Good jump,bad jump,and option valuation

I develop a new class of closed‐form option pricing models that incorporate variance risk premium and symmetric or asymmetric double exponential jump diffusion. These models decompose the jump component into upward and downward jumps using two independent exponential distributions and thus capture the impact of good and bad news on asset returns and option prices. The empirical results show that the model with an asymmetric double exponential jump diffusion improves the fit on Shanghai Stock Exchange 50ETF returns and options and provides relatively better in‐ and out‐of‐sample pricing performance.     

Efficient quadrature and node positioning for exotic option valuation

We combine the best features of two highly successful quadrature option pricing streams, improving the linked issues of numerical precision and abscissa positioning. Coupling the recombining abscissa (node) approach used in Andricopoulos, A., Widdicks, M., Duck, P., and Newton, D.P. ( 2003 ) (AWDN as well as AWND, 2007 ) with the Gauss‐Legendre Quadrature (GQ) method of Sullivan, M.A. ( 2000 ) yields highly accurate and efficient option prices for a range of standard and exotic specifications including barrier options and in particular for NGARCH, CEV, and jump‐diffusion processes. The improvements are due to manner in which GQ positions nodes and the use of these values without interpolation. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Volatility and jump risk in option returns

We examine the importance of volatility and jump risk in the time-series prediction of S&P 500 index option returns. The empirical analysis provides a different result between call and put option returns. Both volatility and jump risk are important predictors of put option returns. In contrast, only volatility risk is consistently significant in the prediction of call option returns over the sample period. The empirical results support the theory that there is option risk premium associated with volatility and jump risk, and reflect the asymmetry property of S&P 500 index distribution.     

American option valuation: Implied calibration of GARCH pricing models

This study analyzes the issue of American option valuation when the underlying exhibits a GARCH‐type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation‐based methods being considered in previous studies. The EBT‐based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Jump variance risk: Evidence from option valuation and stock returns

We study jump variance risk by jointly examining both stock and option markets. We develop a GARCH option pricing model with jump variance dynamics and a nonmonotonic pricing kernel featuring jump variance risk premium. The model yields a closed-form option pricing formula and improves in fitting index options from 1996 to 2015. The model-implied jump variance risk premium has predictive power for future market returns. In the cross-section, heterogeneity in exposures to jump variance risk leads to a 6% difference in risk-adjusted returns annually.     

Multifactor and analytical valuation of treasury bond futures with an embedded quality option

A closed‐form pricing solution is proposed for the quality option embedded in Treasury bond futures contracts, under a multifactor and D. Heath, R. Jarrow, and A. Morton (1992) Gaussian framework. Such an analytical solution can be obtained through a conditioning approximation, in the sense of M. Curran (1994) and L. Rogers and Z. Shi (1995), or via a rank 1 approximation, following A. Brace and M. Musiela (1994). Monte Carlo simulations show that both approximations are extremely accurate and easy to calculate. Application of the proposed pricing model to the EUREX market from January 2000 through May 2004, yields an excellent fit and an insignificant estimate of the quality option magnitude. On average, this delivery option accounts for only of the futures prices. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:275–303, 2007     

Improving volatility prediction and option valuation using VIX information: A volatility spillover GARCH model

We develop a new generalized autoregressive conditional heteroskedasticity (GARCH) model that accounts for the information spillover between two markets. This model is used to detect the usefulness of the CBOE volatility index (VIX) for improving the performance of volatility forecasting and option pricing. We find the significant ability of VIX to predict stock volatility both in-sample and out-of-sample. VIX information also helps to greatly reduce the option pricing error. The proposed volatility spillover GARCH model performs better than the related approaches proposed by Kanniainen et al. (2014, J Bank Finance, 43, pp. 200-211) and P. Christoffersen et al. (2014, J Financ Quant Anal, 49, pp. 663–697).     

Pricing basket and Asian options under the jump‐diffusion process

This study derives approximate valuation formulas for basket options and Asian options under the jump‐diffusion process. To obtain an approximation for options prices under the jump‐diffusion process, we extend the Taylor expansion method developed by Ju N. ( 2002 ) under the diffusion process. We show that the Taylor expansion method, suggested in this study, provides better pricing performance as compared to log‐normal or four‐moment methods. The performance improvement using the Taylor expansion method increases as the time to maturity increases. In addition, our numerical analysis shows that jump effects become significant when the expected jump sizes take large negative values. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 31:830–854, 2011     

A scalable algorithm for the market basket analysis

The market basket is defined as an itemset bought together by a customer on a single visit to a store. The market basket analysis is a powerful tool for the implementation of cross-selling strategies. Especially in retailing, it is essential to discover large baskets, since it deals with thousands of items. Although some algorithms can find large itemsets, they can be inefficient in terms of computational time. The aim of this paper is to present an algorithm to discover large itemset patterns for the market basket analysis. In this approach, the condensed data are used and is obtained by transforming the market basket problem into a maximum-weighted clique problem. Firstly, the input data set is transformed into a graph-based structure and then the maximum-weighted clique problem is solved using a meta-heuristic approach in order to find the most frequent itemsets. The computational results show large itemset patterns with good scalability properties.     

Pathwise moderate deviations for option pricing

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling enables us to transfer these results into small‐time, large‐time, and tail asymptotics for diffusions, as well as for option prices and realized variances. In passing, we highlight some intuitive relationships between moderate deviations rate functions and their large deviations counterparts; these turn out to be useful for numerical purposes, as large deviations rate functions are often difficult to compute.     

Alternative tilts for nonparametric option pricing

This study generalizes the nonparametric approach to option pricing of Stutzer, M. (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie–Read family of divergence measures. Alhough the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk‐neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black–Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston, S. L. (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:983–1006, 2010     

Models and optimal designs for conjoint choice experiments including a no-choice option

In a classical conjoint choice experiment, respondents choose one profile from each choice set that has to be evaluated. However, in real life, the respondent does not always make a choice: often he/she does not prefer any of the options offered. Therefore, including a no-choice option in a choice set makes a conjoint choice experiment more realistic. In the literature, three different models are used to analyze the results of a conjoint choice experiment with a no-choice option: the no-choice multinomial logit model, the extended no-choice multinomial logit model, and the nested no-choice multinomial logit model. We develop optimal designs for the two most appealing of these models using the D-optimality criterion and the modified Fedorov algorithm and compare these optimal designs with a reference design, which is constructed while ignoring the no-choice option, in terms of estimation and prediction accuracy. We conclude that taking into account the no-choice option when designing a no-choice experiment only has a marginal effect on the estimation and prediction accuracy as long as the model used for estimation matches the data-generating model.     

A simplified pricing model for volatility futures

We develop a general model to price VIX futures contracts. The model is adapted to test both the constant elasticity of variance (CEV) and the Cox–Ingersoll–Ross formulations, with and without jumps. Empirical tests on VIX futures prices provide out‐of‐sample estimates within 2% of the actual futures price for almost all futures maturities. We show that although jumps are present in the data, the models with jumps do not typically outperform the others; in particular, we demonstrate the important benefits of the CEV feature in pricing futures contracts. We conclude by examining errors in the model relative to the VIX characteristics. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:307–339, 2011     

Accessing healthy food: availability and price of a healthy food basket in Scotland

Access to healthy food and its marketing have been asserted as limitations on changing behaviour to improve diet. A retailer survey in Scotland is reported that considered availability and affordability of a basket of indicator healthy food items, termed the Healthy Eating Indicator Shopping Basket (HEISB). It comprised 35 items drawn from 5 major food groups. A census of HEISB availability in 466 stores was undertaken in a sample of locations that varied on dimensions of urban-rural and affluent-deprived. Around half of the supermarkets surveyed stocked all the items. Availability of healthy food items was generally seen to be adequate but there were notable variations in availability for specific items. There were large variations in price for the HEISB items across the stores and the survey areas. The total HEISB median price varied by store type. Basket price tended to rise with deprivation with a caveat of the lowest prices in the most deprived areas. Accessibility to a range of healthy food depends more on the presence of medium and large stores than being in a deprived or affluent area.