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