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billyx524
Topic Author
Posts: 45
Joined: February 12th, 2016, 4:48 pm

option delta

January 21st, 2020, 12:10 am

Hi,

Does anyone know a no-arbitrage proof that call option delta has to be between 0 and 1?  We know that Black Scholes model N(d1) tells us that it is between 0 and 1, but is there a no-arbitrage argument?

Thanks
 
 
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billyx524
Topic Author
Posts: 45
Joined: February 12th, 2016, 4:48 pm

Re: option delta

January 21st, 2020, 2:11 am

Thanks a lot.  The deeper I go into models, the more I ask myself, "how do we know our models derivations/results" are correct.  Sometimes getting confused between real financial markets and mathematical models
 
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frolloos
Posts: 1619
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

Re: option delta

January 21st, 2020, 6:18 am

Thanks a lot.  The deeper I go into models, the more I ask myself, "how do we know our models derivations/results" are correct.  Sometimes getting confused between real financial markets and mathematical models
Define "correct". Aren't all models approximations? Some are good/realistic approximations, others are mathematically interesting but may not be appropriate to explain a particular phenomenon. 
 
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fomisha
Posts: 63
Joined: December 30th, 2003, 4:28 pm

Re: option delta

February 11th, 2020, 3:34 pm

It can be below 0 or above 1.

On the subject of delta calculation take a look at this article:
https://www.linkedin.com/pulse/spot-vol ... y-klassen/
 
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lePiddu
Posts: 20
Joined: March 17th, 2015, 2:15 pm

Re: option delta

February 12th, 2020, 8:17 am

@billy524 

Totally agree with @frolloos. As long as the assumptions on which your model is based are met, the model is correct by definition. 

You may be interested in what happens when some assumptions are violated. You are going to need a measure of the "performance" achieved by your model and find the impact in terms of this performance. Not an easy task I would say, but some typical examples are "hedging in the black-scholes world with the wrong volatility" or "disregarding second order movements in yield curves" or "reality is mean reverting, model is not".

You should always test the sensitivity of your model to the misspecification of its characteristics. 
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