Emergence of macro-variables by evaluation and clustering of micro- activities

Recent finance and economic forecasting and risk calculation failures made obvious that macro-modelling without micro-foundation may be treacherous. Reliable macro-modelling requires the consistent bundling of individual actions into intermediate and macro-variables exploiting the individual actions’ coordination and its dynamics. The degree of coordination may range from chaos – absence of coordination – to determined situations caused by macro-level equilibrium dictating any agent's actions and inhibiting interactions. Coordination clusters individual actions into real decision units such as companies, political parties and unions. It structures the emergent intermediate and macro-level situations vitally.The paper presents first a centennial history of prominent scholars’ quotes questioning the equilibrium paradigm, a short survey of prevailing paradigm's deficiencies laid bare once again by the latest financial crises.It proposes second discrete choice (DC) – successfully applied in different fields – to model the individual agent's decision. DCs innovative integration into a Markov process provides a steady foundation to model interactions of individual agents consistently.The final section justifies the actions’ proposed interactive bundling by referring to recent advances in data processing and network topology. The dynamic modelling of the actions’ and interactions’ coordination breaks fresh grounds both with regards to mathematical, computational and economic modeling requirements. The combination of latest developments in data processing like Big Data and the recently (re)discovered network topology capabilities may cope with these challenges.     

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.     

A cross-currency Lévy market model

The Lévy Libor or market model which was introduced in Eberlein and Özkan (The Lévy Libor model. Financ. Stochast., 2005, 9, 327–348) is extended to a multi-currency setting. As an application we derive closed form pricing formulas for cross-currency derivatives. Foreign caps and floors and cross-currency swaps are studied in detail. Numerically efficient pricing algorithms based on bilateral Laplace transforms are derived. A calibration example is given for a two-currency setting (EUR, USD).     

Optimal excess-of-loss reinsurance and dividend payments with both transaction costs and taxes

In this paper we study the optimal excess-of-loss reinsurance and dividend strategy for maximizing the expected total discounted dividends received by shareholders until ruin time. Transaction costs and taxes are required when dividends occur. The problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality, we obtain analytical solutions for the optimal return function and the optimal strategy.     

Models for stock returns

Historically, the normal variance model has been used to describe stock return distributions. This model is based on taking the conditional stock return distribution to be normal with its variance itself being a random variable. The form of the actual stock return distribution will depend on the distribution for the variance. In practice, the distributions chosen for the variance appear to be very limited. In this note, we derive a comprehensive collection of formulas for the actual stock return distribution, covering some sixteen flexible families. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. We feel that this work could serve as a useful reference and lead to improved modelling with respect to stock market returns.     

Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

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.     

Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

This paper develops two novel methodologies for pricing and hedging European-style barrier option contracts under the jump to default extended constant elasticity of variance (JDCEV) model, namely: a stopping time approach based on the first passage time densities of the underlying asset price process through the barrier levels; and a static hedging portfolio approach in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. In doing so, both valuation methodologies are extended to a more general set-up accommodating endogenous bankruptcy, time-dependent barriers and the commonly observed stylized facts of a positive link between default and equity volatility and of a negative link between volatility and stock price. The two proposed numerical methods are shown to be accurate, easy to implement and efficient under both the JDCEV model and the nested constant elasticity of variance model.     

Auditor quality effects on the relationship between accruals,cash flows and equity returns: a variance decomposition analysis

In this paper, we examine the relative importance of the cash flow and accruals components of earnings in explaining the variation in UK company equity returns, together with the extent to which these relationships vary by auditor quality. We use a multivariate time-series approach that can be reconciled to a log-linear theoretical valuation model and, unlike the standard linear regression of returns on earnings components, accommodates time-varying discount rates. Based on a decomposition of the variance of equity returns, cash flows and accruals, our results indicate that both cash flow news and accruals news are important drivers of UK equity returns, although cash flows are more influential than accruals. We also find that variation in both earnings components has a more significant effect on returns for clients of large auditors. Finally, our results provide mixed evidence on the question of whether the impact of auditor quality is highest for the accruals component of earnings.