"Approximate Arbitrage", co-authored with Antonio Bernardo, UCLA Finance Working Paper #18-99. Pure arbitrage is an opportunity to make money for nothing. The central assumption of Finance theory is that pure arbitrage opportunities do not exist in the market. This no-arbitrage assumption imposes some constraints that help pin down prices of risky securities, but often these constraints are not very restrictive. We propose a rigorous definition of what constitutes an approximate arbitrage opportunity. Intuitively, this is an investment that entails some risk of loss but is "almost too good to be true". We show that ruling out the existence of approximate arbitrage opportunities imposes some more restrictive constraints that help predict more accurately the price of risky securities. Abstract and paper.
"Relative Pricing of Options with Stochastic Volatility", co-authored with Pedro Santa-Clara and Shu Yan, UCLA Finance Working Paper #9-98. We use the no-arbitrage condition to characterize the risk-neutral drift of implied volatilities. This enables us to price and hedge non-vanilla options relatively to vanilla options. Abstract and paper.
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