Offsetting a sold put without short stock
Question
You have written a put on a stock. You cannot short the stock and cannot trade any other options. How can you hedge?
Short answer
Sell forwards or futures on the stock (or on a closely correlated index). A written put gains when the stock rises and loses when it falls, i.e. it has positive delta, so you need a position with negative delta. A short futures or forward position supplies that without borrowing shares; rebalance the number of contracts as the put's delta changes. Selling shares of the stock you already own also works.
Adapted from Crack, Heard on the Street, Q2.43, p.30; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- The One-Period Binomial Model: Replication, Delta Hedging, and Risk-Neutral Pricing
- Derivation — From Binomial Trees to Black-Scholes in the Continuous Limit
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