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

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

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

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.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

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/

On the subject of delta calculation take a look at this article:

https://www.linkedin.com/pulse/spot-vol ... y-klassen/

@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.

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

You may be interested in

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

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