Anomalous Diffusions in Option Prices: Connecting Trade Duration and the Volatility Term Structure

Volatility Time and Properties of Option Prices

We use a notion of stochastic time, here called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity of the option price in the volatility. The volatility time is obtained as the almost surely unique stopping time solution to a random ordinary differential equation related to volatility. This enable...

Heterogeneous Beliefs, Option Prices, and Volatility Smiles∗

In an economy in which investors with different time preferences have heterogeneous beliefs about a dividend’s mean growth rate, the volatility of the stock that claims the dividend is stochastic in equilibrium. The prices of the vanilla European options that are written on this stock admit closed-form solutions, hence their hedging deltas. The implied volatility surface exhibits the observed p...

Approximation for Option Prices under Uncertain Volatility

In this paper, we study the asymptotic behavior of the worst case scenario option prices as the volatility interval in an uncertain volatility model (UVM) degenerates to a single point, and then provide an approximation procedure for the worst case scenario prices in a UVM with small volatility interval. Numerical experiments show that this approximation procedure performs well even as the size...

The term structure of equity option implied volatility

This paper investigates the relationship between the slope of the implied volatility (IV) term structure and future option returns. In Fama-Macbeth regressions we demonstrate that implied volatility slopes are positively correlated with future returns on short-term at-the-month straddles. A strategy that buys straddles with high IV slopes and short sells straddles with low IV slopes returns sev...

Testing the volatility term structure using option hedging criteria