Delta hedging

CFA Level II Derivatives
#1

Hello guys, I hope revision is going well for you.

There is a formula for hedging : number of options = number of shares / delta

Scenario: The delta of the put option (thus negative) moves towards 0 (let’s say from -0.5 to -0.1), then according to formula, the number of options required for hedging would increase (let’s say from -10 to -15), given then number of shares remains the same.

Is it correct to interpret this by saying that 1) we would now need to short 15 put options compared to 10 as before; 2) we short 5 more put options to reach delta hedge

Thanks

#2

The formula is: number of options = - number of shares / delta. (Note the negative sign.)

You sell (short) call options (positive delta) or buy put options (negative delta).

Thus, in your example, you’re already long 10 put options, so you would have to buy (not sell) 5 more put options to maintain the delta hedge.

#3

Makes sense, thank you !

#4

You’re welcome.

#5

Hi I m confused on this one why did you put a negative sign?

#6

Is it because we are long the stock so in order to have a delta neutral portfolio we have to short calls hence the negative sign?

#7

So you can either short calls or buy put if you are long stock… ?

#8

Yes, this is the way I interpret this. If you are long stock, you only want to protect yourself against the risk that share price will fall. This can be done by either shorting calls or buying puts as both of them benefit when price falls

#9

Thanks

#10

What??

So there are two formulas…

For protecting the stock from going down = # of short calls nedded = # shares hedged/ Delta call.

What is the other one?

#11

Yes.

#12

what I understand for this is to consider offseting position,

suppose you long stock, if stock price increases, we need a call option to offset the return to make our position neutral, so we have to short calls, if stock price decreases, we recoup the losses through the selling of calls.