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by mj
June 28th, 2017, 1:17 am
Forum: Book And Research Paper Forum
Topic: Recombining Trinomial Tree
Replies: 6
Views: 1504

Re: Recombining Trinomial Tree

See also  Chan, Jiun Hong and Joshi, Mark S. and Tang, Robert and Yang, Chao, Trinomial or Binomial: Accelerating American Put Option Price on Trees (September 1, 2008). Available at SSRN:  https://ssrn.com/abstract=1261745  or  http://dx.doi.org/10.2139/ssrn.1261745 RE works if the pay-off is smoot...
by mj
June 9th, 2017, 12:02 am
Forum: Numerical Methods Forum
Topic: nested Monte Carlo
Replies: 0
Views: 650

nested Monte Carlo

We have done a new paper on how to do nested Monte Carlo using small number of sub-simulation paths. I'd be interested in any comments. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2983510 There are many applications including CVA, VIX, PFE, VAR capital modelling. I think this paper will be i...
by mj
October 3rd, 2016, 3:57 am
Forum: Numerical Methods Forum
Topic: local vol with stochastic vol and stochastic rates
Replies: 5
Views: 1330

local vol with stochastic vol and stochastic rates

We have done a paper on how to calibrate local vol when both volatility and rates are stochastics.

I'd be interested in any comments.

http://ssrn.com/abstract=2840628
by mj
April 14th, 2016, 4:38 am
Forum: Programming and Software Forum
Topic: circle-ellipse inheritance problem
Replies: 81
Views: 5092

circle-ellipse inheritance problem

<t>Sorry to be late to the discussion. I suspect the interviewer of the OP was getting at the Liskov sustainability principle. The idea is that the inherited class should support all the methods of the base class. An ellipse naturally has methods to set the major and minor axes sizes but a circle do...
by mj
April 2nd, 2016, 9:36 am
Forum: Technical Forum
Topic: Variance Gamma formula of Madan-Carr-Chang
Replies: 4
Views: 1654

Variance Gamma formula of Madan-Carr-Chang

have you tried writing the price as an integral over Black--scholes prices? this gives an alternative way to evaluate the price which you can check against.
by mj
March 2nd, 2016, 10:59 pm
Forum: Technical Forum
Topic: power numeraire
Replies: 2
Views: 1784

power numeraire

Thanks. Do you have any specific references?
by mj
March 2nd, 2016, 10:59 pm
Forum: Technical Forum
Topic: Exact simulation of brownian motion and of its integral
Replies: 18
Views: 3019

Exact simulation of brownian motion and of its integral

<r>you get into tricky issues when factor reducing and then using a long step scheme since time-dependent vol and drift state-dependence render the model full factor. I discuss these issues in detail in More Mathematical Finance. See also our paper <URL url="http://ssrn.com/abstract=907385">http://s...
by mj
February 29th, 2016, 8:54 pm
Forum: Technical Forum
Topic: Exact simulation of brownian motion and of its integral
Replies: 18
Views: 3019

Exact simulation of brownian motion and of its integral

This is well known... The easy way is simply to approximate by a discrete sum and then let the number of steps go infinity. Yes, it is bivariate normal. So all you need to compute are the variances and covariances.
by mj
February 28th, 2016, 9:13 am
Forum: Book And Research Paper Forum
Topic: MultiThreaded Sobol Sequences
Replies: 2
Views: 3019

MultiThreaded Sobol Sequences

there's a GPU Sobol generator in the CUDA SDK
by mj
February 26th, 2016, 1:48 am
Forum: Technical Forum
Topic: power numeraire
Replies: 2
Views: 1784

power numeraire

I have done a little note on how to use powers of the stock price as numeraire. It actually has quite a few implications both theoretical and practical. I'd be interested in any comments.http://ssrn.com/abstract=2735944
by mj
February 3rd, 2016, 8:24 pm
Forum: Technical Forum
Topic: CVA
Replies: 11
Views: 2877

CVA

yes, that is what we were thinking. use the regression to determine the region you are in but evaluate the cash-flows directly.
by mj
January 28th, 2016, 9:56 pm
Forum: Technical Forum
Topic: CVA
Replies: 11
Views: 2877

CVA

<t>Well, regression methods are convergent in the sense that as the number of basis functions and paths go to infinity, the regression converges to the true value. However, just increasing the number of basis functions whilst keeping the number of paths fixed is often unwise in that there is increas...
by mj
January 28th, 2016, 2:44 am
Forum: Numerical Methods Forum
Topic: American options -- Reference prices
Replies: 265
Views: 17441

American options -- Reference prices

<t>I'd like to see some benchmarks for S is 120,K is 100, r=0.08, the volatilityis 0.2, the dividend rate q is 0.08, and the expiry T is 3This was studied in Quantitative Finance, Vol. 12, No. 1, January 2012, 17?20On the analytical/numerical pricing of American putoptions against binomial tree pric...
by mj
January 27th, 2016, 11:02 pm
Forum: Technical Forum
Topic: CVA
Replies: 11
Views: 2877

CVA

OK i can see that that case would be trickier. I think there might be some ways around it, however. Can you point to, or send me, a spec of what you would like a model to be able to do?
by mj
January 26th, 2016, 6:50 pm
Forum: Technical Forum
Topic: CVA
Replies: 11
Views: 2877

CVA

as long you model the early exercise decision and all cash-flows correctly, I don't see how collateral is a problem.
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