This paper describes our work pricing options in the binomial model on leveraged exchange traded funds (ETFs) with three different approaches. A leveraged exchange traded fund attempts to achieve a similar daily return as the index it follows but at a specified positive or negative multiple of the return of the index. We price options on these funds using the leveraged multiple, predetermined by the leveraged ETF, of the volatility of the index. The initial approach is a basic time step approach followed by the standard Cox, Ross, and Rubinstein method. The final approach follows a different format which we will call the Trigeorgis pricing model. We demonstrate the difficulties in pricing these options based off the dynamics of the indices the ETFs follow.

This study examines the use of leveraged exchange traded funds (LETFs) within a portfolio insurance framework to reduce exposure to downside risk. Investors have learned the importance of mitigating this risk having experienced two “once in a century” events in the last 20 years with the tech crash in the early 2000s and the financial crisis in 2008. Current portfolio insurance strategies are either option based (Leland & Rubinstein, 1976) or constant proportional portfolio insurance (CPPI), (Black & Jones, 1987). The cost of option based strategies can be quite high while a CPPI strategy requires constant rebalancing. This study combines the advantages of each by using LETFs to attain the leverage options provide, while at the same time allowing a greater percentage of the portfolio to be invested in bonds since a position in LETFs relative to a typical market index magnifies equity exposure. Thus, where a standard CPPI strategy may require 50% of the portfolio to be invested in equities, using a 3x LETF only requires approximately 16.7%. Results suggest the use of LETFs within a portfolio insurance framework result in better returns, higher Sharpe, Sortino, Omega, and cumulative prospect values while reducing Value at Risk (VaR) and Excess Shortfall below VaR. This twist on the use of LETFs will be of interest to any investor concerned with mitigating downside risk while allowing participation in increasing markets.