Question

Characterize the behavior of the hedge ratio (for a European call option) in the limit as it gets farther in the money and as it gets farther out of the money.

Answer 1

Hedge ratio compares the value of a position protected through the use of a hedge with the size of the entire position itself. Example - if one is holding $20,000 in foreign equity, one is exposed to currency risk. If he hedges $10,000 worth of the equity with a currency position, hedge ratio is 0.5 (10 / 20).
Hedge ratio is also called delta of an option. Delta is amount by which underlying option will change in price for small changes in the stock price. An option with a delta of 0.70 means the option will move $0.70 for every $1.00 move in the stock. Coming to relationship -
When call is moving farther Out of money, hedge ratio approaches Zero and when it moves further In the Money, it reaches a value of +1. So range is 0 to 1. Once it has reached +1, curve moves linearly.