Black Scholes v Fourier transform

[Quantinator]

Hi everyone,
Is the Fourier transform much better than the Black Scholes model?

 

[pingu]

Hi everyone,
Is the Fourier transform much better than the Black Scholes model?

Yes.

http://math.stackexchange.com/quest...some-real-world-application-of-fourier-series

 

[Quantinator]

Yes.

http://math.stackexchange.com/quest...some-real-world-application-of-fourier-series

Thanks for the reply.

Do they overlap in any way?
http://banach.millersville.edu/~bob/book/BlackScholes/main.pd
I am fconfused because I came across this where they solved the black scholes equation by fourier transform.

 

[Daniel Duffy]

Ah, got it; you want to price BS using FT
http://ta.twi.tudelft.nl/mf/users/oosterle/oosterlee/COS.pdf
And early paper by Carr and Madan.

 

[Quantinator]

Ah, got it; you want to price BS using FT
http://ta.twi.tudelft.nl/mf/users/oosterle/oosterlee/COS.pdf
And early paper by Carr and Madan.

Hi. I have seen that paper, thanks anayway.
I do not want to price BS with FT. I just want to look at options pricing using FT on its own.
My dissertation basically says that BS is not good because of normal assumptions due to GBM etc... and hence I have decided to use FT because it is a levy process. And then I just look at FT on its own with regards to options pricing. What do you think?

 

[Quantinator]

Is that right or wrong?

 

[Daniel Duffy]

Is that right or wrong?

I think right, if I have understood correctly.

A good place IMO is the work of Alan Lewis (a overview is given in the book of Cont and Tankov).

Alternatively, (which I prefer to be honest as I know it better) is to use numerical methods to solve the PIDE for the exponential Levy process.

Depending on time pressures, you could do both approaches and compare them. Then throw in a Monte Carlo for good measure (see Glasserman; Haug; Platen on SDEs with jumps.)

http://www.proba.jussieu.fr/pageperso/ramacont/papers/pide.pdf

hth

BTW is it MSc/MFE or PhD dissertation?

 

[Daniel Duffy]

Thanks for the reply.

Do they overlap in any way?
http://banach.millersville.edu/~bob/book/BlackScholes/main.pd
I am fconfused because I came across this where they solved the black scholes equation by fourier transform.

That link seems to be broken.

 

[Quantinator]

http://banach.millersville.edu/~bob/book/BlackScholes/main.pdf
Thanks for your help, you seem very knowledgeable.
It is an undergraduate dissertation so it doesnt have to be too complicated.
Sorry, here it is again.

 

[Daniel Duffy]

thanks
good luck with the dissertation.

 

[Quantinator]

thanks
good luck with the dissertation.

Thank you. It is for undergraduate and I am not sure what path to follow.
I want to solely look at Option pricing using FT but would that be to complicated?
The link I attached above, that is solving the BS using FT so it is different to what I am looking for? (I think)

 

[Ole Bueker]

The question of difficulty should be based on your education and what your advisor is saying. Based on the little information you have provided, it is hard to say if the topic is on the right level for you. But I would assume that the topic is too advanced for a typical undergraduate dissertation.

 

[Quantinator]

The question of difficulty should be based on your education and what your advisor is saying. Based on the little information you have provided, it is hard to say if the topic is on the right level for you. But I would assume that the topic is too advanced for a typical undergraduate dissertation.

That is what I am worried about. I am just a little confused, Options pricing using FT is completely different to solving the BS using FT (in the link above)?

 

[KennyLam]

That is what I am worried about. I am just a little confused, Options pricing using FT is completely different to solving the BS using FT (in the link above)?

Your questions and comments seem to imply a fundamental misunderstanding of the topics that you are asking about. A financial model is essentially a set of assumptions that can be used to solve for useful properties of securities in financial markets such as price or various risk metrics. Black-Scholes is a very well known model for options pricing. Heston and SABR are other examples of such models.

The Fourier transform is a mathematical technique that is applied in various fields. It is a useful tool in solving for certain stochastic differential equations. It is not a financial model or a Levy process as you stated. They are two completely different things. FT, however, is a method that can be useful in obtaining certain properties of Levy processes. Duffy posted a link on how it can be used to obtain the vanilla call price in the Black-Scholes model. Probably its most well known use in finance is it's ability to help obtain a semi-closed form solution for the vanilla call price in the Heston model.

To compare FT with Black-Scholes is a bit nonsensical, which likely explains some of the confusion in this topic.

 

[pingu]

To compare FT with Black-Scholes is a bit nonsensical, which likely explains some of the confusion in this topic.

you just killed the fun.

 

[KennyLam]

you just killed the fun.

Had to be done. It's not very nice to waste the time of someone like Duffy.

 

[Quantinator]

Your questions and comments seem to imply a fundamental misunderstanding of the topics that you are asking about. A financial model is essentially a set of assumptions that can be used to solve for useful properties of securities in financial markets such as price or various risk metrics. Black-Scholes is a very well known model for options pricing. Heston and SABR are other examples of such models.

The Fourier transform is a mathematical technique that is applied in various fields. It is a useful tool in solving for certain stochastic differential equations. It is not a financial model or a Levy process as you stated. They are two completely different things. FT, however, is a method that can be useful in obtaining certain properties of Levy processes. Duffy posted a link on how it can be used to obtain the vanilla call price in the Black-Scholes model. Probably its most well known use in finance is it's ability to help obtain a semi-closed form solution for the vanilla call price in the Heston model.

To compare FT with Black-Scholes is a bit nonsensical, which likely explains some of the confusion in this topic.

Thank you for the clarification. Bear with me please, I came across stuff like this and I thought it was a financial model or a levy process. http://maxmatsuda.com/Papers/2004/Matsuda Intro FT Pricing.pdf
What would be the alternatives to FT please?

 

[Daniel Duffy]

Is that right or wrong?

One missing thing is we don't know who you are.
Are you a white belt or black belt if you get my drift?

 

[Quantinator]

One missing thing is we don't know who you are.
Are you a white belt or black belt if you get my drift?

I assume you are referring to my level of education? I am about to start my third year as a pure mathematician.
I know F all about the subject but it is something I am interested in and I am trying to build my knowledge by researching online. There are many basic things I am stuck on and need up understanding the basic concepts so that is why I am here.

 

[Daniel Duffy]

I assume you are referring to my level of education? I am about to start my third year as a pure mathematician.
I know F all about the subject but it is something I am interested in and I am trying to build my knowledge by researching online. There are many basic things I am stuck on and need up understanding the basic concepts so that is why I am here.

Yes, what your background is.
Pure maths (BTW I have a BA Mod in pure and applied maths myself so I am eligible to say something on the subject) is not necessarily the best preparation for computational finance. Depends in what you have done. Numerical analysis, applied Functional Analysis, methods and hard analysis are more useful than group theory, algebraic anything IMO.

A methods-driven maths approach is handy. Pure maths is not necessarily a guarantee for finance IMO.

And can you program in C or C++?
What kind of maths topics have you done?