I know Dr W owns the website, but Quantessential strikes me as quite a good name for the framework... if he can be persuded to donote it to the wider cause... EDIT: Correct title for Dr W

Last edited by rmax on October 3rd, 2011, 10:00 pm, edited 1 time in total.

- SierpinskyJanitor
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It seems someone already had the same idea: http://www.quantessential.com/ BTW, I don´t mean Dr.W but rather:Quantessential ResearchQuantessential Research is a research firm. It is based in Boston, Massachusetts.101 Tremont StreetSuffolkBoston, MA 02108-5004United States

Last edited by SierpinskyJanitor on October 3rd, 2011, 10:00 pm, edited 1 time in total.

Not what who is shows:Registrant:Wilmott (WILMO35128)5Moscow Road, , W2 4SWGBDomain name: quantessential.comTechnical contact:Admin, Domain (DA566653)Easily Limited3rd Floor, Prospero House241 Borough High StreetBorough, London, SE1 1GAGB

Here is a feature request inspired by a current discussion in the Student Forum.99% of the time, when people code up a pricer for American-style options, they just output an option value.Well, I want to see the early exercise boundary, too!

Last edited by Alan on October 3rd, 2011, 10:00 pm, edited 1 time in total.

Totally agree with Alan request. That's something really interesting to have a look at this even from a practical point of view.

Last edited by frenchX on October 3rd, 2011, 10:00 pm, edited 1 time in total.

- Cuchulainn
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QuoteOriginally posted by: AlanHere is a feature request inspired by a current discussion in the Student Forum.99% of the time, when people code up a pricer for American-style options, they just output an option value.Well, I want to see the early exercise boundary, too!I know 1 method: use Landau transformation front fixing to transform the PDE to interval [0,1]. It is now NL because involves coupled V and B(t). Then solve for these 2 quantities. Maybe a nice ADE project for FX. Concrete and doable.

Last edited by Cuchulainn on October 3rd, 2011, 10:00 pm, edited 1 time in total.

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http://www.datasimfinancial.com

http://www.datasim.nl

http://www.datasimfinancial.com

http://www.datasim.nl

Good. Related to that, I often want to use Mathematica graphics. So, the ideal code would give me the option of seeing a visual of the boundary or just outputtingthe raw data for it that I display myself.

I was thinking about building a code (in Matlab, my C++ skill is not good enough) for pricing American option for Levy process using FFT method with forward grid shooting. Once you have a pricing tree structure, you just have to keep in memories the point for which you have smooth pasting I guess. Fixed point transformation into a nonlinear PDE would be nice for BS world but for general jump diffusion or SV model it would be awfull I think. Moreover the best would be a code which gives the boundary and the value. Once you have a kick pricing stuff, the critical boundary is just given by Option_value(S*)=Payoff(S*) But I keep in mind of using a ADE scheme for the optimal boundary in the BS world. that's a nice idea (I'll try leung+duffy pelleat idea). But I really think about other idea to obtain the optimal boundary (the NL PDE is not the best way I think).

Last edited by frenchX on October 3rd, 2011, 10:00 pm, edited 1 time in total.

I'll give a try on Friday evening. Forward grid shooting with FFT and characteristic function and keep in memories the value S* such as Option(S*)=Payoff(S*) for each time step. Sounds easy on the paper !! (I already have the algo now the implementation, always the trickier part).

Last edited by frenchX on October 3rd, 2011, 10:00 pm, edited 1 time in total.

Alan, would S* (the critical spot price) be of interest to you?Definitions:http://finance.bi.no/~bernt/gcc_prog/al ... 1133.htmIf so, I think you can access it in QuantLib using criticalPrice member function (of BaroneAdesiWhaleyApproximationEngine):http://quantlib.sourcearchive.com/docum ... ce.htmlYou can see an example of using the BaroneAdesiWhaleyApproximationEngine in AmericanOptionTest::testBaroneAdesiWhaleyValues here:http://quantlib.sourcearchive.com/docum ... ource.html

Last edited by Polter on October 3rd, 2011, 10:00 pm, edited 1 time in total.

@Thijs, email sent@Polter, Not so much interested in that approximation.Would like to see early exercise boundaries accurately and quickly generated in models with continuous and discrete dividends, including:(i) GBM, (ii) exp Levy models, (iii) stoch. vol models, (iv) SVJ, etc. For example, for Case (iii) with cont div yields,I have a penalty method implemented in Mathematica, but it is a little slow for my tastes. Don't have a case (iv) implemented at all, although I have some algorithm ideas for it that I could contribute. Here is a related: Feature Request: a library of methods for converting a set of observed American-style option prices to estimatesof what the corresponding Euro-style prices would be, if they were trading. [This is a quite common problem neededfor smile fitting and modelling in a variety of contexts.]

Last edited by Alan on October 3rd, 2011, 10:00 pm, edited 1 time in total.

Alan: I see, that's certainly far less-trivial, but also more interesting!BTW: for European<->American conversion is the idea to invert-around-the-implied-volatility? As in:0. given o_European_value (the observed European option price)1. find out implied-volatility (IV) "sigma_implied" via inversion of o_European (the European option price as a function of IV)2. obtain O_American_value as a result of evaluating O_American(sigma_implied)and analogously in the other direction?// the inversion-oriented method

Last edited by Polter on October 3rd, 2011, 10:00 pm, edited 1 time in total.

That method is a basic one, but if the underlying follows any process other than GBM, it is only an approximation (andsometimes quite a poor one). So, I think there is a need for additional (model-dependent) approaches.

I see, good point!Does this imply the need for calibration (problem might be overdetermined, so no bijection, so no inversion) in general:0. given o_European_value (the observed European option price)1. find out model-dependent implied-parameters (IP) "parameters_implied" via calibration of o_European (the European option price as a function of IP)2. obtain O_American_value as a result of evaluating O_American(parameters_implied)and analogously in the other direction?// the model-dependent-calibration-oriented method The need-to-be-configurable points seem to be the models for obtaining o_European & O_American, calibration objective function (at least)?

Last edited by Polter on October 3rd, 2011, 10:00 pm, edited 1 time in total.

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