This book provides an analysis, under both discrete-time and
continuous-time frameworks, on the price dynamics of leveraged
exchange-traded funds (LETFs), with emphasis on the roles of leverage
ratio, realized volatility, investment horizon, and tracking errors.
This study provides new insights on the risks associated with LETFs. It
also leads to the discussion of new risk management concepts, such as
admissible leverage ratios and admissible risk horizon, as well as the
mathematical and empirical analyses of several trading strategies,
including static portfolios, pairs trading, and stop-loss strategies
involving ETFs and LETFs. The final part of the book addresses the
pricing of options written on LETFs. Since different LETFs are designed
to track the same reference index, these funds and their associated
options share very similar sources of randomness. The authors provide a
no-arbitrage pricing approach that consistently value options on LETFs
with different leverage ratios with stochastic volatility and jumps in
the reference index. Their results are useful for market making of these
options, and for identifying price discrepancies across the LETF options
markets. As the market of leveraged exchange-traded products become a
sizeable connected part of the financial market, it is crucial to better
understand its feedback effect and broader market impact. This is
important not only for individual and institutional investors, but also
for regulators.
