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croot
Topic Author
Posts: 104
Joined: July 23rd, 2006, 8:30 pm

### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

Anyone have this paper?

spursfan
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Joined: October 7th, 2001, 3:43 pm

### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

Dominique says it is an internal BAML working paper - though most of the material is present in the Andersen-Piterbarg books

croot
Topic Author
Posts: 104
Joined: July 23rd, 2006, 8:30 pm

### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

I know, A&P Book 1 p.333: "Much of the material is based on Bang[2009], which can be consulted for additional details".It'd be nice to send it, if need be in a discretely wrapped pm.

Antonio
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Location: Imperial College London
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### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

Dear croot,I do not have Andersen & Piterbarg's book, but is the method they present (based on Bang) any different than what is already in the papers Albrecher-Schoutens-Kahl-Lord-Zeliade...?Best,

croot
Topic Author
Posts: 104
Joined: July 23rd, 2006, 8:30 pm

### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

They state that using alpha=1/2 and the BS control variate with vol taken at 0 is the best thing to do for rewards with no sweat.Then there is a 5pp. section 8.4.4 "Refinements of Numerical Implementation" making heavy references to this paper by Bang.The idea there seems to apply whether or not you use the BS control variate, it's about computing the right tail of the integral (no mapping of [0 inf) to [0 1] here) as the sum of two terms, the main one given as E_{1} exponential integral functions.Me, I just want a method using CF and/or saddlepoint that will compute call prices to 4 places relative accuracy for all logmoneyness in [-2.3, 2.3] and "all" param combos.

mj
Posts: 3449
Joined: December 20th, 2001, 12:32 pm

### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

I don't have Bang's paper but we did our own analysis:http://ssrn.com/abstract=1941464

logos01
Posts: 67
Joined: August 12th, 2009, 1:18 pm

### "Numerical computation of fourier transforms in heston model" D. Bang [2009]

In the paper from Mark Joshi, it looks like the integrand (3.9) need extra care at 0. This is one nice thing about the Lewis formula (3.7). Isn't it one reason why moment matching using (3.5) is particularly important for (3.9) (if the derivatives are matched then the value of the integrand is 0 at 0)?