DELTA (By that I mean the Continuous-Time Delta)
ANALYTIC DEFINTION- change in CB price for a given change in the Underlying Stock price.
MEANING - equity sensitivity for a CB.Tells the arbitrageur how many shares to SHORT against a long bond position.
CALCULATION - It's taken as N(d1) discounted by the stock's dividend yield.
NUMERIC RANGE OF DELTA:
* Approaches one as CB moves deep-in-the-money.
* Approaches zero as the stock price falls.
MORE ABOUT DELTA:
What we've talked about is the continuous-time delta. Suppose you expect to rebalance the hedge for every 5% move in the stock price - so you can calculate the change in value for a down move and for an up move, average them, and that's your delta. It's still one number - but you factor in any asymmetric behaviours.
GAMMA
Sensitivity of delta to changes in Stock Price. A higher gamma implied the convertible's hedge must be rebalanced more frequently.
The interesting thing about gamma is it's variation with moneyness. Gamma is low for deep-in-the-money convertibles and for a far-out-the-money convertible. ATM CBs have the highest gammas.
ANALYTIC DEFINTION- change in CB price for a given change in the Underlying Stock price.
MEANING - equity sensitivity for a CB.Tells the arbitrageur how many shares to SHORT against a long bond position.
CALCULATION - It's taken as N(d1) discounted by the stock's dividend yield.
NUMERIC RANGE OF DELTA:
* Approaches one as CB moves deep-in-the-money.
* Approaches zero as the stock price falls.
MORE ABOUT DELTA:
What we've talked about is the continuous-time delta. Suppose you expect to rebalance the hedge for every 5% move in the stock price - so you can calculate the change in value for a down move and for an up move, average them, and that's your delta. It's still one number - but you factor in any asymmetric behaviours.
GAMMA
Sensitivity of delta to changes in Stock Price. A higher gamma implied the convertible's hedge must be rebalanced more frequently.
The interesting thing about gamma is it's variation with moneyness. Gamma is low for deep-in-the-money convertibles and for a far-out-the-money convertible. ATM CBs have the highest gammas.
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