Deriving the arbitrage pricing theory when the number of factors is unknown

This paper examines the use of proxies (or reference variables) for the true factors in the arbitrage pricing theory (APT). It generalizes other authors' existing work and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility of fewer reference variables than the true factors is also considered, but the APT is not shown to hold, in the same sense, for this case. This work builds on an earlier paper by Ingersoll (Ingersoll J 1984 J. Finance 39 1021-39), and our propositions can be thought of as specializations of his theorems. Similar to Nawalkha (Nawalkha S 1997 J. Financial Economics 46 357-81), our work does not use the mathematics of Hilbert and Banach spaces and, thus, is open to a much wider audience. The practical implication of our results is that model builders should be generous with the number of factors they use, as excessively parsimonious models suffer from inaccuracy.     

The representation of American options prices under stochastic volatility and jump-diffusion dynamics

This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [Rev. Financial Stud., 1993, 6, 327–343], and by a Poisson jump process as introduced by Merton [J. Financial Econ., 1976, 3, 125–144]. Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalizes in an intuitive way the structure of the solution to the corresponding European option pricing problem obtained by Scott [Math. Finance, 1997, 7(4), 413–426], but here in the case of a call option and constant interest rates.     

The performance of enhanced-return index funds: evidence from bootstrap analysis

We apply the bootstrap technique proposed by Kosowski et al. [J. Finance, 2006, 61, 2551–2595] in conjunction with Carhart's [J. Finance, 1997, 52, 57–82] unconditional and Ferson and Schadt's [J. Finance, 1996, 51, 425–461] conditional four-factor models of performance to examine whether the performances of enhanced-return index funds over the 1996 to 2007 period are based on luck or superior ‘enhancing’ skills. The advantages of using the bootstrap to rank fund performance are many. It eliminates the need to specify the exact shape of the distribution from which returns are drawn and does not require estimating correlations between portfolio returns. It also eliminates the need to explicitly control for potential ‘data snooping’ biases that arise from an ex-post sort. Our results show evidence of enhanced-return index funds with positive and significant alphas after controlling for luck and sampling variability. The results are robust to both stock-only and derivative-enhanced index funds, although the spread of cross-sectional alphas for derivative-enhanced funds is slightly more pronounced. The study also examines various sub-periods within the sample horizon.     

Valuation of forward start options under affine jump-diffusion models

Under the general affine jump-diffusion framework of Duffie et al. [Econometrica, 2000, 68, 1343–1376], this paper proposes an alternative pricing methodology for European-style forward start options that does not require any parallel optimization routine to ensure square integrability. Therefore, the proposed methodology is shown to possess a better accuracy–efficiency trade-off than the usual and more general approach initiated by Hong [Forward Smile and Derivative Pricing. Working paper, UBS, 2004] that is based on the knowledge of the forward characteristic function. Explicit pricing solutions are also offered under the nested jump-diffusion setting proposed by Bakshi et al. [J. Finance, 1997, 52, 2003–2049], which accommodates stochastic volatility and stochastic interest rates, and different integration schemes are numerically tested.     

Fast Ninomiya–Victoir calibration of the double-mean-reverting model

Abstract

We consider the three-factor double mean reverting (DMR) option pricing model of Gatheral [Consistent Modelling of SPX and VIX Options, 2008], a model which can be successfully calibrated to both VIX options and SPX options simultaneously. One drawback of this model is that calibration may be slow because no closed form solution for European options exists. In this paper, we apply modified versions of the second-order Monte Carlo scheme of Ninomiya and Victoir [Appl. Math. Finance, 2008, 15, 107–121], and compare these to the Euler–Maruyama scheme with full truncation of Lord et al. [Quant. Finance, 2010, 10(2), 177–194], demonstrating on the one hand that fast calibration of the DMR model is practical, and on the other that suitably modified Ninomiya–Victoir schemes are applicable to the simulation of much more complicated time-homogeneous models than may have been thought previously.     

A novel Monte Carlo approach to hybrid local volatility models

We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18–20], [Int. J. Theor. Appl. Finance, 1998, 1, 61–110] models. In particular, we consider the stochastic local volatility model—see e.g. Lipton et al. [Quant. Finance, 2014, 14, 1899–1922], Piterbarg [Risk, 2007, April, 84–89], Tataru and Fisher [Quantitative Development Group, Bloomberg Version 1, 2010], Lipton [Risk, 2002, 15, 61–66]—and the local volatility model incorporating stochastic interest rates—see e.g. Atlan [ArXiV preprint math/0604316, 2006], Piterbarg [Risk, 2006, 19, 66–71], Deelstra and Rayée [Appl. Math. Finance, 2012, 1–23], Ren et al. [Risk, 2007, 20, 138–143]. For both model classes a particular (conditional) expectation needs to be evaluated which cannot be extracted from the market and is expensive to compute. We establish accurate and ‘cheap to evaluate’ approximations for the expectations by means of the stochastic collocation method [SIAM J. Numer. Anal., 2007, 45, 1005–1034], [SIAM J. Sci. Comput., 2005, 27, 1118–1139], [Math. Models Methods Appl. Sci., 2012, 22, 1–33], [SIAM J. Numer. Anal., 2008, 46, 2309–2345], [J. Biomech. Eng., 2011, 133, 031001], which was recently applied in the financial context [Available at SSRN 2529691, 2014], [J. Comput. Finance, 2016, 20, 1–19], combined with standard regression techniques. Monte Carlo pricing experiments confirm that our method is highly accurate and fast.     

Firm characteristics,alternative factors,and asset-pricing anomalies: evidence from Japan

Based on the errors-in-variables-free approach proposed by Brennan et al. [J. Financial Econ., 1998, 49, 345–373], we investigate the competing explanatory capabilities of alternative multi-factor models when examining various asset-pricing anomalies using Japanese data for the period 1978–2006. We find that turnover and book-to-market (BM) ratio are the two major characteristics that significantly explain the average stock returns. A further sub-period analysis reveals that the turnover effect is significant only before 1990, but cannot be explained by any multifactor models. In contrast, the BM premium is significant only after 1990, and can be explained by the Fama–French three-factor model. Thus, the results suggest that asset-pricing anomalies documented in the literature are not universal, and may be different across different markets.     

BOOK REVIEWS

Book reviewed in this article: Aggregate Theory and Policy: Capital and Growth. By John R. Hicks . Aggregate Theory and Policy: Essays in Monetary Policy in Honor of Elmer Wood. Edited by Pinkney C. Walker . Business Finance and Investments: Financial Accounting Theory. By Harold Bierman , Jr . Business Finance and Investments: Investment Decisions and Capital Costs. By James T. S. Porterfield . Financial Institutions and Markets: The Financial Sector and Economic Development: The Mexican Case. By Robert L. Bennett . Financial Institutions and Markets: Valuations of Securities as of December 31, 1965. By Committee on Valuation of National Association of Insurance Commissioners . Financial Institutions and Markets: Analytics and Institutions of Money and Banking. By William J. Frazer , Jr . and William P. Yohe . Financial Institutions and Markets: How to Analyze a Bank Statement. By F. L. Garcia . Financial Institutions and Markets: Cycles in Government Securities: Determinants of Changes in Ownership. By Michael E. Levy . Financial Institutions and Markets: California Banking in a Growing Economy: 1946–1975. Edited by Hyman P. Minsky . Financial Institutions and Markets: Government Securities Market. By Ira O. Scott , Jr . Financial Institutions and Markets: Readings in Money, National Income, and Stabilization Policy. Edited by Warren L. Smith and Ronald L. Teigen . International Finance: Foreign Exchange, Capital Flows, and Monetary Policy. By E. Ray Canterbery . International Finance: International Finance. By Richard Ward . International Finance: Report of the Study Group on the Creation of Reserve Assets: Report to the Deputies of the Group of Ten. Public Finance: Development Finance: Planning and Control. By Ursula K. Hicks . Public Finance: Federal Budget Policy. By David J. Ott and Attiat F. Ott . Public Finance: Pros and Cons of the Property Tax. By Dick Netzer . Public Finance: Fiscal Neutrality Toward Economic Growth: Analysis of a Tax Principle. By Edmund S. Phelps .     

An index of market shocks based on multiscale analysis*

Abstract

Financial markets are places of sudden and violent price movements. Nevertheless, financial crises lack a universally recognized way of assessing their gravity. This has motivated the measure recently proposed and applied to the exchange rates market by Zumbach et al (2000a Int. J. Theor. Appl. Finance 3 347–55). This measure relies on an analogy with geophysics: the scale of market shocks (SMS) is equivalent to the Richter scale used for earthquakes. More precisely, as a market is the place where economic agents—with different investment horizons—interact, the SMS definition is a weighted aggregation of volatility measures corresponding to these different horizons. In this paper, we implement and apply a similar measure to stock markets, and adapt it to take into account some extra features of these markets.

The volatilities are first described, and then used to assess the market instability perceived by a market participant. The evolution of our index of market shocks (IMS)—after rescaling for easy interpretation—is presented using different computational methods.

The IMS is then compared with another multiscale measure, the multifractal spectrum width, and we also investigate the links between the IMS and the daily close-to-close returns and volatility. Finally, we describe the recent turbulence on the French market using the IMS as an exploratory tool, concluding that the events of September 2001 proved to be a major shock compared to the Russian and Asian crises.     

BOOK REVIEWS

Book reviewed in this article: Portfolio Aspects of Corporate Capital Budgeting. By E. Eugene Carter. Company Finance and the Capital Market. By E. W. Davis and K. A. Yeomans. Cash Management. By Richard Homonoff and David Wiley Mullins, Jr. Financial Markets and the Economy. By Charles N. Henning, William Pigott and Robert Haney Scott. National Monetary Policies and the International Financial System. Edited by Robert Z. Aliber. Problems of Balance of Payments and Trade. Nasrollah S. Fatemi (editor). International Trade and Development Theory. Ronald E. Findlay. The Economics of Common Currencies. Harry G. Johnson and Alexander K. Swoboda Monetary Aggregate and Monetary Policy. By Richard G. Davis et al. Real Estate Finance by William R. Beaton.     

An improved convolution algorithm for discretely sampled Asian options

We suggest an improved FFT pricing algorithm for discretely sampled Asian options with general independently distributed returns in the underlying. Our work complements the studies of Carverhill and Clewlow [Risk, 1990, 3(4), 25–29], Benhamou [J. Comput. Finance, 2002, 6(1), 49–68], and Fusai and Meucci [J. Bank. Finance, 2008, 32(10), 2076–2088], and, if we restrict our attention only to log-normally distributed returns, also Ve?e? [Risk, 2002, 15(6), 113–116]. While the existing convolution algorithms compute the density of the underlying state variable by moving forward on a suitably defined state space grid, our new algorithm uses backward price convolution, which resembles classical lattice pricing algorithms. For the first time in the literature we provide an analytical upper bound for the pricing error caused by the truncation of the state space grid and by the curtailment of the integration range. We highlight the benefits of the new scheme and benchmark its performance against existing finite difference, Monte Carlo, and forward density convolution algorithms.     

BOOK REVIEWS

Book reviewed in this article: Lucia S. Chang and Kenneth S. Most, The Perceived Usefulness of Financial Statements for Investors' Decisions S. Henderson and G. Peirson, Issues in Financial Accounting Michael Grobstein, Stephen E. Loeb and Robert D. Neary, Auditing: A Risk Analysis Approach M. Edgar Barrett and William J. Brims (eds.), Case Problems in Management Accounting Michael T. Skully (ech), Financial Institutions and Markets in the Southwest Pacific — A Study of Australia, Fiji, New Zealand and Papua New Guinea Tom Clark (ed.), Leasing Finance Harvey Crapp and Michael T. Skully, Credit Unions for Australians R.A. Brealey, An Introduction to Risk and Return J. Matatko & D. Stafford, Key Developments in Personal Finance Paul Latimer, Australian Business Law     

BOOK REVIEWS

Book reviewed in this article: Aggregate Theory and Policy; Money and Banking By Douglas Fisher . The Economics of Corporation Finance. By Sergei P. Dobrovolsky . Portfolio Analysis. By Jack Clark Francis and Stephen H. Archer . The Analytical Theory of Finance. By William H. Jean . Security Analysis and Portfolio Management. By Henry A. Latan É and Donald L. Tuttle . Managerial Finance: A Systems Approach. By Eugene M. Lerner . Financial Performance of Conglomerates. By Henry H. Lynch . Portfolio Management. By Keith V. Smith Investments: New Analytic Techniques. By J. Peter Williamson . Financial Institutions and Markets; Banking Markets and Financial Institutions. Edited by Thomas G. Gies and Vincent P. Apilado . The Ownership Income of Management. By Wilbur G. Lewellen . Economics of the Canadian Corporate Bond Market, by J. Ross Peters . The Electronic Money: Evolution of an Electronics Funds-Transfer System. By Dennis W. Richardson .     

Dynamic factor long memory volatility

In this paper, we develop a long memory orthogonal factor (LMOF) multivariate volatility model for forecasting the covariance matrix of financial asset returns. We evaluate the LMOF model using the volatility timing framework of Fleming et al. [J. Finance, 2001, 56, 329–352] and compare its performance with that of both a static investment strategy based on the unconditional covariance matrix and a range of dynamic investment strategies based on existing short memory and long memory multivariate conditional volatility models. We show that investors should be willing to pay to switch from the static strategy to a dynamic volatility timing strategy and that, among the dynamic strategies, the LMOF model consistently produces forecasts of the covariance matrix that are economically more useful than those produced by the other multivariate conditional volatility models, both short memory and long memory. Moreover, we show that combining long memory volatility with the factor structure yields better results than employing either long memory volatility or the factor structure alone. The factor structure also significantly reduces transaction costs, thus increasing the feasibility of dynamic volatility timing strategies in practice. Our results are robust to estimation error in expected returns, the choice of risk aversion coefficient, the estimation window length and sub-period analysis.     

Learning minimum variance discrete hedging directly from the market

Option hedging is a critical risk management problem in finance. In the Black–Scholes model, it has been recognized that computing a hedging position from the sensitivity of the calibrated model option value function is inadequate in minimizing variance of the option hedge risk, as it fails to capture the model parameter dependence on the underlying price (see e.g. Coleman et al., J. Risk, 2001, 5(6), 63–89; Hull and White, J. Bank. Finance, 2017, 82, 180–190). In this paper, we demonstrate that this issue can exist generally when determining hedging position from the sensitivity of the option function, either calibrated from a parametric model from current option prices or estimated nonparametricaly from historical option prices. Consequently, the sensitivity of the estimated model option function typically does not minimize variance of the hedge risk, even instantaneously. We propose a data-driven approach to directly learn a hedging function from the market data by minimizing variance of the local hedge risk. Using the S&P 500 index daily option data for more than a decade ending in August 2015, we show that the proposed method outperforms the parametric minimum variance hedging method proposed in Hull and White [J. Bank. Finance, 2017, 82, 180–190], as well as minimum variance hedging corrective techniques based on stochastic volatility or local volatility models. Furthermore, we show that the proposed approach achieves significant gain over the implied BS delta hedging for weekly and monthly hedging.     

BOOK REVIEWS

Book reviewed in this article: Growth and Stability in a Mature Economy. By John Cornwall . Money in Britain 1959–1969. Edited by David R. Croome and Harry G. Johnson . Macroeconomics—Theory and Policy. By Fred R. Glahe . The Term Structure of Interest Rates: Financial Intermediaries and Debt Management. By Jacob B. Michaelsen . Intermediate Macroeconomics: Output, Inflation, and Growth. By D. C. Rowan and Thomas Mayer . Multinational Business Finance. By David K. Eiteman and Arthur L. Stonehill . International Managerial Finance. By J. Fred Weston and Bart Sorge . Finance. By William H. Jean . Federal Reserve System. By Benjamin Haggott Beckhart . National Housing Models. By R. Bruce Ricks . The Role of Private Placements in Corporate Finance. By Eli Shapiro and Charles R. Wolf . The Growth and Role of UK Financial Institutions 1880–1962. By David K. Sheppard . The Economics of Business Investment Abroad. By H. Peter Gray . The Financial Role of Multi-National Enterprises. By W. A. P. Manser .     

BOOK REVIEWS

Book reviewed in this article: Financial Statement Analysis. By George Foster An Introduction to Financial Accounting Theory by Scott Henderson and Graham Peirson. A. R. Drebin and H. Bierman, Jr., Managerial Accounting: J. Fred Weston and Eugene F. Brigham, Managerial Finance H. B Mayo, Basic Finance: An Introduction to Money And Financial Management     

Book Reviews

Book reviewed in this article: Principles of Financial Management. By BENTON GUP. The International Monetary System, 1945–1981. By ROBERT SOLOMON The Economics of Private Pensions. By ALICIA H. MUNNELL. Personal Finance. By JOHN D. PENSON, Jr., DONALD R. LEVI, and CLAIR J. NIXON. Financial Econometrics for Researchers in Finance and Accounting. By H. RUSSELL FOGLER and SUNDARAM GANAPATHY. Stochastic Methods in Economics and Finance. By A. G. MALLIARIS and W. A. BROCK. International Finance: Text and Cases. By GEORGE FEIGER and BERTRAND JACQUILLAT.     

The multivariate Variance Gamma model: basket option pricing and calibration

In this paper, we propose a methodology for pricing basket options in the multivariate Variance Gamma model introduced in Luciano and Schoutens [Quant. Finance 6(5), 385–402]. The stock prices composing the basket are modelled by time-changed geometric Brownian motions with a common Gamma subordinator. Using the additivity property of comonotonic stop-loss premiums together with Gauss-Laguerre polynomials, we express the basket option price as a linear combination of Black & Scholes prices. Furthermore, our new basket option pricing formula enables us to calibrate the multivariate VG model in a fast way. As an illustration, we show that even in the constrained situation where the pairwise correlations between the Brownian motions are assumed to be equal, the multivariate VG model can closely match the observed Dow Jones index options.     

Book Reviews

Book reviewed in this article: The Modern Theory of Corporate Finance. Edited by MICHAEL C. JENSEN and CLIFFORD W. SMITH, Jr. Money, Banking, and Financial Markets. By J. WALTER ELLIOTT. Bank Management; Text and Cases. By GEORGE H. HEMPEL, ALAN B. COLEMAN, and DONALD G. SIMONSON. Personal Finance. By R. MALCOLM RICHARDS, S. KERRY COOPER, and DONALD R. FRASER.