Abstract
We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via ‘buy-and-hold until barrier’ and ‘short until barrier’ strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.
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Notes
The straightforward concept of univariate pairs trading is often extended into more sophisticated strategies. We could implement a strategy in a quasi-multivariate framework where one security is traded against a weighted portfolio of co-moving securities. Another strategy involves trading groups of stocks against other groups of stocks that co-move together.
For a recent application, see Perera et al. (2018).
See Glasserman and Kou (2011).
Actually, any barrier level greater than the initial stock price can be chosen but since we assume that the risk-free rate is greater than zero, the barrier level should also grow with the risk-free rate. The particular choice of the barrier level as \(S_0(1+\gamma )e^{r_f t}\) is to simplify the mathematical notation since we are working with the discounted stock price process.
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Acknowledgements
Ahmet Sensoy gratefully acknowledges support from the Turkish Academy of Sciences - Outstanding Young Scientists Award Program (TUBA-GEBIP).
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Akyildirim, E., Fabozzi, F.J., Goncu, A. et al. Statistical arbitrage in jump-diffusion models with compound Poisson processes. Ann Oper Res 313, 1357–1371 (2022). https://doi.org/10.1007/s10479-021-03965-w
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DOI: https://doi.org/10.1007/s10479-021-03965-w