Excursion Risk

36 Pages Posted: 16 Nov 2020

See all articles by Anna Ananova

Anna Ananova

University of Oxford

Rama Cont

University of Oxford

Renyuan Xu

Mathematical Institute, University of Oxford

Date Written: November 2, 2020

Abstract


The risk and return profiles of a broad class of dynamic trading strategies, including pairs trading and other statistical arbitrage strategies, may be characterized in terms of excursions of the market price of a portfolio away from a reference level. We propose a mathematical framework for the risk analysis of such strategies, based on a description in terms of price excursions, first in a pathwise setting, without probabilistic assumptions, then in a Markovian setting.

We introduce the notion of δ-excursion, defined as a path which deviates by δ from a reference level before returning to this level. We show that every continuous path has a unique decomposition into δ-excursions, which is useful for scenario analysis of dynamic trading strategies, leading to simple expressions for the number of trades, realized profit, maximum loss and drawdown. As δ is decreased to zero, properties of this decomposition relate to the local time of the path.

When the underlying asset follows a Markov process, we combine these results with Ito's excursion theory to obtain a tractable decomposition of the process as a concatenation of independent δ-excursions, whose distribution is described in terms of Ito's excursion measure. We provide analytical results for linear diffusions and give new examples of stochastic processes for flexible and tractable modeling of excursions. Finally, we describe a non-parametric scenario simulation method for generating paths whose excursion properties match those observed in empirical data.

Keywords: excursion theory, mathematical finance, statistical arbitrage, model risk, Markov process, mean-reversion strategy, drawdown risk.

JEL Classification: C02, C58, C63, G32, G17

Suggested Citation

Ananova, Anna and Cont, Rama and Xu, Renyuan, Excursion Risk (November 2, 2020). Available at SSRN: https://ssrn.com/abstract=3723980 or http://dx.doi.org/10.2139/ssrn.3723980

Anna Ananova

University of Oxford ( email )

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://https://www.maths.ox.ac.uk/people/rama.cont

Renyuan Xu

Mathematical Institute, University of Oxford ( email )

Andrew Wiles Building
Radcliffe Observatory Quarter (550)
Oxford, OX2 6GG
United Kingdom

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