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by AvH
September 4th, 2008, 1:43 pm
Forum: Numerical Methods Forum
Topic: Broadie and Glasserman's Stochastic Mesh: Example Code?
Replies: 1
Views: 51017

Broadie and Glasserman's Stochastic Mesh: Example Code?

<t>say you have three nodes at the first time: A1, B1 and C1 which go over in the nodes A2, B2, and C2.Then define the transition probabilities of going from node A1->A2 as p(A1,A2).Say A1 is two-dimensional A1 = (x1,y1), A2 = (x2,y2), then p(A1,A2) = P[ (X2,Y2) = (x2,y2) | (X1,Y1) = (x1,y1) ] ('Biv...
by AvH
September 4th, 2008, 1:29 pm
Forum: Numerical Methods Forum
Topic: g2++ swaption formula
Replies: 21
Views: 120471

g2++ swaption formula

<r>A few practical tips:- As the derivative in the root finding procedure for y can be easily calculated, a Newton-Raphson procedure seems the most obvious.- Note that the integral is actually a bounded function against a normal distribution (make a plot of the integrand and you'll be surprised how ...
by AvH
August 6th, 2008, 12:42 pm
Forum: Technical Forum
Topic: Complex logarithm in Heston model
Replies: 7
Views: 51896

Complex logarithm in Heston model

The paper of Lord and Kahl or the paper of Schoutens might help.see http://ssrn.com/abstract=1105998 or http://perswww.kuleuven.be/~u0009713/HestonTrap.pdf
by AvH
July 4th, 2008, 9:20 am
Forum: Technical Forum
Topic: stochastic discount factor in a Black Scholes Hull White model
Replies: 4
Views: 53311

stochastic discount factor in a Black Scholes Hull White model

I already suspected that ;-)Perhaps you can use the fact that both the zero-coupon bond option as well as the stock price follows a log-normal distribution which is equivalent to a two-stock Black-Scholes economy (with correlated assets) ...
by AvH
July 3rd, 2008, 1:05 pm
Forum: Technical Forum
Topic: stochastic discount factor in a Black Scholes Hull White model
Replies: 4
Views: 53311

stochastic discount factor in a Black Scholes Hull White model

Can't you use RN valuation and use exp[-int r(u) du] (i.e. one over the money market account) as stochastic discount factor ? \edit typo
by AvH
July 2nd, 2008, 8:12 am
Forum: Numerical Methods Forum
Topic: Calibration of a HW-HW-Heston Cross-Currency Model
Replies: 19
Views: 61467

Calibration of a HW-HW-Heston Cross-Currency Model

<t>No problem, I was also confused initially and it took me some time to figure it out. Indeed the restriction is very odd and unnecessary. I can only guess for the reason behind it, but it might be that the resulting ODE's become a little bit messier ... anyway the author could have been more clear...
by AvH
June 30th, 2008, 8:25 am
Forum: Technical Forum
Topic: monte carlo heston convergence
Replies: 13
Views: 55406

monte carlo heston convergence

<r>QuoteOriginally posted by: piterbargjust use this:<URL url="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=946405that"><LINK_TEXT text="http://papers.ssrn.com/sol3/papers.cfm? ... 946405that">http://papers.ssrn.com/sol3/papers.cfm?abstract_id=946405that</LINK_TEXT></URL> should sort you outVV...
by AvH
June 30th, 2008, 6:37 am
Forum: Numerical Methods Forum
Topic: Calibration of a HW-HW-Heston Cross-Currency Model
Replies: 19
Views: 61467

Calibration of a HW-HW-Heston Cross-Currency Model

<r>QuoteOriginally posted by: piterbargare you sure abut that? that was not my impression at all. Perhaps the vector notations confused you? I shall go back and check-V- First of all, imho, the author is not really explicit about the correlation assumptions, so one has to distill it from the formula...
by AvH
June 28th, 2008, 8:41 am
Forum: Numerical Methods Forum
Topic: Calibration of a HW-HW-Heston Cross-Currency Model
Replies: 19
Views: 61467

Calibration of a HW-HW-Heston Cross-Currency Model

<r>QuoteOriginally posted by: piterbargSomebody just published the same in a journalhttp://<URL url="http://www.worldscinet.com/cgi-bin/details.cgi?id=voliss:ijtaf_1103&type=tocInternational"><LINK_TEXT text="www.worldscinet.com/cgi-bin/details.cgi ... ernational">www.worldscinet.com/cgi-bin/det...
by AvH
June 20th, 2008, 7:33 pm
Forum: Numerical Methods Forum
Topic: I have a c code for Sobol sequence generation
Replies: 13
Views: 57098

I have a c code for Sobol sequence generation

Ok thanks: that is pretty clear ... since it might indeed be hard to align the variates, JoeKuo07 might indeed be the better option if these results hold in general.
by AvH
June 19th, 2008, 9:56 pm
Forum: Numerical Methods Forum
Topic: Calibration of a HW-HW-Heston Cross-Currency Model
Replies: 19
Views: 61467

Calibration of a HW-HW-Heston Cross-Currency Model

<t>QuoteOriginally posted by: bluffbodyNumerically speaking I experience difficulties to compute the closed-form characteristic function (of the domestic T-forward log FX-rate) of the HWHWSchobel-Zhu model. Problems come of course from the hypergeometric functions contained in the A(t) coefficient o...
by AvH
June 15th, 2008, 6:46 pm
Forum: Numerical Methods Forum
Topic: Levenberg-Marquardt in matlab
Replies: 2
Views: 59820

Levenberg-Marquardt in matlab

<r>The built-in function lsqnonlin (available in the optimization toolbox) can also use the LM-algorithm.See <URL url="http://www.mathworks.com/access/helpdesk/help/toolbox/optim/index.html?/access/helpdesk/help/toolbox/optim/ug/lsqnonlin.html"><LINK_TEXT text="http://www.mathworks.com/access/helpde...
by AvH
June 13th, 2008, 10:35 am
Forum: Numerical Methods Forum
Topic: I have a c code for Sobol sequence generation
Replies: 13
Views: 57098

I have a c code for Sobol sequence generation

mj,how do the newly added initialization numbers (in QL-SobolGenerator) of Joe and Kuo compared those of Jäckel, is this difference noticeable ?
by AvH
June 12th, 2008, 10:17 am
Forum: Book And Research Paper Forum
Topic: Andreasen (2006): "Closed Form Pricing of FX Options under Stochastic Rates and Volatility"
Replies: 7
Views: 58841

Andreasen (2006): "Closed Form Pricing of FX Options under Stochastic Rates and Volatility"

<r>Interesting results Vladimir, which I was not aware off: I have only calibrated the model to equity quotes and not FX ones. For the equity market the SZ-HW model can fit the markt quite well (similar to Heston), but I will need to test it on FX quotes.Anyway, we are a bit in parallel (or off-topi...
by AvH
June 12th, 2008, 9:36 am
Forum: Numerical Methods Forum
Topic: Calibration of a HW-HW-Heston Cross-Currency Model
Replies: 19
Views: 61467

Calibration of a HW-HW-Heston Cross-Currency Model

<t>The distribution of the variance in the Heston model is Non-central Chi-squared distributed with (usually) a small degrees of freedom, while the distribution of the SZ model is distributed as an ordinary Chi-Squared distribution. Then your statement would imply that for high vol of variance the n...
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