We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

This paper applies to the static hedge of barrier options a technique, mean-square hedging, designed to minimize the size of the hedging error when perfect replication is not possible. It introduces an extension of this technique which preserves the computational efficiency of mean-square...

We analyze the impact of funding costs and margin requirements on prices of index options traded on the CBOE. We propose a model that gives upper and lower bounds for option prices in the absence of arbitrage in an incomplete market with differential borrowing and lending rates. We show that...

The monthly trading volume and proportion of Zero-Day-to-Expiry (0DTE) options have increased from zero to 26 million contracts and from zero to 40% between 2011 and 2022. We study how 0DTE option trading affects the volatility of the underlying asset. We find that more 0DTE options trading...

The option implied volatility spread and skew predict stock returns. These variables also reflect the expected cost of borrowing stock to sell short. The stock borrowing fee implied from options prices predicts changes in quoted borrowing fees and stock returns; however, the volatility spread...

Many financial instruments are designed with embedded leverage such as options and leveraged exchange traded funds (ETFs). Embedded leverage alleviates investors' leverage constraints and, therefore, we hypothesize that embedded leverage lowers required returns. Consistent with this hypothesis,...

Fixed income Asian options are frequently adopted by companies to hedge interest rate risk. Having a payoff structure depending on the cumulative short-term rate makes them particularly informativeabout interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate...

We develop a new option pricing framework that tightly integrates with how institutional investors manage options positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no-arbitrage constraints on its current shape. Within this framework, we...

A classic result by Merton (1973) is that, except just before expiration or dividend payments, one should never exercise a call option and never convert a convertible bond. We show theoretically that this result is overturned when investors face frictions. Early option exercise can be optimal...

Since the collapse of the Metallgesellschaft AG due to hedging losses in 1993, energy practitioners have been concerned with the ability to hedge long-dated linear and non-linear oil liabilities with short-dated futures and options. This paper identifies a model-free non-parametric approach to...