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by jherekhealy
August 24th, 2023, 10:21 am
Forum: Numerical Methods Forum
Topic: iv for all and all for iv
Replies: 124
Views: 66208

Re: iv for all and all for iv

Nice paper jaesmine, I also had proposed the idea of solving on the log price to speed up calculations a while ago in a blog post (and based on the nice guess of Dan Stefanica and Rados Radoicic).
https://quantsrus.github.io/post/implied_volatility_algorithms_go_julia/
by jherekhealy
July 23rd, 2021, 2:59 pm
Forum: Technical Forum
Topic: Pricing Dividend Options
Replies: 4
Views: 4856

Re: Pricing Dividend Options

The typical kind of contracts are options on dividend futures. https://www.eurex.com/ex-en/markets/did/exd/EURO-STOXX-50-Index-Dividend-Options-946274 In this case the underlying is simply a future, and there is no need for an assumption of the individual future dividends, unless we price the front ...
by jherekhealy
February 22nd, 2021, 1:56 pm
Forum: Technical Forum
Topic: American options with two free boundaries
Replies: 46
Views: 14749

Re: American options with two free boundaries

Just saw this thread late. It turns out the double exercise boundary happens naturally for American options under negative interest rates. And you may use the integral formulation to solve the exercise boundary, using similar techniques as in the single boundary case (see Andersen an Lake for exampl...
by jherekhealy
January 7th, 2021, 8:29 am
Forum: Technical Forum
Topic: N-VOL -> LN-VOL Hagan?
Replies: 4
Views: 4924

Re: N-VOL -> LN-VOL Hagan?

In practice, a much simpler way is to just apply the Bachelier formula and invert the price using your favorite Black implied vol solver.
by jherekhealy
November 29th, 2020, 4:24 pm
Forum: Technical Forum
Topic: Arbitrage Free Interpolation of Implied Volatility on Time Dimension
Replies: 2
Views: 3946

Re: Arbitrage Free Interpolation of Implied Volatility on Time Dimension

or you could just use total variance interpolation as every other practitioner. Yes, it may introduce spurious arbitrages in between interpolation nodes, but that's very very rare in practice.
by jherekhealy
October 12th, 2020, 3:28 pm
Forum: Numerical Methods Forum
Topic: Monotone Schemes: what are they and why are they good?
Replies: 78
Views: 17815

Re: Monotone Schemes: what are they and why are they good?

The proof of Crank-Nicolson montonicity (for a small enough time-step) is in Pooley et al. "Numerical Convergence Properties of Option Pricing PDEs with Uncertain Volatility". A different more general proof is also in Boley & Crouzeix "Conservation de la positivité lors de la disc...
by jherekhealy
September 29th, 2020, 9:08 am
Forum: Numerical Methods Forum
Topic: Monotone Schemes: what are they and why are they good?
Replies: 78
Views: 17815

Re: Monotone Schemes: what are they and why are they good?

The Crank-Nicolson scheme becomes monotone for small enough time-steps (in relation to the space-steps ^2). Either the limit corresponds to the explicit scheme stability limit or to twice the latter, I don't remember exactly.
by jherekhealy
September 29th, 2020, 9:01 am
Forum: Technical Forum
Topic: Interpolation of a Implied Volatility Surface
Replies: 20
Views: 12899

Re: Interpolation of a Implied Volatility Surface

I don't recall all the details of the Fengler paper, but the core idea is that you trade-off accuracy wrt market quotes vs. smoothness. More importantly, no smoothing at all may not be possible if you want an arbitrage-free interpolation. For example, a cubic smoothing spline with smoothing=0 is jus...
by jherekhealy
June 5th, 2020, 12:46 pm
Forum: Student Forum
Topic: Heston test suite
Replies: 18
Views: 17406

Re: Heston test suite

Thanks for the clarifications Alan.

I have created a small Julia package if anyone needs reference numbers of option prices under Heston with a high accuracy.

https://github.com/jherekhealy/CharFuncPricing.jl
by jherekhealy
June 4th, 2020, 5:17 pm
Forum: Student Forum
Topic: Heston test suite
Replies: 18
Views: 17406

Re: Heston test suite

I don't think that the reference prices on the blog are accurate to all digits stated. I tried a Julia implementation of the cos method, using arbitrary precision real and complex balls, and end up with 7.9588781132567682852132606076142930308986569372596 for strike 80. The error with the table is -2...
by jherekhealy
June 4th, 2020, 9:59 am
Forum: Student Forum
Topic: Control variate for heston model
Replies: 1
Views: 12152

Re: Control variate for heston model

This is somewhat old, but I can, share a few results presented in my book in the context of LV:
* some simple candidates are forward price or atm option.
* the discretization in time error may impact the choice of control variate. The forward price control variate is good in this sense.
by jherekhealy
October 3rd, 2019, 9:35 am
Forum: Numerical Methods Forum
Topic: Smoothing splines (clamped spline)
Replies: 35
Views: 18357

Re: Smoothing splines (clamped spline)

You are a bit harsh on Wystup. There is the notion of smoothing kernel in maths: https://en.wikipedia.org/wiki/Kernel_smoother
Although I agree that his method is really a Gaussian RBF interpolation, as he chooses the weights to pass exactly through the points.
by jherekhealy
September 26th, 2019, 8:36 am
Forum: Numerical Methods Forum
Topic: Smoothing splines (clamped spline)
Replies: 35
Views: 18357

Re: Smoothing splines (clamped spline)

The use of kernels to model the RND (risk neutral density) is well known in the litterature, especially, a mixture of lognormals leads to a simple linear combination of Black-Scholes formulas. Wystup kernel method is a bit stranger, as I think it is applied to vols in delta directly. The implied den...
by jherekhealy
July 21st, 2019, 10:13 pm
Forum: Numerical Methods Forum
Topic: Smoothing splines (clamped spline)
Replies: 35
Views: 18357

Re: Smoothing splines (clamped spline)

Yes, the BFIT routine of de Boor will do what you're after. FYI, this is part of the NSWC Fortran library https://raw.githubusercontent.com/jacob ... src/nswc.f
by jherekhealy
January 8th, 2019, 8:36 pm
Forum: Book And Research Paper Forum
Topic: Best Options Books Today
Replies: 4
Views: 12826

Re: Best Options Books Today

I can recommend my book ;), "Applied Quantitative Finance for Equity Derivatives", which you can find in hardback on Lulu or in paperback on Amazon, see this thread.
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