Option pricing using Markov chains

[Naucle]

Hello everyone,

I'm working on a school project and I'm trying to understand option pricing using Markov chains, which (I think) could help me understand CPPI pricing using Markov chains. Do you people have any useful documents that explicitly describe the method with examples (excel spreadsheets are very welcomed) . I would be very very thankful.

Thank you.

 

[CasanovaJ]

Hello everyone,

I'm working on a school project and I'm trying to understand option pricing using Markov chains, which (I think) could help me understand CPPI pricing using Markov chains. Do you people have any useful documents that explicitly describe the method with examples (excel spreadsheets are very welcomed) . I would be very very thankful.

Thank you.

http://en.wikipedia.org/wiki/Geometric_Brownian_motion

http://en.wikipedia.org/wiki/Black–Scholes_model

 

[Naucle]

http://en.wikipedia.org/wiki/Geometric_Brownian_motion

http://en.wikipedia.org/wiki/Black–Scholes_model

I thank you for you reply, but I am not looking for the closed formulas, I clearly stated "
Option pricing using Markov chains"

 

[CasanovaJ]

I thank you for you reply, but I am not looking for the closed formulas, I clearly stated "
Option pricing using Markov chains"

http://investexcel.net/binomial-option-pricing-excel/

 

[yetanotherquant]

I thank you for you reply, but I am not looking for the closed formulas, I clearly stated "
Option pricing using Markov chains"

IMO you are trying to get an answer to a wrong question.
Markov processes (roughly said, these are the Markov chains in continuous time) are very comfortable to work with (for option pricing as well). But there is no fundamental relation between them and option prices (there is such between the martingales and option pricing).

To be closer to your questions, well, Markov processes are convenient for option pricing because the simplest way to price an option is a (binary) tree and Markov processes allow usage of recombining trees, which drastically reduces computational complexity.

 

[Naucle]

IMO you are trying to get an answer to a wrong question.
Markov processes (roughly said, these are the Markov chains in continuous time) are very comfortable to work with (for option pricing as well). But there is no fundamental relation between them and option prices (there is such between the martingales and option pricing).

To be closer to your questions, well, Markov processes are convenient for option pricing because the simplest way to price an option is a (binary) tree and Markov processes allow usage of recombining trees, which drastically reduces computational complexity.

I have actually found this document : http://www.math.ntu.edu.tw/~hchen/jointseminar/markovchain.pdf
But I couldn't understand it, for exemple, I don't get how they got thir payoffs in the page 11 and how they used their markov matrix for the markov chains interpretation.

 

[yetanotherquant]

Forget this paper (unless you really have to study it).
It is written in 2000 - a pretty outdated stuff.
And believe me, this Markov chain approach is not what every quant must know.
Well, I am not a guru of numerical finance but I am in business for 8 years and I have never seen that suchlike approach was applied in practice.
Trees, (Least-Square) Monte-Carlo and PDE/Finite Difference are common approaches and they are usually sufficient.
Numerical accuracy is usually important but remember, "your model is only as good as your data are" (c) E. Derman

 

[Naucle]

Forget this paper (unless you really have to study it).
It is written in 2000 - a pretty outdated stuff.
And believe me, this Markov chain approach is not what every quant must know.
Well, I am not a guru of numerical finance but I am in business for 8 years and I have never seen that suchlike approach was applied in practice.
Trees, (Least-Square) Monte-Carlo and PDE/Finite Difference are common approaches and they are usually sufficient.
Numerical accuracy is usually important but remember, "your model is only as good as your data are" (c) E. Derman

That's all I needed to know, thank you.

 

[yetanotherquant]

You are welcome!

A general remark: there are a lot of papers on quantitative finance, that are written just to be written. Academic guys (who never traded an option) need publications to make career. They develop rigorous mathematical models (that still often contain errors since almost no peer reviewer checks every detail). But even if the model is correct it is often as complicated as useless.

That's why if you really what to learn practical stuff, have a look on models that are implemented in QuantLib and OpenGamma. I don't say "try to understand the program code" (though it definitely won't hurt you). I just say - have a look which models are implemented by practitioners (who would never waste their time for implementation of useless models).