Physical Sciences and Mathematics Commons^™

Short-Time Expansions For Call Options On Leveraged Etfs Under Exponential Lévy Models With Local Volatility, José E. Figueroa-López, Ruoting Gong, Matthew Lorig

Mathematics Faculty Publications

In this article, we consider the small-time asymptotics of options on a leveraged exchange-traded fund (LETF) when the underlying exchange-traded fund (ETF) exhibits both local volatility and jumps of either finite or infinite activity. We show that leverage modifies the drift, volatility, jump intensity, and jump distribution of a LETF in addition to inducing the possibility of default, even when the underlying ETF price remains strictly positive. Our main results are closed-form expressions for the leading-order terms of off-the-money European call and put LETF option prices near expiration, with explicit error bounds. These results show that the price of an …