Abstract
The popularity of ETFs has also led to increased trading of options written on ETFs.
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- 1.
See del Baño Rollin et al. (2009) for a summary of results on the Heston characteristic function.
- 2.
In order for \(\varPsi \left (\omega -i\gamma \right )\) to be well defined, we must also ensure that \(\mathbb{E}^{\mathbb{Q}}\left \{S^{\gamma }\right \} < \infty \).
- 3.
- 4.
For example, according to the summary prospectus of the Direxion Daily S&P 500 Bull 3x Shares: “Gain Limitation Risk: If the Fund’s underlying index moves more than 33% on a given trading day in a direction adverse to the Fund, you would lose all of your money. Rafferty will attempt to position the Fund’s portfolio to ensure that the Fund does not lose more than 90% of its NAV on a given day. The cost of such downside protection will be limitations on the Fund’s gains. As a consequence, the Fund’s portfolio may not be responsive to Index gains beyond 30% in a given day. For example, if the Index were to gain 35%, the Fund might be limited to a daily gain of 90% rather than 105%, which is 300% of the Index gain of 35%.” This suggests a two-sided cap on the jump sizes. Source: http://www.direxioninvestments.com/products/direxion-daily-sp-500-bull-3x-etf.
- 5.
See pages 14–18 of their paper.
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Leung, T., Santoli, M. (2016). Options on Leveraged ETFs. In: Leveraged Exchange-Traded Funds. SpringerBriefs in Quantitative Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-29094-2_4
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