On Trading American Put Options with Interactive Volatility

TL;DR

This paper develops a stochastic volatility model incorporating hitting times to analyze optimal stopping strategies for American put options, providing explicit rules and discussing practical trading implications in volatile markets.

Contribution

Introduces a novel stochastic volatility model with hitting times and derives explicit optimal stopping rules for American puts, including complex cases with disconnected continuation regions.

Findings

Explicit optimal stopping rules are derived for various scenarios.

The model accounts for hitting times, adding realism to volatility modeling.

Practical trading strategies are discussed based on the stopping rules.

Abstract

We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset price hits a certain level) is exponentially distributed. We obtain explicit optimal stopping rules in various cases one of which is interestingly complex because of an unexpected disconnected continuation region. Finally, we discuss in detail how these stopping rules could be used for trading an American put when the trader expects a market drop in the near future.