Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics

When studying a time series of implied Risk Neutral Densities (RNDs) or other implied statistics, one is faced with the problem of maturity dependence, given that option contracts have a fixed expiry date. Therefore, estimates from consecutive days are not directly comparable. Further, we can only obtain implied RNDs for a limited set of expiration dates. In this paper we introduce two new methods to overcome the time to maturity problem. First, we propose an alternative method for calculating constant time horizon Economic Value at Risk (EVaR), which is much simpler than the method currently being used at the Bank of England. Our method is based on an empirical scaling law for the quantiles in a log-log plot, and thus, we are able to interpolate and extrapolate the EVaR for any time horizon. The second method is based on an RND surface constructed across strikes and maturities, which enables us to obtain RNDs for any time horizon. Removing the maturity dependence of implied RNDs and related statistics is useful in many applications, such as in (i) the construction of implied volatility indices like the VIX, (ii) the assessment of market uncertainty by central banks (iii) time series analysis of EVaR, or (iv) event studies.

The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing

Crisis events such as the 1987 stock market crash, the Asian Crisis and the bursting of the Dot-Com bubble have radically changed the view that extreme events in financial markets have negligible probability. This paper argues that the use of the Generalized Extreme Value (GEV) distribution to model the Risk Neutral Density (RND) function provides a flexible framework that captures the negative skewness and excess kurtosis of returns, and also delivers the market implied tail index of asset returns. We obtain an original analytical closed form solution for the Harrison and Pliska (1981) no arbitrage equilibrium price for the European option in the case of GEV asset returns. The GEV based option prices successfully remove the well known pricing bias of the Black-Scholes model. We explain how the implied tail index is efficacious at identifying the fat tailed behaviour of losses and hence the left skewness of the price RND functions, particularly around crisis events.

Voluntary Contributions to Personal Pension Plans: Evidence from the British Household Panel Survey

In this paper, we use data from the British Household Panel Survey (BHPS) for the years 1992 to 1998 to study the determinants of saving in the form of voluntary contributions to personal pension plans (PPPs). We first estimate a probit model with selection for the probability of making these voluntary contributions. We then estimate a random-effects tobit regression for the amounts contributed and compare the results with those of a similar regression for conventional saving. Our findings suggest that voluntary contributions to PPPs are made essentially for retirement purposes, whereas conventional saving is undertaken for precautionary motives. The former type of saving is thus unlikely to offset the latter completely.

Computability and Evolutionary Complexity: Markets As Complex Adaptive Systems (CAS)

The purpose of this Feature is to critically examine and to contribute to the burgeoning multi disciplinary literature on markets as complex adaptive systems (CAS). Three economists, Robert Axtell, Steven Durlauf and Arthur Robson who have distinguished themselves as pioneers in different aspects of how the thesis of evolutionary complexity pertains to market environments have contributed to this special issue. Axtell is concerned about the procedural aspects of attaining market equilibria in a decentralized setting and argues that principles on the complexity of feasible computation should rule in or out widely held models such as the Walrasian one. Robson puts forward the hypothesis called the Red Queen principle, well known from evolutionary biology, as a possible explanation for the evolution of complexity itself. Durlauf examines some of the claims that have been made in the name of complex systems theory to see whether these present testable hypothesis for economic models. My overview aims to use the wider literature on complex systems to provide a conceptual framework within which to discuss the issues raised for Economics in the above contributions and elsewhere. In particular, some assessment will be made on the extent to which modern complex systems theory and its application to markets as CAS constitutes a paradigm shift from more mainstream economic analysis

The New Evolutionary Computational Paradigm of Complex Adaptive Systems: Challenges and Prospects for Economics and Finance

The new evolutionary computational paradigm of market systems views these as complex adaptive systems. The major premise of 18th century classical political economy was that order in market systems is spontaneous or emergent, in that it is the result of 'human action but not of human design'. This early observation on the disjunction between system wide outcomes and capabilities of micro level rational calculation marks the provenance of modern evolutionary thought. However, it will take a powerful confluence of two 20th century epochal developments for the new evolutionary computational paradigm to rise to the challenge of providing long awaited explanations of what has remained anomalies or outside the ambit of traditional economic analysis. The first of these is the Gödel-Turing-Post results on incompleteness and algorithmically unsolvable problems that delimit formalist calculation or deductive methods. The second is the Anderson-Holland-Arthur heterogeneous adaptive agent theory and models for inductive search, emergence and self-organized criticality which can crucially show and explicitly study the processes underpinning the emergence of ordered complexity. Multi-agent model simulation of asset price formation and the innovation based structure changing dynamics of capitalist growth are singled out for analysis of this disjunction between non-anticipating global outcomes and computational micro rationality

Systemic Risk from Global Financial Derivatives; A Network Analysis of Contagion and Its Mitigation with Super-Spreader Tax

Financial network analysis is used to provide firm level bottom-up holistic visualizations of interconnections of financial obligations in global OTC derivatives markets. This helps to identify Systemically Important Financial Intermediaries (SIFIs), analyse the nature of contagion propagation, and also monitor and design ways of increasing robustness in the network. Based on 2009 FDIC and individually collected firm level data covering gross notional, gross positive (negative) fair value and the netted derivatives assets and liabilities for 202 financial firms which includes 20 SIFIs, the bilateral flows are empirically calibrated to reflect data-based constraints. This produces a tiered network with a distinct highly clustered central core of 12 SIFIs that account for 78 percent of all bilateral exposures and a large number of  financial intermediaries (FIs) on the periphery. The topology of the network results in the “Too- Interconnected-To-Fail” (TITF) phenomenon in that the failure of any member of the central tier will bring down other members with the contagion coming to an abrupt end when the ‘super-spreaders’ have demised. As these SIFIs account for the bulk of capital in the system, ipso facto no bank among the top tier can be allowed to fail, highlighting the untenable implicit socialized guarantees needed for these markets to operate at their current levels. Systemic risk costs of highly connected SIFIs nodes are not priced into their holding of capital or collateral. An eigenvector centrality based ‘super-spreader’ tax has been designed and tested for its capacity to reduce the potential socialized losses from failure of SIFIs

Dynamic Learning, Herding and Guru Effects in Networks

It has been widely accepted that herding is the consequence of mimetic responses by agents interacting locally on a communication network. In extant models, this communication network linking agents, by and large, has been assumed to be fixed. In this paper we allow it to evolve endogenously by enabling agents to adaptively modify the weights of their links to their neighbours by reinforcing �good� advisors and breaking away from �bad� advisors with the latter being replaced randomly from the remaining agents. The resulting network not only allows for herding of agents, but crucially exhibits realistic properties of socio-economic networks that are otherwise difficult to replicate: high clustering, short average path length and a small number of highly connected agents, called "gurus". These properties are now well understood to characterize �small world networks� of Watts and Strogatz (1998).

Novelty And Surprises In Complex Adaptive System (CAS) Dynamics: A Computational Theory of Actor Innovation

The work of John von Neumann in the 1940's on self-reproducing machines as models for biological systems and self-organized complexity provides the computational legacy for CAS. Following this, the major hypothesis emanating from Wolfram (1984), Langton (1992, 1994), Kaufmann (1993) and Casti (1994) is that the sine qua non of complex adaptive systems is their capacity to produce novelty or 'surprises' and the so called Type IV innovation based structure changing dynamics of the Wolfram-Chomsky schema. The Wolfram-Chomsky schema postulates that on varying the computational capabilities of agents, different system wide dynamics can be generated: finite automata produce Type I dynamics with unique limit points or homogeneity; push down automata produce Type II dynamics with limit cycles; linear bounded automata generate Type III chaotic trajectories with strange attractors. The significance of this schema is that it postulates that only agents with the full powers of Turing Machines capable of simulating other Turing Machines, which Wolfram calls computational universality can produce Type IV irregular innovation based structure changing dynamics associated with the three main natural exponents of CAS, evolutionary biology, immunology and capitalist growth. Langton (1990,1992) identifies the above complexity classes for dynamical systems with the halting problem of Turing machines and famously calls the phase transition or the domain on which novel objects emerge as 'life at the edge of chaos'. This paper develops the formal foundations for the emergence of novelty or innovation. Remarkably, following Binmore(1987) who first introduced to game theory the requisite dose of mechanism with players modelled as Turing Machines with the Gödel (1931) logic involving the Liar or the pure logic of opposition, we will see that only agents qua universal Turing Machines which can make self-referential calculation of hostile objectives can bring about adaptive novelty or strategic innovation

Can cash hold its own? International comparisons: Theory and evidence

A number of papers predict the imminent demise of currency use in transactions while some make a case for its continued use due to its distinctive feature of anonymity. Notwithstanding the latter, this paper shows on both theoretical and empirical grounds, that cash use is sustainable for the foreseeable future because of the cost competitiveness of ATM networked cash to the consumer relative to electronic POS card substitutes. Indeed, since the mid-1990s, Finland, Canada and France which are countries in the vanguard of EFTPOS development, have experienced a resurgence of ATM cash use as measured by its expenditure share.

Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics

When studying a time series of implied Risk Neutral Densities (RNDs) or other implied statistics, one is faced with the problem of maturity dependence, given that option contracts have a fixed expiry date. Therefore, estimates from consecutive days are not directly comparable. Further, we can only obtain implied RNDs for a limited set of expiration dates. In this paper we introduce two new methods to overcome the time to maturity problem. First, we propose an alternative method for calculating constant time horizon Economic Value at Risk (EVaR), which is much simpler than the method currently being used at the Bank of England. Our method is based on an empirical scaling law for the quantiles in a log-log plot, and thus, we are able to interpolate and extrapolate the EVaR for any time horizon. The second method is based on an RND surface constructed across strikes and maturities, which enables us to obtain RNDs for any time horizon. Removing the maturity dependence of implied RNDs and related statistics is useful in many applications, such as in (i) the construction of implied volatility indices like the VIX, (ii) the assessment of market uncertainty by central banks (iii) time series analysis of EVaR, or (iv) event studies