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Let's say I'm an options trader, and I want to go long volatility on a particular underlying. How do I capture this volatility mispricing? How do I convert my forecast into a bet with a cash payoff.

For example, I know that I could buy a straddle. Now let's say realized vol is high. What do I actually do? Do I sell the option, because the price of the option has gone up with higher new implied vol? Or do I exercise the appropriate option leg to buy the stock at a cheaper price and then sell it at the new higher market price? Is there any theory or literature about which is better?

I also know that a static position in an option, dynamically delta hedged, has a payoff that is the difference between the hedge variance rate and the realized variance rate, weighted by half the dollar gamma (see Carr & Madan 2002). I have the same question here: is the idea that the option's value has increased proportional to change in variance, and I cash out by selling the option at the higher implied vol, i.e. higher cash price?

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It sounds like you believe volatility will be higher than is currently priced in the markets.

  1. In your first example of buying a straddle, you are long vega and long gamma. In other words, you are long both implied volatility and realized volatility and will profit if both of these go up.

Being long implied volatility, you would benefit from being able to sell the straddle for more than you paid for it. Let's say the stock did not move at all, but the market repriced the volatility and implied volatility went up. The straddle you bought would now be more expensive and you would then sell it to profit. Of course the repricing would have to happen quick enough to overcome the time decay you experience from owning the straddle.

The position will also benefit from being long gamma. With the straddle, you are making a bet that the underlying will move sufficiently in-the-money on either leg of the straddle by an amount that will be greater than the premium paid for both the long put and the long call. If this move happens before the expiry of your straddle, you could profit by selling the straddle, thereby capturing the realized volatility, as well as recovering some of the premium you paid for the straddle. If you hold on until expiration, you would just exercise the leg that is in-the-money (letting the other leg expire worthless). If the moneyness of the leg you are exercising is greater than the premium you paid for the straddle, you will profit.

  1. The second example you provide, where you are buying and option and dynamically hedging hedging, you are once again long vega and long gamma.

In order to profit from the long vega position, the market would once again have to reprice volatility and you can again sell the option richer than you paid for it.

As for benefitting from being long gamma, this would be a little different. You would dynamically hedge the option by delta hedging and profit from gamma extraction to benefit from the stock moving up or down with sufficient volatility. This would profitable if realized volatility were greater than the implied volatility, or cost of the option.

Of course, the position could also be profitable without delta hedging. Here you would be depending on your getting the directionality correct. If the underlying were to move sufficiently higher, in the case of a long call (or lower in the case of a long put), before your option expires, you could sell the option and capture the delta and recover some premium. Or exercise the option at maturity if it should finish in-the-money. Again, if the moneyness is greater than you paid for the option, you would profit.

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I can answer the first paragraph:

For example, I know that I could buy a straddle. Now let's say realized vol is high. What do I actually do? Do I sell the option, because the price of the option has gone up with higher new implied vol?

  • The price of the option strategy (not option, because a straddle is a pair of options) does not go up because of the higher new IV, prices and IV are just different ways of quoting the option. The price of the option strategy has gone up because it is now more ITM, whether the underlying spot price is lower or higher (and therefore making the put or call more ITM, respectively).

Or do I exercise the appropriate option leg to buy the stock at a cheaper price and then sell it at the new higher market price? Is there any theory or literature about which is better?

  • You do not want to exercise the option (most times), you should sell the option strategy to another party because it still has time value in it (more chance to be ITM). Therefore, exercising the option strategy is less than optimal. You can reference John Hull's book.
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