Excursion Risk


Ananova, A
Cont, R
Xu, R

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

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Journal Article