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The `volatility smile' is one of the well-known biases of Black-Scholes models for pricing options. In this paper, we introduce a robust method of reducing this bias by pricing subject to a deterministic functional volatility = (S; t). This instantaneous volatility is chosen as a spline whose weights are determined by a regularised numerical strategy that… (More)

- Mark McDonald, Omer Suleman, Stacy Williams, Sam Howison, Neil F Johnson
- Physical review. E, Statistical, nonlinear, and…
- 2005

In a system containing a large number of interacting stochastic processes, there will typically be many nonzero correlation coefficients. This makes it difficult to either visualize the system's interdependencies, or identify its dominant elements. Such a situation arises in foreign exchange (FX), which is the world's biggest market. Here we develop a… (More)

- Marya Bazzi, Mason A. Porter, Stacy Williams, Mark McDonald, Daniel J. Fenn, Sam D. Howison
- Multiscale Modeling & Simulation
- 2016

Networks are a convenient way to represent complex systems of interacting entities. Many networks contain “communities” of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the detection of communities in temporal networks represented as multilayer networks. As a focal example, we… (More)

- D Lamper, S D Howison, N F Johnson
- Physical review letters
- 2002

The dynamical evolution of many economic, sociological, biological, and physical systems tends to be dominated by a relatively small number of unexpected, large changes ("extreme events"). We study the large, internal changes produced in a generic multiagent population competing for a limited resource, and find that the level of predictability increases… (More)

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 nextstep and multi-step predictions. In addition to the possibility of identifying profit opportunities, the technique… (More)

Abstract We consider the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation we provide closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility. We describe a general partial differential equation framework… (More)

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk. As an example, and as our main motivation, we investigate option pricing under the class… (More)

We discuss the ‘continuity correction’ that should be applied to relate the prices of discretely sampled barrier options and their continuouslysampled equivalents. Using a matched asymptotic expansions approach we show that the correction of Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) can be applied in a very wide variety of cases. We… (More)

- S. Jonathan Chapman, Sam D. Howison, John R. Ockendon
- SIAM Review
- 1992

Abstract. This paper reviews the derivation of some macroscopic models for superconductivity and also some of the mathematical challenges posed by these models. The paper begins by exploring certain analogies between phase changes in superconductors and those in solidification and melting. However, it is soon found that there are severe limitations on the… (More)

Limit order books (LOBs) match buyers and sellers in more than half of the world’s financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into… (More)