TY - JOUR

T1 - Statistical arbitrage in the multi-Asset black-scholes economy

AU - Göncü, Ahmet

AU - Akyildirim, Erdinc

N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - In this study, we consider the statistical arbitrage definition given in Hogan, S, R Jarrow, M Teo and M Warachka (2004). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies, Journal of Financial Economics, 73, 525-565 and derive the statistical arbitrage condition in the multi-Asset Black-Scholes economy building upon the single asset case studied in Göncü, A (2015). Statistical arbitrage in the Black Scholes framework. Quantitative Finance, 15(9), 1489-1499. Statistical arbitrage profits can be generated if there exists at least one asset in the economy that satisfies the statistical arbitrage condition. Therefore, adding a no-statistical arbitrage condition to no-Arbitrage pricing models is not realistic if not feasible. However, with an example we show that what excludes statistical arbitrage opportunities in the Black-Scholes economy, and possibly in other complete market models, is the presence of uncertainty or stochasticity in the model parameters. Furthermore, we derive analytical formulas for the expected value and probability of loss of the statistical arbitrage portfolios and compute optimal boundaries to sell the risky assets in the portfolio by maximizing the expected return with a constraint on the probability of loss.

AB - In this study, we consider the statistical arbitrage definition given in Hogan, S, R Jarrow, M Teo and M Warachka (2004). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies, Journal of Financial Economics, 73, 525-565 and derive the statistical arbitrage condition in the multi-Asset Black-Scholes economy building upon the single asset case studied in Göncü, A (2015). Statistical arbitrage in the Black Scholes framework. Quantitative Finance, 15(9), 1489-1499. Statistical arbitrage profits can be generated if there exists at least one asset in the economy that satisfies the statistical arbitrage condition. Therefore, adding a no-statistical arbitrage condition to no-Arbitrage pricing models is not realistic if not feasible. However, with an example we show that what excludes statistical arbitrage opportunities in the Black-Scholes economy, and possibly in other complete market models, is the presence of uncertainty or stochasticity in the model parameters. Furthermore, we derive analytical formulas for the expected value and probability of loss of the statistical arbitrage portfolios and compute optimal boundaries to sell the risky assets in the portfolio by maximizing the expected return with a constraint on the probability of loss.

KW - Black-Scholes economy

KW - Statistical arbitrage

KW - optimal limit orders

UR - http://www.scopus.com/inward/record.url?scp=85121978885&partnerID=8YFLogxK

U2 - 10.1142/S201049521750004X

DO - 10.1142/S201049521750004X

M3 - Article

AN - SCOPUS:85121978885

SN - 2010-4952

VL - 12

JO - Annals of Financial Economics

JF - Annals of Financial Economics

IS - 1

M1 - 1750004

ER -