There's more to volatility than volume

It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading, which cause both clustered volatility and heavy tails in price returns. We investigate this hypothesis using tick by tick data from the New York and London Stock Exchanges and show that only a small fraction of volatility fluctuations are explained in this manner. Clustered volatility is still very strong even if price changes are recorded on intervals in which the total transaction volume or number of transactions is held constant. In addition the distribution of price returns conditioned on volume or transaction frequency being held constant is similar to that in real time, making it clear that neither of these are the principal cause of heavy tails in price returns. We analyse recent results of Ane and Geman (2000 Ane, T and Geman, H. 2000. Order flow, transaction clock, and normality of asset returns. J. Finance, 55(5): 2259–2284. [Crossref], [Web of Science ®] , [Google Scholar]: J. Finance, 55, 2259–2284) and Gabaix et al. (2003 Gabaix, X, Gopikrishnan, P, Plerou, V and Stanley, H.E. 2003. A theory of power-law distributions in financial market fluctuations. Nature, 423: 267–270. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]: Nature, 423, 267–270), and discuss the reasons why their conclusions differ from ours. Based on a cross-sectional analysis we show that the long-memory of volatility is dominated by factors other than transaction frequency or total trading volume.     

Political influences on the costs of banking crises in emerging market economies: testing the U-shaped veto player hypothesis

While there has been considerable research on the consequences of financial crises, there has been little empirical research on the possible effects of the role of domestic political institutions that influence a government's ability to implement crisis management policies. This paper investigates the impact of domestic institutions, characterized by a U-shaped veto player framework, on the output costs of banking crises. The analysis extends MacIntyre's qualitative study (2001 MacIntyre, Andrew. 2001. Institutions and investors: The politics of the economic crisis in Southeast Asia. International Organization, 55(1): 81–122. [Crossref], [Web of Science ®] , [Google Scholar]) of the relationship between veto players and policy risks in the Asian financial crises. For a large sample of emerging market economies, we find support for McIntyre's hypotheses that both too few and too many veto players are associated with greater costs of banking crises.     

Pricing and capital requirements for with profit contracts: modelling considerations

The aim of this paper is to provide an assessment of alternative frameworks for the fair valuation of life insurance contracts with a predominant financial component, in terms of impact on the market consistent price of the contracts, the embedded options, and the capital requirements for the insurer. In particular, we model the dynamics of the log-returns of the reference fund using the so-called Merton (1976 Merton, RC. 1976. Option pricing when underlying stock returns are discontinuous. J. Finan. Econ., : 125–144.  [Google Scholar]) process, which is given by the sum of an arithmetic Brownian motion and a compound Poisson process, and the Variance Gamma (VG) process introduced by Madan and Seneta (1990 Madan, DB and Seneta, E. 1990. The variance gamma (VG) model for share market returns. J. Bus., 63: 511–524. [Crossref], [Web of Science ®] , [Google Scholar]), and further refined by Madan and Milne (1991 Madan, DB and Milne, F. 1991. Option pricing with VG martingale components. Math. Finan., 1: 39–45. [Crossref] , [Google Scholar]) and Madan et al. (1998 Madan, DB, Carr, P and Chang, E. 1998. The variance gamma process and option pricing. Eur. Finan. Rev., 2: 79–105. [Crossref] , [Google Scholar]). We conclude that, although the choice of the market model does not affect significantly the market consistent price of the overall benefit due at maturity, the consequences of a model misspecification on the capital requirements are noticeable.     

Nonlinear dynamics in economics and finance and unit root testing

The recent financial crisis exposed the inability of traditional theoretical and empirical models to parsimoniously capture the rich dynamics of the economic environment. This has stimulated the interest of both academics and practitioners in the development and application of more sophisticated models. By allowing for the presence of nonlinearities, complex dynamics, multiple equilibria, structural breaks and spurious trends, these latter models resemble more closely the properties of economic and financial time series. In this article, we illustrate the flexibility of a family of econometric models, namely the exponential smooth transition autoregressive (ESTAR), to encompass several of the above characteristics. We then re-assess the power of the ESTAR unit root test developed by Kapetanios, Shin and Snell ((2003) Kapetanios, G., Shin, Y. and Snell, A. 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2): 359–79. (doi:10.1016/S0304-4076(02)00202-6)[Crossref], [Web of Science ®] , [Google Scholar]) in the presence of nuisance parameters typically encountered in the literature and compare its performance with that of the augmented Dickey-Fuller and the Enders and Granger ((1998) Enders, W. and Granger, C. W.J. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3): 304–11. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) tests. Our results show the lack of dominance of any particular test and that the power is not independent to priors about the nuisance parameters. Finally, we examine several asset price deviations from fundamentals and one hyper-inflation series and find contradictory results between the nonlinear fitted models and unit root tests. The findings highlight that new testing procedures with higher power are desirable in order to shed light on the behavior of financial and economic series.     

Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modelling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e. of the volume of the LOB, or the exponential recovery of the bid–ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy of a risk-neutral investor, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005 Obizhaeva, A and Wang, J. 2005. Optimal trading strategy and supply/demand dynamics, Preprint Available online at: http://www.rhsmith.umd.edu/faculty/obizhaeva/OW060408.pdf (accessed 16 February 2009)[Crossref] , [Google Scholar]). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.     

An endogenous volatility approach to pricing and hedging call options with transaction costs

Standard delta hedging fails to exactly replicate a European call option in the presence of transaction costs. We study a pricing and hedging model similar to the delta hedging strategy with an endogenous volatility parameter for the calculation of delta over time. The endogenous volatility depends on both the transaction costs and the option strike prices. The optimal hedging volatility is calculated using the criterion of minimizing the weighted upside and downside replication errors. The endogenous volatility model with equal weights on the up and down replication errors yields an option premium close to the Leland [J. Finance, 1985 Leland, HE. 1985. Option pricing and replication with transaction costs. J. Finance, 40: 1283–1301. [Crossref], [Web of Science ®] , [Google Scholar], 40, 1283–1301] heuristic approach. The model with weights being the probabilities of the option's moneyness provides option prices closest to the actual prices. Option prices from the model are identical to the Black–Scholes option prices when transaction costs are zero. Data on S&P 500 index cash options from January to June 2008 illustrate the model.     

Enhanced policy iteration for American options via scenario selection

Kolodko and Schoenmakers (2006 Kolodko, A and Schoenmakers, J. 2006. Iterative construction of the optimal Bermudan stopping time. Finan. Stochast., 10: 27–49. [Crossref], [Web of Science ®] , [Google Scholar]) and Bender and Schoenmakers (2006 Bender, C, Kolodko, A and Schoenmakers, J. 2006. Iterating cancelable snowballs and related exotics in a many-factor Libor model. Risk, September: 126–130.  [Google Scholar]) introduced a policy iteration that allows the achievement of a tight lower approximations of the price for early exercise options via a nested Monte Carlo simulation in a Markovian setting. In this paper we enhance the algorithm by a scenario selection method. It is demonstrated by numerical examples that the scenario selection can significantly reduce the number of inner simulations actually performed, and thus can greatly speed up the method (by up to a factor of 15 in some examples). Moreover, it is shown that the modified algorithm retains the desirable properties of the original, such as the monotone improvement property, termination after a finite number of iteration steps, and numerical stability.     

Latin American stock markets’ volatility spillovers during the financial crises: a multivariate FIAPARCH-DCC framework

The main purpose of this paper is to analyse the volatility spillovers in Latin American emerging stock markets. A multivariate Fractionally Integrated Asymmetric Power ARCH model with dynamic conditional correlations of Engle (1982 Engle, R. F. 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50: 987–1007. [Crossref], [Web of Science ®] , [Google Scholar]) with a Student-t distribution is employed. We examine whether considering for long memory and asymmetry in emerging stock markets behaviour may provide more insights into the volatility spillovers phenomenon. In this paper we select daily frequency stock indexes covering four emerging countries in Latin America for the period (January 1995–September 2009). Our results point out the importance of volatility spillovers in these countries. Moreover, long memory and asymmetry in emerging stock market dynamics seem to provide more insights into the transmission of volatility shocks. More interestingly, the analysis of the DCCEs behaviour over time via multivariate cointegration, vector error correction model and the Cholesky variance decomposition shows shifts behaviour around major Latin American financial crisis and recent subprime crisis. On the practical side, these results may be useful for international portfolio managers and Latin American stock market authorities.     

The effect of pseudo‐immediacy on intertemporal choices

An interesting phenomenon, which we dub the ‘pseudo‐immediacy effect’, was detected in intertemporal choices. The majority of our participants preferred the smaller but sooner (SS) outcome to the larger but later (LL) outcome when a pseudo‐immediacy reward was framed, but a higher proportion of participants preferred the LL outcome to the SS outcome when the pseudo‐immediate format was removed. Such a shift violated the invariance principle which requires that the preference order between options does not depend on the manner in which they are described. With reference to the pseudo‐certainty effect reported by Kahneman and Tversky in 1984 Kahneman, D. and Tversky, A. 1984. Choice, values, and frames. American Psychologist, 39: 341–50. [Crossref], [Web of Science ®] , [Google Scholar], our findings typically support the notion that risk and delay are psychologically equivalent and that the same psychological process underlies risk and intertemporal choice.     

A modified Corrado test for assessing abnormal security returns

Event studies typically use the methodology developed by Fama et al. [1969 Fama, E., Fisher, L., Jensen, M. and Roll, R. 1969. The adjustment of stock prices to new information. International Economic Review, 10(1): 1–21. [Crossref] , [Google Scholar]. The adjustment of stock prices to new information. International Economic Review 10, no. 1: 1–21] to segregate a stock's return into expected and unexpected components. Moreover, conventional practice assumes that abnormal returns evolve in terms of a normal distribution. There is, however, an increasing tendency for event studies to employ non-parametric testing procedures due to the mounting empirical evidence which shows that stock returns are incompatible with the normal distribution. This paper focuses on the widely used non-parametric ranking procedure developed by Corrado [1989 Corrado, C. 1989. A nonparametric test for abnormal security price performance in event studies. Journal of Financial Economics, 23(2): 385–95. [Crossref], [Web of Science ®] , [Google Scholar]. A nonparametric test for abnormal security price performance in event studies. Journal of Financial Economics 23, no. 2: 385–95] for assessing the significance of abnormal security returns. In particular, we develop a consistent estimator for the variance of the sum of ranks of the abnormal returns, and show how this leads to a more efficient test statistic (as well as to less cumbersome computational procedures) than the test originally proposed by Corrado (1989 Corrado, C. 1989. A nonparametric test for abnormal security price performance in event studies. Journal of Financial Economics, 23(2): 385–95. [Crossref], [Web of Science ®] , [Google Scholar]). We also use the theorem of Berry [1941 Berry, A. 1941. The accuracy of the Gaussian approximation to the sum of independent variates. Transactions of the American Mathematical Society, 49(1): 122–36. [Crossref] , [Google Scholar]. The accuracy of the Gaussian approximation to the sum of independent variates. Transactions of the American Mathematical Society 49, no. 1: 122–36] and Esseen [1945 Esseen, C. 1945. Fourier analysis of distribution functions: A mathematical study of the Laplace–Gaussian law. Acta Mathematica, 77(1): 1–125. [Crossref], [Web of Science ®] , [Google Scholar]. Fourier analysis of distribution functions: A mathematical study of the Laplace–Gaussian law. Acta Mathematica 77, no. 1: 1–125] to demonstrate how the distribution of the modified Corrado test statistic developed here asymptotically converges towards the normal distribution. This shows that describing the distributional properties of the sum of the ranks in terms of the normal distribution is highly problematic for small sample sizes and small event windows. In these circumstances, we show that a second-order Edgeworth expansion provides a good approximation to the actual probability distribution of the modified Corrado test statistic. The application of the modified Corrado test developed here is illustrated using data for the purchase and sale by UK directors of shares in their own companies.     

Optimal time to sell a stock in the Black–Scholes model: comment on ‘Thou shalt buy and hold’, by A. Shiryaev,Z. Xu and X.Y. Zhou

We reconsider the problem of the optimal time to sell a stock studied by Shiryaev et al. (2008 Shiryaev, A, Xu, Z and Zhou, XY. 2008. Thou shalt buy and hold. Quant. Finan., 8: 765–776. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) (following in this issue of Quantitative Finance) using path integral methods. These methods allow us to confirm the results obtained by these authors and extend them to the entire parameter region. We also obtain the full distribution of the time t_m at which the maximum of the price is reached for arbitrary values of the drift.     

Stochastic integrals driven by fractional Brownian motion and arbitrage: a tale of two integrals

Recent research suggests that fractional Brownian motion can be used to model the long-range dependence structure of the stock market. Fractional Brownian motion is not a semi-martingale and arbitrage opportunities do exist, however. Hu and Øksendal [Infin. Dimens. Anal., Quant. Probab. Relat. Top., 2003, 6, 1–32] and Elliott and van der Hoek [Math. Finan., 2003 Elliott, RJ and van de Hoek, J. 2003. A general fractional white noise theory applications to finance. Math. Finan., 13: 301–330. [Crossref], [Web of Science ®] , [Google Scholar], 13, 301–330] propose the use of the white noise calculus approach to circumvent this difficulty. Under such a setting, they argue that arbitrage does not exist in the fractional market. To unravel this discrepancy, we examine the definition of self-financing strategies used by these authors. By refining their definitions, a new notion of continuously rebalanced self-financing strategies, which is compatible with simple buy and hold strategies, is given. Under this definition, arbitrage opportunities do exist in fractional markets.     

Do emerging markets with consistent returns have better future performance?

Using monthly data for 25 emerging markets around the world, it is found that emerging markets with recently consistent stock returns tend to have future returns that continue in the same direction. The effects are long-lived for negative consistency, and imply that capital flows are much more sensitive to market downturns than market upturns. Additionally, the longer a market has had consistently negative (positive) stock returns, the more negative (positive) are future returns. These results serve as confirmation that the consistency effects of Grinblatt and Moskowitz [J. Finan. Econ., 2004 Grinblatt, M and Moskowitz, T. 2004. Predicting stock price movements from the pattern of past returns. J. Finan. Econ., 71: 541–579. [Crossref], [Web of Science ®] , [Google Scholar], forthcoming] and Watkins [J. Behav. Finan., 2003 Watkins, B. 2003. Riding the wave of investor sentiment: an analysis of consistency as a predictor of future stock returns. J. Behav. Finan., 4: 1–32.  [Google Scholar], 4, 1–32] exist in emerging markets around the world.     

The augmented Black–Litterman model: a ranking-free approach to factor-based portfolio construction and beyond

The Fama and French factor-ranking approach (1992, 1993, etc.) has been extensively applied in quantitative fund management. However, this approach suffers from hidden factor view, information inefficiency, etc. issues. Based on the Black–Litterman model (1992; as explained in Cheung 2010b Cheung, W. 2010b. The Black–Litterman model explained. J. Asset Mgmt., 11: 229–243. [Crossref] , [Google Scholar]), we develop a technique that endogenizes the ranking process and elegantly resolves these issues. This model explicitly seeks forward-looking factor views and smoothly blends them to deliver robust allocation to securities. Our numerical experiments show this is an intuitive and practical framework for factor-based portfolio construction, and beyond. This article features: (1) a new and unified framework for strategy combination, factor mimicking and security-specific bets; (2) an elegant and ranking-free approach to factor style construction; (3) worked examples based on the FTSE EUROTOP 100 universe; (4) insight into the classic issue of confidence parameter setting; and (5) implementation guidance in an appendix.     

Food for Thought? A Rejoinder on Peer-review and RAE2008 Evidence

This Rejoinder responds to criticisms made by Simon Hussain (2011) Hussain, S. 2011. Food for thought on the ABS Academic Journal Quality Guide. Accounting Education: an international journal, 20(6), : 545–559. [Taylor & Francis Online] , [Google Scholar] about the construction and operation of the Association of Business Schools' (ABS) Academic Journal Quality Guide. In this paper the broad purposes of journal lists and guides are outlined before an account is given of the long history and multiple forms of these lists, particularly in the field of Accounting. Having described the main features of different types of journal list, the advantages and benefits of the approach adopted in the compilation of the ABS Journal Quality Guide is outlined. The paper then ends by noting that one of the copy-editing mistakes identified by Dr Hussain has been rectified, but the remaining concerns about the rating of accounting education and accounting history journals reflect the absence of these titles from journal citation reports and international journal lists. Furthermore, the lower rating of Accounting & Finance research in the RAE2008 in comparison with Business & Management Studies research in the same year and Accounting & Finance research in 2001, has more to do with the way in which the Accounting & Finance Panel calibrated and normalized its judgements than with the ratings contained within the ABS Guide.     

Dynamic liquidation under market impact

The optimal liquidation problem with transaction costs, which includes a positive fixed cost, and market impact costs, is studied in this paper as a constrained stochastic optimal control problem. We assume that trading is instantaneous and the dynamics of the stock to be liquidated follows a geometric Brownian motion. The solution to the impulse control problem is computed at each time step by solving a linear partial differential equation and a maximization problem. In contrast to results obtained from the static formulation of Almgren and Chriss [J. Risk, 2000 Almgren, R and Chriss, N. 2000. Optimal execution of portfolio transactions. J. Risk, 3: 5–39. [Crossref] , [Google Scholar], 3, 5–39], when risk is not considered, the optimal liquidation strategy from our stochastic control formulation depends on temporary market impact cost and permanent market impact cost parameters. In addition, our computational results indicate the following properties of the optimal execution strategy from the stochastic control formulation. Due to the existence of a no-transaction region, it may not be optimal for some individuals to sell their assets on some trading dates. As the value of the permanent market impact parameter increases, the expected optimal amount liquidated at the terminal time increases. As the value of the quadratic temporary impact cost parameter increases, the expected optimal amount liquidated at trading times tends to be uniform, and the no-transaction region shrinks. In the presence of quadratic temporary market impact costs, in contrast to optimal strategies that result from fixed and/or proportional transaction costs alone, portfolios in the selling region are neither re-balanced into the no-transaction region nor into the sell and no-transaction interface.     

Turbo warrants under stochastic volatility

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]) has considered the pricing of turbo warrants under the Black–Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.     

Investor relations,information asymmetry and market value

Evidence to date on the market value of investor relations (IR) strategies is limited. We test the market relevance of IR activity directly employing a proprietary database measuring IR quality across all firms listed on NYSE, Amex and NASDAQ. Although, in theory, ‘repackaging’ and communicating existing information should have no market impact, we find that firms with higher quality IR strategies are rewarded with significantly higher valuation multiples. In addition, increase in IR quality is associated with increases in analyst following and liquidity. Overall, our findings are generally stronger for small firms which are more likely to be ‘neglected’. Our evidence is consistent with effective IR successfully raising firm visibility leading to enhanced recognition and reduced information asymmetry in line with Merton (1987 Merton, R., 1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance, 42 (3), 483–510. doi: 10.1111/j.1540-6261.1987.tb04565.x[Crossref], [Web of Science ®] , [Google Scholar]) and thus ‘fairer’ firm valuation as argued by IR professionals.     

Do financial returns have finite or infinite variance? A paradox and an explanation

One of the major points of contention in studying and modelling financial returns is whether or not the variance of the returns is finite or infinite (sometimes referred to as the Bachelier–Samuelson Gaussian world versus the Mandelbrot stable world). A different formulation of the question asks how heavy the tails of the financial returns are. The available empirical evidence can be, and has been, interpreted in more than one way. The apparent paradox, which has puzzled many a researcher, is that the tails appear to become less heavy for less frequent (e.g. monthly) returns than for more frequent (e.g. daily) returns, a phenomenon not easily explainable by the standard models. Inspired by the prelimit theorems of Klebanov, Rachev and Szekely (1999 Klebanov, L, Rachev, S and Szekely, G. 1999. Pre-limit theorems and their applications. Acta Applicandae Mathematicae, 58: 159–174.  [Google Scholar]) and Klebanov, Rachev and Safarian (2000 Klebanov, L, Rachev, S and Safarian, M. 2000. Local prelimit theorems and their applications to finance. Appl. Math. Lett., 13: 73–78.  [Google Scholar]), we provide an explanation of this paradox. We show that, for financial returns, a natural family of models are those with tempered heavy tails. These models can generate observations that appear heavy tailed for a wide range of aggregation levels before becoming clearly light tailed at even larger aggregation scales. Important examples demonstrate the existence of a natural scale associated with the model at which such an apparent shift in the tails occurs.