Is Time Synthetic Volatility?

D

deltahedge

Hey ETers,

I'm slightly at a loss as to how to attribute the reason as to why a put sale can be a profitable despite the underlying not moving and the IV remaining constant, yet only the passage of time.

Long story short, let's assume I've sold some $10 puts 4 months ago on a biotech stock when it was trading at $12. I thought IV was high at the time due to an overreaction by the market on some bad news. When I sold the puts they had an IV of 85% and the price of the puts was 1.83.

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Fast forward to today and let's assume they've retained their IV of 85%, yet due to time decay the puts trade at .91 cents.

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My question is in this instance is it fair to characterize the profit as making money due to IV being too high and shorting the vol? Or is it simply attributable to time decay? Technically the IVs have not changed, so I'm just at a loss as to how one can say they made money being short volatility when IV has not moved at all?

Thanks for all those who can clear up my understanding (or lack thereof) :).
 
If you sell a 12-month hurricane insurance policy to someone in New Orleans, and 6 months go by with no hurricane, don't you think you've made money deservedly? You put yourself at risk by betting there would be no hurricane. There was none, so you won the bet - or at least you're winning it so far. You should be able to buy that policy back (if hurricane insurance policies were traded on exchanges like options are) at much less than you paid for it - even if the probability of a hurricane (the equivalent of volatility) is no less than it was.

Same with the put. You put yourself at risk for a period of time by selling someone price insurance. You could have lost money on that had the price of that stock gone down. But it didn't, so of course you've made money.

That said, the fact that IV was high when you sold it was indeed a reasonable factor in your decision to sell. Everything else being equal, the higher the IV, the higher the theta.
 
Quote from dmo:

If you sell a 12-month hurricane insurance policy to someone in New Orleans, and 6 months go by with no hurricane, don't you think you've made money deservedly? You put yourself at risk by betting there would be no hurricane. There was none, so you won the bet - or at least you're winning it so far. You should be able to buy that policy back (if hurricane insurance policies were traded on exchanges like options are) at much less than you paid for it - even if the probability of a hurricane (the equivalent of volatility) is no less than it was.

Same with the put. You put yourself at risk for a period of time by selling someone price insurance. You could have lost money on that had the price of that stock gone down. But it didn't, so of course you've made money.

That said, the fact that IV was high when you sold it was indeed a reasonable factor in your decision to sell. Everything else being equal, the higher the IV, the higher the theta.
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Thanks for the clarification dmo :).

However in regards to your statement that the volatility is akin to the probability of the option expiring ITM I believe is slightly off, if anything (and again this statement too is also fallacious from a mathematical perspective but it has been used at times as a proxy for estimation) would be the delta of the put.

Ironically though if you examine the deltas they haven't changed that much either for 200 DTE or 80 DTE (from 27 to 25).
 
Given that the only parameter that has changed is time it is obvious that the gain in the short put is solely due to time decay. Of course you give a fairly artificial example -- the stock dropped down on bad news and its implied volatility went up, and then months later the stock hasn't moved at all but the implied volatility is as high as it was during the panic. In the real world the implied volatility would have declined once the market realized that the bad news was fully priced in.

In any case it has long been recognized in option pricing that an increase in volatility is roughly equivalent to time going backwards, and a decrease to time moving forwards. In BS, aside from the discount factor related to rT, everywhere the time to expiration T occurs it is as part of the product sigma * sqrt(T). So doubling the volatility is equivalent to increasing the time to expiration by a factor of 4.
 
I agree with what dmo and rew have said - one thing that might be confusing you is people make comments like I made money going "short IV" and it really was because of time value - but remember that when time value completely runs out, IV will fall to basically 0 - check IVs near the close of market Friday. So if a person sells a put or call and it expires worthless, certainly it was because time ran out, but it is also true that IV fell to 0 at that point.

JJacksET4
 
Quote from deltahedge:



However in regards to your statement that the volatility is akin to the probability of the option expiring ITM I believe is slightly off, if anything (and again this statement too is also fallacious from a mathematical perspective but it has been used at times as a proxy for estimation) would be the delta of the put.
More...

Yes, the delta is often used as a proxy for the likelihood of an option expiring in the money. But an option with a delta of 1 - virtual certainty that it will expire ITM - has time value of near zero. An option with delta of 1 would be equivalent to a hurricane insurance policy on a house in New Orleans, after it had already been destroyed by Katrina. That insurance policy would also be "in the money." Payout would be a certainty. The value of such a policy would be determined by the cost to repair or replace the house, not the probability of a future hurricane.

But if we're talking about the probability of a future event that would cause an option seller to lose money - and would thus make him demand a high time premium from a buyer - then we're talking about volatility. Conceptually that would be the equivalent of the probability of of a hurricane in the hurricane-insurance business.
 
Quote from rew:

Given that the only parameter that has changed is time it is obvious that the gain in the short put is solely due to time decay. Of course you give a fairly artificial example -- the stock dropped down on bad news and its implied volatility went up, and then months later the stock hasn't moved at all but the implied volatility is as high as it was during the panic. In the real world the implied volatility would have declined once the market realized that the bad news was fully priced in.

In any case it has long been recognized in option pricing that an increase in volatility is roughly equivalent to time going backwards, and a decrease to time moving forwards. In BS, aside from the discount factor related to rT, everywhere the time to expiration T occurs it is as part of the product sigma * sqrt(T). So doubling the volatility is equivalent to increasing the time to expiration by a factor of 4.
More...

Thanks for the information rew :).

On a slightly separate note, I'm wondering what is the appropriate way to assess implied volatility?

Technically it's plausible that the front months volatility drops a significant amount and the stock moves up, but the further back months volatility can remain elevated (perhaps an impending FDA decision). In light of that scenario is it fair to say IV has dropped? Or in another scenario ATM volatility in the back months has remained constant but there has been an increase in the vertical skew such that the IV of the OTM options has increased.

If one applies a VIX-esque methodology to calculate "IV" in the above scenario IV would effectively remain unchanged as the VIX methodology of calculating IV does not offer much weight to back months and especially OTM back month IVs. Yet, if one looked at the volatility "surface" you would see a spike at those OTM strikes.

General thoughts/comments/musings/jokes are all appreciated :D
 
Quote from dmo:

Yes, the delta is often used as a proxy for the likelihood of an option expiring in the money. But an option with a delta of 1 - virtual certainty that it will expire ITM - has time value of near zero. An option with delta of 1 would be equivalent to a hurricane insurance policy on a house in New Orleans, after it had already been destroyed by Katrina. That insurance policy would also be "in the money." Payout would be a certainty. The value of such a policy would be determined by the cost to repair or replace the house, not the probability of a future hurricane.

But if we're talking about the probability of a future event that would cause an option seller to lose money - and would thus make him demand a high time premium from a buyer - then we're talking about volatility. Conceptually that would be the equivalent of the probability of of a hurricane in the hurricane-insurance business.
More...

Interesting. Thanks for the clarification of your earlier example, I can now see why you would relate an option's volatility as the premium which would imply the probability of a hurricane in the property insurance field.
 
Quote from deltahedge:

Thanks for the information rew :).

On a slightly separate note, I'm wondering what is the appropriate way to assess implied volatility?

Technically it's plausible that the front months volatility drops a significant amount and the stock moves up, but the further back months volatility can remain elevated (perhaps an impending FDA decision). In light of that scenario is it fair to say IV has dropped? Or in another scenario ATM volatility in the back months has remained constant but there has been an increase in the vertical skew such that the IV of the OTM options has increased.

If one applies a VIX-esque methodology to calculate "IV" in the above scenario IV would effectively remain unchanged as the VIX methodology of calculating IV does not offer much weight to back months and especially OTM back month IVs. Yet, if one looked at the volatility "surface" you would see a spike at those OTM strikes.

General thoughts/comments/musings/jokes are all appreciated :D
More...

The appropriate way to assess IV is to measure it individually and separately at each strike, in each month. Keep doing so and playable anomalies will occasionally reveal themselves. If atm option iv doesn't change but the skew becomes steeper than it's ever been - then think about selling the damn skew, not what the appropriate one-word iv description is!
 
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