How Delta-Hedged Long Options Can Benefit from High Realized Volatility
Article Quant Q&A · Author: mark leeds
Summary
The document explains the intuition behind buying an option when its implied volatility appears lower than a forecast of realized volatility. A long option position has positive gamma: as the underlying rises, its delta increases and a trader can sell some underlying to restore delta neutrality; after a fall, the trader can buy underlying. This repeated rebalancing creates a buy-low, sell-high pattern.
If the underlying moves more than was priced into the option, those hedge adjustments can generate gains that exceed the option’s cost, assuming the forecast is close to realized conditions. The answers frame the comparison as a contest between the trader’s volatility estimate and the market’s implied volatility. They give intuition rather than a formal P&L derivation, and do not account for transaction costs, discrete hedging, changing implied volatility, or other real-world risks. The proposed edge depends on forecasting volatility better than the market.
Key ideas
- A long option position has positive gamma, so its delta changes as the underlying moves.
- Delta rebalancing after rises and falls can create a buy-low, sell-high trading pattern.
- Realized volatility above the volatility priced into the option may make hedge gains exceed the premium paid.
- Profit depends on the volatility forecast being more accurate than the market’s pricing, and practical frictions are not analyzed.
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# Intution behind buying the option when implied vol seems low # Intution behind buying the option when implied vol seems low Hi All: I've started reading "volatility trading" by Euan Sinclair and it's a very nice book. It's not so theoretical but instead focuses on the practicalities when dealing with trading options. I've never worked in options ( so just understand the basics from textbooks such as cox and rubinstein, baxter rennie etc ) and I've often had the following question and I figured ( since reading this book, reminded me of my question ) I would ask here. The book touches on the topic but, so far, doesn't give the intuition I'm looking for. So, here goes. You have say a stock XXX. You calculate the implied vol of one of one of its calls. It doesn't matter which one. Next you find that the volatility that you estimate over the life of the call is MUCH, MUCH, MUCH greater than the implied vol of the call. So, you buy the call and hedge your position by selling the correct number of shares of the stock. You modify your hedge as needed and do this until the option expires. Now, according to Sinclair, ( and of course this is true ), the end result should be that you generate some profit if your volatility estimate was a decent estimate in hindsight. The part I don't understand regarding the profit is the following. In a world where the implied vol was equal to the true volatility that occurred, the hedging cost should be equal to the value of the option. So, what goes on in the case where your forecast is greater than the implied vol and, in hindsight was pretty close to correct ? Does it mean that the hedging cost is less than the value of the option so hedging doesn't cost as much so you end up profiting ? Conversely, if your forecast is MUCH, MUCH less than the implied vol, then the standard profiting attempt is to sell the call and buy the stock in the appropriate amount. But, hopefully if I can understand the first case described above, then I will understand the case where one sells the call. Also, if this question is covered in cox and rubinstein or baxter and rennie (it's been so long since I looked at them that I could have forgotten), I can check those out. Thanks for any insights-wisdom. ## Answer by user73732 (score 1, accepted) https://quant.stackexchange.com/a/79963 The intuition behind delta hedging and profiting slightly when market vol has underestimated realized volatility can be represented in the "buy low sell high" hedging strategy. When you own optionality, you are long gamma. Essentially if prices go up, you get longer delta (underlying) and would "sell high" to keep your exposure delta neutral. If prices go down, you get shorter delta and would "buy low" to keep your exposure delta neutral. If the market realized volatility is higher than the implied volatility (what you paid for the option), in an ideal world, repeating this to expiry should net you the vol difference in profit. ## Answer by Brian B (score 6) https://quant.stackexchange.com/a/55576 Note: what you call true volatility is often termed realized volatility. When you purchase a call or a put, each time the underlying increases in value, your hedge modification consists of selling a little bit. When it drops in value, you buy a little bit. Those buy-low/sell-high elements are a replication strategy that, as you note, would be expected to match the cost of your option purchase, all else being equal. When realized volatility is higher than the implied volatility that drove your purchase price, you get "extra" hedge trading opportunities because the stock is moving up and down more than expected. Those trades pay off more than what you paid for the option, and are the source of profit. (Great choice of book, by the way) ## Answer by nbbo2 (score 3) https://quant.stackexchange.com/a/55577 The implied volatility is not G_d given, but comes from the collective judgement of market participants. If you are right and the market is wrong (unlikely in my personal experience but perhaps true for you) then you can make money when you are proven right by future developments (i.e. by future realized volatility being close to your prediction and higher than the market expected). In other words the creation of options has opened up a new field for human beings to compete in making predictions (just as they have always tried to predict future events).
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