Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations

Nian Yao ()
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Nian Yao: College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong Province 518060, P. R. China

International Journal of Financial Engineering (IJFE), 2018, vol. 05, issue 02, 1-37

Abstract: In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.

Keywords: Large deviation principle; leveraged exchanged-traded fund; optimal leverage ratio (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S2424786318500160

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