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athos


Total Posts: 2
Joined: Jul 2014
 
Posted: 2017-03-16 16:08
I'm reading Nassim Taleb's book "Dynamic Hedging", on page 22 he says:

"Consequently, a straddle will be qual to two calls delta neutral or two puts delta neutral (of the same strike). Assume that the forward delta of a put is 30%,
"Straddle = 2P + .6F = 2(C-F) + .6F = 2C - 2F + .6F = 2C - 1.4F"

I really couldn't understand this, according to wiki straddle page "A straddle involves buying a call and put with same strike price and expiration date", so one has: Straddle=P+C.

In Taleb's example, he's assuming C=0.3F and P=−0.7, so

Straddle=P+C=−0.7F+0.3F=0.4F

This doesn't tally with his equation Straddle=2P+.6F=2(C−F)+.6F=2C−2F+.6F=2C−1.4F. What's the catch?

C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.

TakeItAndRun


Total Posts: 89
Joined: Apr 2010
 
Posted: 2017-03-17 12:01
To fully understand your question, the text before 'Consequently' would have helped. So what follows is purely speculative.

I guess it could be a general definition of a delta-neutral straddle: a delta-neutral straddle may consist of two delta-neutral options (same strike, same expiry).
Hence Straddle = 2P +.6F (delta of straddle = 0) = etc...

In your case P+C with delta(C) = 0.3 and delta(P) = -0.7 is not a delta-neutral straddle.

tbretagn


Total Posts: 243
Joined: Oct 2004
 
Posted: 2017-03-17 15:08
Taleb is literally playing with put call parity. A put is a call plus forward.
In the second example he says to assume the put delta is 30% (not 70% as in the previous example)

Et meme si ce n'est pas vrai, il faut croire en l'histoire ancienne

dVega/dRho


Total Posts: 5
Joined: Oct 2015
 
Posted: 2017-03-17 16:03
"Consequently, a straddle will be qual to two calls delta neutral or two puts delta neutral (of the same strike). Assume that the forward delta of a put is 30%,
"Straddle = 2P + .6F = 2(C-F) + .6F = 2C - 2F + .6F = 2C - 1.4F"

> if you buy a put the fwd delta is -0.3
> if you buy a call so by put call parity call fwd delta must be +0.7
> so if you buy the straddle; long call and long put give fwd delta of 0.4

"In Taleb's example, he's assuming C=0.3F and P=−0.7, so"
> this is where you are going wrong - if you buy the put the delta is -0.3 so by put call parity call must be +0.7

"Straddle=P+C=−0.7F+0.3F=0.4F"
> thus, P+C = -0.3+0.7=0.4

"This doesn't tally with his equation Straddle=2P+.6F=2(C−F)+.6F=2C−2F+.6F=2C−1.4F. What's the catch?"
> thus, 2P(-0.6)+0.6F = 0 which is delta neutral
> i.e. -0.6F from the straddle plus the delta exchange of +0.6F makes the trade delta neutral
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