David Lamper

Application of multi-agent games to the prediction of financial time-series

We report on a technique based on multi-agent games which has potential use in the prediction of future movements of financial time series. A third-party game is trained on a black-box time series, and is then run into the future to extract next-step and multi-step predictions. In addition to the possibility of identifying profit opportunities, the technique may prove useful in the development of improved risk management strategies.

Trading Volume in Models of Financial Derivatives

This paper develops a subordinated stochastic process model for an asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, the paper makes use of the under-used market statistic of transaction count as a suitable proxy for the information flow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn. Both the asset price and the number of trades are used in parameter estimation. The underlying process is found to be fast mean reverting, and this is exploited to perform an asymptotic expansion. The implied volatility skew is then used to calibrate the model.

Anatomy of extreme events in a complex adaptive system

Large changes tend to dictate the long-term dynamical behaviour of many real-world complex systems in both the natural and social sciences. We provide an analytic, microscopic analysis of extreme events arising in an adaptive population comprising competing agents (e.g. species, cells, traders, data-packets). Our results reveal a taxonomy of such extreme events, and provide a microscopic understanding as to their build-up and likely duration.

Monte Carlo Valuation of American Options

An American option is a contract giving its holder the right to buy (call option) or sell (put option) one unit of an underlying security of value S for a prearranged amount. This right can be exercised at any time prior to the expiration date T. In contrast, a European option can be exercised only at the expiry. Define the amount paid to the holder of an American option at the moment of exercise, the payoff, as Ψ (S, t) ≥ 0; a standard contract is a put option where Ψ = max(K − S, 0) and K is the strike price. The discounted exercise value of the option is Z(t) = Ψ (t) / B(t), where B(t) is the value at time t of

An investigation of crash avoidance in a complex system

1 invested in a riskless money market account at t = 0. American option valuation can be characterised as an optimal stopping problem. The time 0 value of an American option is given by

Toward an Understanding of Financial Markets using Multi-agent Games

V(0) = \mathop {\sup }\limits_{0\tau T} E\left[ {Z\left( \tau \right)} \right]

The science of complexity

(1) where the supremum is taken over all the possible stopping times τ less than the expiration date T, and the expectation is taken over the risk-neutral probability density. This is the primal problem.

Trading Volume and Stochastic Volatility

Complex systems can exhibit unexpected large changes, e.g. a crash in a financial market. We examine the large endogenous changes arising within a non-trivial generalization of the minority game: the grand canonical minority game. Using a Markov-Chain description, we study the many possible paths the system may take. This ‘many-worlds’ view not only allows us to predict the start and end of a crash in this system, but also to investigate how such a crash may be avoided. We find that the system can be ‘immunized’ against large changes: by inducing small changes today, much larger changes in the future can be prevented.