joint credit migration and counterparty default risk of three firms. As an application we provide closed form expressions for the joint distribution of default times, default correlations, and default swap spreads in the presence of counterparty default risk. Vienna Institute of Finance is funded by WWTF (Vienna Science and Technology Fund).     

A General Affine Earnings Valuation Model

We introduce a methodology, with two applications, that incorporates stochastic interest rates, heteroskedasticity and risk aversion into the residual income model. In the first application, goodwill is an affine (constant plus linear term) function where the constant and linear coefficients are time-varying. Homoskedastic risk gives rise to a constant risk premium, while heteroskedastic risk gives rise to linear state-dependent risk premiums. In the second application, we present a class of models where a non-linear function for the price-to-book ratio can be derived. We show how interest rates, risk, profitability and growth affect the price-to-book ratio.     

Beyond Single-Factor Affine Term Structure Models

This article proposes a new approach to testing for the hypothesisof a single priced risk factor driving the term structure ofinterest rates. The method does not rely on any parametric specificationof the state variable dynamics or the market price of risk.It simply exploits the constraint imposed by the no-arbitragecondition on instantaneous expected bond returns. In order toachieve our goal, we develop a Kolmogorov-Smirnov test and applyit to data on Treasury bills and bonds for both the United Statesand Spain. We find that the single risk factor hypothesis cannotbe rejected for either dataset.     

On the cumulants of the logarithmic generalized variance and variance ratio

Summary

In dealing with certain extensions of the analysis of variance to samples from a multivariate normal population Wilks [4] introduced the quantity ‘generalized variance’ |S|, where |S| represents the determinant of the sample variances and covariances. He was able to obtain its distribution for a few special cases. The following note gives the general expressions for the cumulants of log |S| which is of interest in present asymptotic multivariate tests (cf. e.g. [2]).     

Zero-intelligence realized variance estimation

Given a time series of intra-day tick-by-tick price data, how can realized variance be estimated? The obvious estimator—the sum of squared returns between trades—is biased by microstructure effects such as bid–ask bounce and so in the past, practitioners were advised to drop most of the data and sample at most every five minutes or so. Recently, however, numerous alternative estimators have been developed that make more efficient use of the available data and improve substantially over those based on sparsely sampled returns. Yet, from a practical viewpoint, the choice of which particular estimator to use is not a trivial one because the study of their relative merits has primarily focused on the speed of convergence to their asymptotic distributions, which in itself is not necessarily a reliable guide to finite sample performance (especially when the assumptions on the price or noise process are violated). In this paper we compare a comprehensive set of nineteen realized variance estimators using simulated data from an artificial “zero-intelligence” market that has been shown to mimic some key properties of actual markets. In evaluating the competing estimators, we concentrate on efficiency but also pay attention to implementation, practicality, and robustness. One of our key findings is that for scenarios frequently encountered in practice, the best variance estimator is not always the one suggested by theory. In fact, an ad hoc implementation of a subsampling estimator, realized kernel, or maximum likelihood realized variance, delivers the best overall result. We make firm practical recommendations on choosing and implementing a realized variance estimator, as well as data sampling.     

Identification of Maximal Affine Term Structure Models

Building on Duffie and Kan (1996) , we propose a new representation of affine models in which the state vector comprises infinitesimal maturity yields and their quadratic covariations. Because these variables possess unambiguous economic interpretations, they generate a representation that is globally identifiable. Further, this representation has more identifiable parameters than the “maximal” model of Dai and Singleton (2000) . We implement this new representation for select three‐factor models and find that model‐independent estimates for the state vector can be estimated directly from yield curve data, which present advantages for the estimation and interpretation of multifactor models.     

Maximum Likelihood Estimation of Latent Affine Processes

This article develops a direct filtration-based maximum likelihoodmethodology for estimating the parameters and realizations oflatent affine processes. Filtration is conducted in the transformspace of characteristic functions, using a version of Bayes’rule for recursively updating the joint characteristic functionof latent variables and the data conditional upon past data.An application to daily stock market returns over 1953–1996reveals substantial divergences from estimates based on theEfficient Methods of Moments (EMM) methodology; in particular,more substantial and time-varying jump risk. The implicationsfor pricing stock index options are examined.     

Best face forward

Most companies serve customers through a broad array of interfaces, from retail sales clerks to Web sites to voice-response telephone systems. But while the typical company has an impressive interface collection, it doesn't have an interface system. That is, the whole set does not add up to the sum of its parts in its ability to provide service and build customer relationships. Too many people and too many machines operating with insufficient coordination (and often at cross-purposes) mean rising complexity, costs, and customer dissatisfaction. In a world where companies compete not on what they sell but on how they sell it, turning that liability into an asset is what separates winners from losers. In this adaptation of their forthcoming book by the same title, Jeffrey Rayport and Bernard Jaworski explain how companies must reengineer their customer interface systems for optimal efficiency and effectiveness. Part of that transformation, they observe, will involve a steady encroachment by machine interfaces into areas that have long been the sacred province of humans. Managers now have opportunities unprecedented in the history of business to use machines, not just people, to credibly manage their interactions with customers. Because people and machines each have their strengths and weaknesses, company executives must identify what people do best, what machines do best, and how to deploy them separately and together. Front-office reengineering subjects every current and potential service interface to an analysis of opportunities for substitution (using machines instead of people), complementarity (using a mix of machines and people), and displacement (using networks to shift physical locations of people and machines), with the twin objectives of compressing costs and driving top-line growth through increased customer value.     

The global minimum variance hedge

Review of Derivatives Research - We explore futures hedging based on the global minimum variance strategy. As evidenced by using eleven of the world’s major stock market indexes and their...     

Fed funds futures variance futures

We develop a novel contract design, the fed funds futures (FFF) variance futures, which reflects the expected realized basis point variance of an underlying FFF rate. The valuation of short-term FFF variance futures is completely model-independent in a general setting that includes the cases where the underlying FFF rate exhibits jumps and where the realized variance is computed by sampling the FFF rate discretely. The valuation of longer-term FFF variance futures is subject to an approximation error which we quantify and show is negligible. We also provide an illustrative example of the practical valuation and use of the FFF variance futures contract.     

最优多因子仿射利率期限结构模型选择

在利用NS模型估计出市场即期利率的基础上,采用卡尔曼滤波方法对多因子Vasieck和CIR模型进行参数估计,最后运用蒙特卡罗模拟方法对交易所国债价格进行模拟,并与实际价格进行比较,进而确定了符合我们国债市场的最优多因子仿射利率期限结构模型。研究结果表明：多因子CIR模型对数据的拟合效果及对国债价格模拟效果要明显优于多因子Vasicek模型;对于多因子CIR模型而言,因子个数增加并没有提高模型的价格模拟效果;两因子CIR模型具有最优的国债价格模拟效果。     

The price of variance risk

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.