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

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  • Nian Yao

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

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.

Suggested Citation

  • Nian Yao, 2018. "Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-37, June.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:02:n:s2424786318500160
    DOI: 10.1142/S2424786318500160
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    6. Tim Leung & Hyungbin Park, 2017. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-33, September.
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    Cited by:

    1. Hyungbin Park, 2021. "Modified Mean-Variance Risk Measures for Long-Term Portfolios," Mathematics, MDPI, vol. 9(2), pages 1-23, January.

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