Heston model - Monte Carlo simulation
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Hello everyone, I would like to evaluate the Heston model using a Monte
Carlo simulation and get the values of the paths back, a kind of array [t, St],
or better to get the average of the paths at certain dates. I went through the sources
but I don’t see how to use the pricing engine for my purpose. Does anyone have an idea to help me? Thank you in advance and Have a nice weekend! Regards, Gilles The information in this e-mail is confidential and may be legally privileged. It is intended solely for the addressee. Access to this e-mail by anyone else is unauthorized. If you have received this communication in error, please address with the subject heading "Received in error," send back to the sender, then delete the e-mail and destroy any copies of it. If you are not the intended recipient, any disclosure, copying, distribution or any action taken or omitted to be taken in reliance on it, is prohibited and may be unlawful. Any opinions or advice contained in this e-mail are subject to the terms and conditions expressed in the governing KPMG client engagement letter. Opinions, conclusions and other information in this e-mail and any attachments that do not relate to the official business of the firm are neither given nor endorsed by it. KPMG cannot guarantee that e-mail communications are secure or error-free, as information could be intercepted, corrupted, amended, lost, destroyed, arrive late or incomplete, or contain viruses. KPMG is the Luxembourg member firm of KPMG international. KPMG International is a Swiss cooperative that serves as a coordinating entity for a network of independent firms operating under the KPMG name. KPMG International provides no services to clients. Each member firm of KPMG International is a legally distinct and separate entity and each describes itself as such. Information about the structure and jurisdiction of your local KPMG member firm can be obtained from your KPMG representative. This footnote also confirms that this e-mail message has been swept by AntiVirus software for the presence of computer viruses. However, the ultimate responsibility for virus checking lies with the recipient of this e-mail. |
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Hello Everyone,
The aim of what I described below would be to evaluate an autocallable bond which is described as following: Issue Size;Notes;Par per Note;Trade Date;Strike Date (Index value);Issue/payment date;Final Valuation Date;Final Redemption Date;Denomination;Issue price per note;Calendar 10000000;10000;1000;24/01/2008;24/01/2008(3809.07);07/02/2008;24/01/2013;07/02/2013;1000;London and TARGET Index/Underlying=STOXX50E; Trigger Level=65% closing value at strike date; Protection Level=100% closing value at strike date; Auto-Call Dates;IF STOXX50E >= Strike level; Then change at Early Redemption Date; to Early Redemption Amount; Next action 26/01/2009; 100% x Protection Level = 3809.07;09/02/2009; 112% x Denomination; -> Notes terminated and no further payment shall be made 25/01/2010; 95% x Protection Level; 08/02/2010; 124% x Denomination; -> Notes terminated and no further payment shall be made 24/01/2011; 90% x Protection Level; 07/02/2011; 136% x Denomination; -> Notes terminated and no further payment shall be made 24/01/2012; 85% x Protection Level; 07/02/2012; 148% x Denomination; -> Notes terminated and no further payment shall be made Auto-Call Dates;IF STOXX50E >= Trigger Level;Then change at Redemption Date;to Redemption Amount 24/01/2013; 65% closing value at strike date; 07/02/2013; 160% x Denomination ; if NOT; 07/02/2013; 100% x (STOXX50E final / STOXX50E initial) x (100/65) Evaluation date: 30/09/2009 Implied volatility:0.25667 Index value at evaluation date: 2872.63 Dividend: 0.033949938 To valuate it I thought of 1) Simulate a brownian motion 2) Evaluate at each auto-call dates le average of St Someone has an idea? Thank you in advance, Regards, Gilles |
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Check
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Re: Heston model - Monte Carlo simulation
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In reply to this post by gbogaert
On Fri, 2009-11-06 at 18:19 +0100, Bogaert, Gilles wrote:
> I would like to evaluate the Heston model using a Monte Carlo > simulation and get the values of the paths back, a kind of array [t, > St], or better to get the average of the paths at certain dates. I > went through the sources but I don’t see how to use the pricing engine > for my purpose. Gilles, you can use a MultiPathGenerator with a Heston process. The class is in <ql/methods/montecarlo/multipathgenerator.hpp>. For an example, look at <test-suite/pathgenerator.cpp> (even though it doesn't use Heston.) Let me know if you need additional help. Luigi -- Prediction is very difficult, especially if it's about the future. -- Niels Bohr ------------------------------------------------------------------------------ Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day trial. Simplify your report design, integration and deployment - and focus on what you do best, core application coding. Discover what's new with Crystal Reports now. http://p.sf.net/sfu/bobj-july _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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Hello Luigi,
Thank you for your advice. Could you give more detailed on the used of the MultiPath Generator? Is it not used for multiple assets? In my case I have one asset. Based on the test-suite, I tried the PathGenerator class. From what I understood, a path is generated each time that generator.next() is called, isn't it? I called it several times (50,000x) and took the last value of the sample with sample.value.back() for each generation. I am then surprised that after relaunching my program several times I always get the same values and average. typedef PseudoRandom::rsg_type rsg_type; typedef PathGenerator<rsg_type>::sample_type sample_type; BigNatural seed = 42; Time length = 10; Size timeSteps = 12; bool brownianBridge = true; Handle<Quote> x0(boost::shared_ptr<Quote>(new SimpleQuote(100.0))); Handle<YieldTermStructure> r(flatRate(0.05, Actual360())); Handle<YieldTermStructure> q(flatRate(0.02, Actual360())); Handle<BlackVolTermStructure> sigma(flatVol(0.20, Actual360())); boost::shared_ptr<StochasticProcess1D> process (new BlackScholesMertonProcess(x0,q,r,sigma)); rsg_type rsg = PseudoRandom::make_sequence_generator(timeSteps, seed); PathGenerator<rsg_type> generator(process, length, timeSteps,rsg, brownianBridge); for (Size i = 0; i <= 50000; i++){ sample_type sample1 = generator.next(); std::cout << sample1.value.at(j) << "\n"; } Thank you in advance for your help and time. For any information, please ask. Regards, Gilles
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Re: Heston model - Monte Carlo simulation
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On Tue, 2009-11-17 at 03:24 -0800, gbogaert wrote:
> Thank you for your advice. Could you give more detailed on the used of the > MultiPath Generator? Is it not used for multiple assets? Not only that. If you pass it the Heston model, it will generate MultiPaths with two components. The first will be the path generated for the underlying and the second the one for the volatility. > In my case I have one asset. Based on the test-suite, I tried the > PathGenerator class. From what I understood, a path is generated each time > that generator.next() is called, isn't it? I called it several times > (50,000x) and took the last value of the sample with sample.value.back() for > each generation. I am then surprised that after relaunching my program > several times I always get the same values and average. That's because you're always feeding the generator the same seed: > BigNatural seed = 42; > [...] > rsg_type rsg = PseudoRandom::make_sequence_generator(timeSteps, seed); If you want your program to use different feeds each time, set the seed to 0. But that will mean you might be unable to reproduce errors if they arised. Luigi -- There are no rules of architecture for a castle in the clouds. -- Gilbert K. Chesterton ------------------------------------------------------------------------------ Let Crystal Reports handle the reporting - Free Crystal Reports 2008 30-Day trial. Simplify your report design, integration and deployment - and focus on what you do best, core application coding. Discover what's new with Crystal Reports now. http://p.sf.net/sfu/bobj-july _______________________________________________ QuantLib-users mailing list [hidden email] https://lists.sourceforge.net/lists/listinfo/quantlib-users |
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