# American Option - Early exercise risk management

This is for American Option Book Management in real trading.

Lets 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 time delta hedging, only discrete time 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 delta hedging alone compensate early exercise settlement cashflow? For my guess, if theres no vega hegding with only disc. time delta hedging, delta hedging alone cannot compensate early exercise cashflow enough. And Vega hedging should be done for covering PL from not optimal early exercise. So when seller cannot hedge vega Risk, what hedge strategy would be the best for managing the book?

Any useful and bright Ideas, let$$`$$s share on that