Re: Heston model - Monte Carlo simulation

Posted by gbogaert on Nov 09, 2009; 8:51am
URL: http://quantlib.414.s1.nabble.com/Heston-model-Monte-Carlo-simulation-tp8160p8164.html

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