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juniuss
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Early Exercise Risk Management for American Option

September 19th, 2019, 9:24 pm

This is for American Option Book Management In real Trading.
 
Let`s suppose,
1. American Option seller(Book manager) only do delta hedging, which means seller cannot do Vega hedging,
2. American Option buyer(Customer) exercise his option when exercise is not that optimal in theory.
3. Seller cannot do continuous delta hedging, only discontinuous hedging on delta Greek.
4. Optimal exercise depends on volatility level, interest rate and so on
 
In this case,
When early exercise (which is not that optimal in theory) happens, can only delta hedging compensate early exercise settlement cashflow?
For my guess, if there`s no vega heding with only discontinous delta hedging, only delta hedging cannot compensate early exercise cashflow enough.
And Vega hedging should be done for covering PL at not optimal early exercise.
So when seller cannot hedge vega Risk, what hedge strategy would be the best for book managing?
 
Any Useful and shine Ideas, let`s share on that 
 
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Alan
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Re: Early Exercise Risk Management for American Option

September 20th, 2019, 2:32 pm

Consider covered call writing: buy the stock, sell a call. There will be a maximum return if the call is optimally exercised. If the call is exercised early (non-optimally), that maximum return will be obtained *sooner*, which is a good thing. 

To take a trivial case, suppose there are no dividends, and so optimally, the call should not be exercised (if at all), until expiration. If it's exercised early, good for you: you just earned the maximum possible return and earlier than expected.

With dividends, while you may expect to lose a dividend if early exercise is optimal and the stock is sufficiently high, again, having the position closed earlier is better -- pretty sure.  :D
 
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DavidJN
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Re: Early Exercise Risk Management for American Option

September 20th, 2019, 4:06 pm

Unless there is no liquidity, in which case much of theory becomes less useful, the suggestion that a market maker can only delta hedge is unrealistic. I say that as a former option trader in a number of underlyings (fixed income, equity, FX).

Simulation is a good framework to investigate your own and Alan's observations. Simulate the price path of the underlying according to your preferred distributional assumption. You can vary the hedge reset period, introduce transactions costs, compare delta-only hedging to delta+vega hedging, you name it.   
 
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bearish
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Re: Early Exercise Risk Management for American Option

September 20th, 2019, 10:04 pm

Consider covered call writing: buy the stock, sell a call. There will be a maximum return if the call is optimally exercised. If the call is exercised early (non-optimally), that maximum return will be obtained *sooner*, which is a good thing. 

To take a trivial case, suppose there are no dividends, and so optimally, the call should not be exercised (if at all), until expiration. If it's exercised early, good for you: you just earned the maximum possible return and earlier than expected.

With dividends, while you may expect to lose a dividend if early exercise is optimal and the stock is sufficiently high, again, having the position closed earlier is better -- pretty sure.  :D
I swear we are hard-wired to think in terms of positive interest rates
 
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Alan
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Re: Early Exercise Risk Management for American Option

September 21st, 2019, 6:46 pm

Fair point. The OP should indicate if he/she is talking about a negative interest rate environment. (I indeed was not). If so, there is the possibility that the "non-optimal" early exercises being seen are actually optimal. Perhaps bearish will elaborate ...
 
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bearish
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Re: Early Exercise Risk Management for American Option

September 21st, 2019, 9:02 pm

Well, Merton's original argument for the non-optimality of early exercise of an American call on a non-dividend paying stock was in part based on the "fact" that the present value of the strike price paid at maturity is strictly less than the strike price paid now. Flip that inequality around, and the argument no longer holds. Of course, with enough time value left, you still don't want to exercise early, but now you actually need a model.

On a mostly unrelated note, Steve Figlewski has a recent working paper where he points out that, if you want/need to exit a long position in an American call on a non-dividend paying stock, it is often optimal to exercise it and sell the stock rather than selling the option, given much higher bid/ask spreads in the option market relative to the underlying stock market. 
 
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Paul
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Re: Early Exercise Risk Management for American Option

September 21st, 2019, 10:02 pm

Steve Figlewski has a recent working paper where he points out that, if you want/need to exit a long position in an American call on a non-dividend paying stock, it is often optimal to exercise it and sell the stock rather than selling the option, given much higher bid/ask spreads in the option market relative to the underlying stock market. 
The sun rises in the East because of the spin of the earth. You can reference me.
 
juniuss
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Re: Early Exercise Risk Management for American Option

September 23rd, 2019, 4:57 am

Consider covered call writing: buy the stock, sell a call. There will be a maximum return if the call is optimally exercised. If the call is exercised early (non-optimally), that maximum return will be obtained *sooner*, which is a good thing. 

To take a trivial case, suppose there are no dividends, and so optimally, the call should not be exercised (if at all), until expiration. If it's exercised early, good for you: you just earned the maximum possible return and earlier than expected.

With dividends, while you may expect to lose a dividend if early exercise is optimal and the stock is sufficiently high, again, having the position closed earlier is better -- pretty sure.  :D
Actual book management would be making delta neutral. 
Total final payoff would not be the same as covered call, cause spot and vol path would be the main factor of Hedged PL.
But I think Hedged PL could be similar to Covered call payoff. 
It means if interest rate > 0, we can get maximum(?) return sooner if Spot and vol path is not too volatile.
This is what i think so far. If there`s misunderstanding, plz let me know 
  
 
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Alan
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Re: Early Exercise Risk Management for American Option

September 23rd, 2019, 2:44 pm

The issue seems to be whether (non-optimal) early exercise is, on balance, a risk or a bonus/windfall to an existent hedging plan. If it's a bonus, you don't need to alter the plan. If it's a risk, you're going to have to weigh it against other risks -- which also might lead you to not alter the plan. 

As DavidJN pointed out, you can simulate these things.  Also, presumably you can do a post-mortem on all the cases that have occurred so far. Did the early exercise help or hurt?  If it hadn't occurred, would you have made more money or less?
 
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Paul
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Re: Early Exercise Risk Management for American Option

September 23rd, 2019, 4:46 pm

Non-optimal exercise of American options, discrete hedging, transaction costs, profit from different vols,... each have at least one chapter in PWOQF.