Hi guys, Need some help on the question below schweser exam book 2 afternoon session q44 *quoted -if the price of the underlying bond increase by 1% due to a yield curve shift, call hedge should be decreased because delta would have increased. Is this correct or incorrect? Answer: correct From my understanding, delta is the change in call price divided by change in price of the underlying asset. If underlying price increase, delta should decrease and not increase right? Can anybody advise on this question??
important : they are out of the money. so if the interest rate goes up by 1 percent, they are less out-of-the money so delta of the call option will rise. ( delta is 1 at the money )
I think you are mixing up return and delta value. they are asking about the delta hedge position, not the delta portfolio return
they are talking about Gamma here, the rate of change of delta given a change in interest rate. gamma is positive when out-of-the money. so if int rate increase, delta will increase, so you need to decrease the delta hedge position.
Thanks for your reply, Summerside! Ok I think I got what you meant by increase in price of asset = more in the money = delta increase and move towards 1. But can you elaborate on the part where “delta increase, so you need to decrease the delta hedge position” ? Let’s say for example Delta = 0.533 and I short 10, 000 calls So my delta hedge position = 0.533 x 10, 000 = 5, 330 shares of stock So if my delta increase to 0.7, shouldn’t by delta hedge position also increase to 0.7 x 10, 000? Thanks!
you got the concept.
the example is fine, let’s work it that way : you have 10 000 share you want to hedge, delta = 0.4
so you need -(10 000/ 0.4) = -25 000 option to hedge the position
if the delta change to 0.7, now you need -10 000 / 0.7 = -14 285 options , so you decrease the hedge by 25000-14285 = 10 714 options
even if the position lost in value, you still have 10 000 share to hedge.
Whether it’s out of the money, at the money, or in the money doesn’t matter: the delta of a call option increases when the price of the underlying increases. If you draw a picture of a call option’s payoff, then its price, you’ll see this clearly.
No, it isn’t. (Look at the picture you drew, above.) A call option’s delta is (nearly) 1 when the option is _ far in the money , but _ less than one at the money.
Gamma is positive everywhere (for both call options and put options).
Please be careful with this stuff.
Thanks for elaborating, Summerside. I finally understand it now!
Thanks S2000 for reinforcing the concept!
My pleasure.