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.