Why Traders Hedge Options and Where Replication PnL Comes From
Summary
A replicating portfolio matches an option’s payoff only under idealized assumptions, including continuous trading, no transaction costs, unlimited divisibility, and known constant volatility. Actual markets violate these conditions, so an option combined with its hedge can generate profit and loss. Trading costs tend to reduce returns, while discrete rebalancing and changes in implied volatility can create gains or losses.
The document describes several reasons to trade an option with a hedge: market makers may seek to earn the difference between transaction prices and estimated fair value; proprietary traders may take a view on realized volatility relative to implied volatility; they may also trade a view on changes in implied volatility while hedging directional exposure. Relative-value traders can buy and sell options they view as mispriced against one another, hedging other risks with the underlying. These are motivations, not guaranteed profits; the discussion gives no empirical results or detailed hedge sizing rules.
Key ideas
- A replicating portfolio depends on assumptions that do not hold exactly in real markets.
- Transaction costs, discrete hedging, and implied volatility changes can affect option hedge PnL.
- Market makers may hedge options to manage exposure while seeking to earn the spread over estimated fair value.
- Traders can hedge options while expressing views on realized volatility, implied volatility, or relative option value.
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Full text
# Why sell an option and use the hedging (replicating) portfolio? # Why sell an option and use the hedging (replicating) portfolio? What is the point of selling an contingent claim, and then using the replicating portfolio to pay off any claim and interest if ultimately you always break even? Might sounds like a silly question. ## Answer by Chris Taylor (score 3, accepted) https://quant.stackexchange.com/a/83568 The replicating portfolio only replicates the payoff of the option under certain unrealistic conditions: - No transaction costs - Continuous trading - Infinite divisibility of the underlying asset - Constant, known volatility of the underlying asset In practice none of those are true, and the result will be that the portfolio which is long the option and short the hedging portfolio will experience profit and loss (PnL). Some components of the PnL will always be negative (e.g. transaction costs from trading in the underlying) but some may be both positive and negative (e.g. PnL due to discrete hedging intervals, or PnL due to fluctuations in the implied volatility of the option). So there can be many reasons to trade a portfolio consisting of an option and its hedging portfolio, e.g. - You are a market maker, so you can sell the option for higher than its fair value or buy it for lower than fair value, and you attempt to make a profit from the spread whilst hedging any unwanted risks by trading in the underlying. - You are a proprietary trader who thinks that the realized volatility of the option will be higher/lower than the implied volatility, and you aim to make a profit by going long/short the option and hedging by trading the underlying, in order to capture the spread between realized and implied volatility. - You are a proprietary trader who thinks that the implied volatility of the option will increase/decrease in the short them, and you aim to make a profit by benefiting from the increase/decrease while hedging any unwanted risks (e.g. delta) by trading in the underlying. - You are a proprietary trader who thinks that two options are mispriced relative to each other (e.g. the first is too cheap compared to the second) and you aim to make a profit by buying one and selling the other, and waiting for theirs prices to converge, while at the same time hedging any unwanted risks by trading a portfolio of the underlying composed of both hedging portfolios.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.