This paper provides a quantitative risk analysis of leveraged ETFs (LETFs) with a focus on the impact of leverage and investment horizon. From the empirical returns of several major LETFs based on the S&P 500 index, the performance of LETFs generally declines as investment horizon increases,...

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF...

This paper studies the optimal timing to liquidate credit derivatives in a general intensity-based credit risk model under stochastic interest rate. We incorporate the potential price discrepancy between the market and investors, which is characterized by risk-neutral valuation under different...

We present a valuation framework that captures the main characteristics of employee stock options (ESOs), which financial regulations now require to be expensed in firms' accounting statements. The value of these options is much less than Black-Scholes prices for corresponding market-traded...

We study the generalized composite pure and randomized hypothesis testing problems. In addition to characterizing the optimal tests, we examine the conditions under which these two hypothesis testing problems are equivalent, and provide counterexamples when they are not. This analysis is useful...

We investigate the effect of using an optimized exit rule on pairs trading. For every asset pair, we optimize the positions so that resulting intraday portfolio value is best fitted to an Ornstein-Uhlenbeck (OU) process through maximum likelihood estimation. Using eight asset pairs, we examine...

We study the problem of dynamically trading multiple futures contracts on different underlying assets subject to portfolio constraints. The spreads between futures and spot prices are modeled by a multidimensional scaled Brownian bridge to account for their convergence at maturity. Under this...

The energy and material processing industries are traditionally characterized by very large-scale physical capital that is custom-built with long lead times and long lifetimes. However, recent technological advancement in low-cost automation has made possible the parallel operation of large...

The energy and material processing industries are traditionally characterized by very large-scale physical capital that is custom-built with long lead times and long lifetimes. However, recent technological advancement in low-cost automation has made possible the parallel operation of large...

This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and...