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by logos01
August 8th, 2018, 9:35 am
Forum: Trading Forum
Topic: And now for some fun with implied densities… (or, the coming Tesla crash?)
Replies: 14
Views: 6200

Re: And now for some fun with implied densities… (or, the coming Tesla crash?)

It turns out that I have been looking at this problem as well https://chasethedevil.github.io/post/tsla-stock-crash-probability/ . Initially this was partly to evaluate the stochastic collocation technique to imply the probability density (it is very simple) as I had written a paper (not yet publish...
by logos01
August 25th, 2017, 11:09 am
Forum: Technical Forum
Topic: Volatility Wing Model in ORC
Replies: 5
Views: 2234

Re: Volatility Wing Model in ORC

This parameterization is not made to be arbitrage free: at x=0 there is a discontinuity in the second derivative.
by logos01
April 9th, 2016, 4:16 pm
Forum: Numerical Methods Forum
Topic: Barrier option with continuous monitoring solved by finite difference
Replies: 42
Views: 40836

Barrier option with continuous monitoring solved by finite difference

<t>Richardson extrapolation is really not as bad as Billy7 suggests. With Dupire local vol, it can be more accurate than a direct second order scheme. Even if it was 2x slower than Crank Nicolson with Rannacher smoothing, the simplicity and robustness of the scheme are impressive.A robust and stable...
by logos01
March 10th, 2016, 4:25 pm
Forum: Technical Forum
Topic: Normal Model & Sabr parameters
Replies: 3
Views: 2781

Normal Model & Sabr parameters

<r>It depends if you mark against shifted lognormal vols or against normal (bp) vols. For shifted lognormal, Alan is more or less correct. For normal, the formula is slightly different.The normal cubic polynomial is detailed in the following paper:<URL url="http://papers.ssrn.com/abstract=2467231">h...
by logos01
December 20th, 2015, 1:03 pm
Forum: Technical Forum
Topic: SABR approximations - best practice?
Replies: 105
Views: 76492

SABR approximations - best practice?

<r>Here is an old blog post around the free boundary SABR with Hagan's PDE approach <URL url="http://chasethedevil.github.io/post/arbitrage-free-sabr-with-negative-rates---alternative-to-shifted-sabr/I"><LINK_TEXT text="http://chasethedevil.github.io/post/arb ... ted-sabr/I">http://chasethedevil.git...
by logos01
November 1st, 2015, 8:29 pm
Forum: Numerical Methods Forum
Topic: Barrier option with continuous monitoring solved by finite difference
Replies: 42
Views: 40836

Barrier option with continuous monitoring solved by finite difference

<r>a blog post about this from a few weeks ago.<URL url="http://chasethedevil.blogspot.fr/2015/09/crank-nicolson-and-rannacher-issues.html"><LINK_TEXT text="http://chasethedevil.blogspot.fr/2015/0 ... ssues.html">http://chasethedevil.blogspot.fr/2015/09/crank-nicolson-and-rannacher-issues.html</LINK...
by logos01
September 19th, 2015, 6:37 pm
Forum: Technical Forum
Topic: Analytical formula for One-Touch with (too) negative interest rates?
Replies: 10
Views: 4080

Analytical formula for One-Touch with (too) negative interest rates?

I have written a paper a while ago around this exact problem: Barrier Options Under Negative Rates in Black-ScholesIt turns out you can just go to complex numbers with the Faddeeva function and it works.
by logos01
July 27th, 2015, 8:34 am
Forum: Numerical Methods Forum
Topic: Heston model calibration
Replies: 19
Views: 9259

Heston model calibration

<t> Quote Quote wait 36h for a solution you will get in 1s with a local minimizer and a clever initial gSomething wrong there. Yeah, I did exaggerate quite a bit, in reality it is around a factor 30 to 300, still very substantial.QuoteI agree that ranges are not set properly. Most suggest [0, 1] ins...
by logos01
July 26th, 2015, 7:50 am
Forum: Numerical Methods Forum
Topic: Heston model calibration
Replies: 19
Views: 9259

Heston model calibration

<t>You don't, in the equity space, the Feller condition is often violated by the best fit.Otherwise you could just use a penalty for non box contraints.I tried DE on something a bit more challenging like Double Heston or even Bates, and noticed that it can be very difficult to find the right paramet...
by logos01
July 25th, 2015, 11:42 am
Forum: Numerical Methods Forum
Topic: Heston model calibration
Replies: 19
Views: 9259

Heston model calibration

<t>The objective function can be also quite important: do you minimize prices, vega weighted prices, vols, weighted vols?While DE works most of the time for Heston, it has its own issues, for example if you have different local minima quite far apart of similar objective values. Unless you have adde...
by logos01
July 1st, 2015, 7:25 am
Forum: Numerical Methods Forum
Topic: C2 shape preserving cubic splines
Replies: 15
Views: 6292

C2 shape preserving cubic splines

If you fix the derivatives as in the paper you referred to, then your interpolation is just C1 and not C2. Or am I missing something?
by logos01
June 28th, 2015, 6:25 pm
Forum: Numerical Methods Forum
Topic: C2 shape preserving cubic splines
Replies: 15
Views: 6292

C2 shape preserving cubic splines

<r>You could try a tension spline, it will be C2 and you can adjust the tension(s) to have a convexity preserving interpolation. It can however a bit painful to enforce in practice (much easier if you consider a single tension).<URL url="http://www.cse.unt.edu/~renka/papers/toms93.pdf">http://www.cs...
by logos01
May 23rd, 2015, 1:54 pm
Forum: Numerical Methods Forum
Topic: Bivariate Normal Integral paper
Replies: 114
Views: 66455

Bivariate Normal Integral paper

<t>Seemed to me that the Genz (popularized by West) algorithm was quite good in terms of accuracy vs speed the last time I checked. There was a minor accuracy issue a while ago, I believe it's now fixed in Genz & Quantlib implementations:Trapped by the Tails of the Bivariate Normal Distribution ...
by logos01
March 19th, 2015, 12:11 pm
Forum: Technical Forum
Topic: Missing upper bound for option prices in the Bachelier model
Replies: 11
Views: 4826

Missing upper bound for option prices in the Bachelier model

<t>The fact that option prices are unbounded under Bachelier is quite intuitive as the process is symmetric: the asset will go up as much as down, when you push the volatility up, you increase the probably of reach highs and lows symmetrically (by definition as it just vol*brownian motion), so on av...
by logos01
February 12th, 2015, 2:56 pm
Forum: Numerical Methods Forum
Topic: Dynamic Creation of Pseudorandom Number Generators
Replies: 149
Views: 13491

Dynamic Creation of Pseudorandom Number Generators

<r>It is possible to do jump-ahead with Mersenne-Twister:<URL url="http://www.iro.umontreal.ca/~lecuyer/myftp/papers/jumpmt.pdfWhen"><LINK_TEXT text="http://www.iro.umontreal.ca/~lecuyer/my ... mt.pdfWhen">http://www.iro.umontreal.ca/~lecuyer/myftp/papers/jumpmt.pdfWhen</LINK_TEXT></URL> I tried, it...