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by VivienB
April 16th, 2018, 1:15 pm
Forum: Programming and Software Forum
Topic: Anyone getting into Rust
Replies: 30
Views: 4033

Re: Anyone getting into Rust

It has some nice features, but so do other mainstream languages. It's in VS2015. It has ADT, what most mainstream languages don't. As an OCaml developer, it is a must have feature ;) It is also supposed to handle first-class functions (when I looked into the language (at his alpha stage), it was no...
by VivienB
October 20th, 2017, 11:53 am
Forum: Student Forum
Topic: Fixing mean reversion parameter in the 1F HW model
Replies: 4
Views: 1428

Re: Fixing mean reversion parameter in the 1F HW model

I'm not too experienced in rates derivatives, so thanks VivienB for adding the nuance / correction! In your opinion then, for the more vanilla derivatives such as swaptions, short rate models are preferable to market models? For the vanilla such as swaptions or caps/floors, a market model with clos...
by VivienB
October 17th, 2017, 8:21 am
Forum: Student Forum
Topic: Fixing mean reversion parameter in the 1F HW model
Replies: 4
Views: 1428

Re: Fixing mean reversion parameter in the 1F HW model

At risk of stating the obvious: the LMM model and its generalizations might be a better choice for modelling / pricing rates derivatives. Not really obvious. It really depends on what you want to price. Furthermore LMM models have a lot of drawbacks: slow calibration and pricing, the correlation st...
by VivienB
August 10th, 2017, 4:07 pm
Forum: Numerical Methods Forum
Topic: Listed option IV curve
Replies: 36
Views: 5428

Re: Listed option IV curve

I tried to fit the raw SVI with the Quasi Explicit Method by Zeliade. The parameters turned out to be too unstable for reference use in real trading (though the model does fit well). The problem seemed to be that there are too many local min's when using iterations in the second step to get the opt...
by VivienB
February 23rd, 2017, 5:41 pm
Forum: General Forum
Topic: Building a swaption implied volatility surface from ATM quotes only using SABR model.
Replies: 8
Views: 1362

Re: Building a swaption implied volatility surface from ATM quotes only using SABR model.

How do you calibrate the SABR model if you have only ATM swaptions? Btw, in the current market situation (i.e. small rates / negative rates), if I had only ATM swaption vols, I would use a Hull-White with a piecewise constant volatility term structure model to extrapolate the vols. You have a close...
by VivienB
February 23rd, 2017, 4:09 pm
Forum: General Forum
Topic: Building a swaption implied volatility surface from ATM quotes only using SABR model.
Replies: 8
Views: 1362

Re: Building a swaption implied volatility surface from ATM quotes only using SABR model.

How do you calibrate the SABR model if you have only ATM swaptions?

Btw, in the current market situation (i.e. small rates / negative rates), if I had only ATM swaption vols, I would use a Hull-White with a piecewise constant volatility term structure model to extrapolate the vols.
by VivienB
January 20th, 2017, 9:22 am
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

You're welcome!

I use the approximation proposed in the Andersen, Piterbarg's book, ie I compute [$]y[$] as if [$] \forall t, x(t) = 0[$]. Then [$]\bar y'(t) = (\alpha^2 - 2\chi \bar y(t)), \bar y(0) = 0 \Rightarrow \bar y(t) = \alpha^2 \frac{1 - e^{-2\chi t}}{2\chi}[$] (ie the same as you).
by VivienB
January 19th, 2017, 4:51 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

With some delay, I made a try on a 20y, 0.5% annual vs E6M swap, with the parameters we agreed on, for different mean reversions. Theoretical price: 921bps. [$] \begin{array}{|c|c|} \hline \chi & price (bps)\\ \hline 10\% & 921\\ 5\% & 921\\ 1\% & 918\\ 0\% & 919\\ -1\% & 919\\ -5\% & 927\\ -6\% & 9...
by VivienB
January 18th, 2017, 4:53 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

This heuristic has been made directly on the SDE, not on the corresponding PDE. It's a classical "drift freezing" method. Obviously, some properties are broken with this approximation, otherwise we wouldn't misprice a swap (this approximation breaks the fitting of the initial yield curve, because b...
by VivienB
January 17th, 2017, 1:42 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

It is not surprising that a naive numerical method fails with negative mean rev, as it implies diverging process, then it probably require a more robust / cleaver numerical method to use. To continue with your analogy, there are similar effect with the heston pde when the Feller condition is violate...
by VivienB
January 17th, 2017, 12:40 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

This heuristic has been made directly on the SDE, not on the corresponding PDE. It's a classical "drift freezing" method. Obviously, some properties are broken with this approximation, otherwise we wouldn't misprice a swap (this approximation breaks the fitting of the initial yield curve, because by...
by VivienB
January 14th, 2017, 1:52 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

I'll give a try on Monday with small values of the mean rev (and negatives). The results I gave were still for a small mean reversion (between 0% and 1%, but can't tell you exactly how much). When the mean rev is negative, it is not surprising to have bad results for long maturities, as in this case...
by VivienB
January 13th, 2017, 3:55 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

Oups sorry there is a typo. I'll edit the formula.
by VivienB
January 13th, 2017, 2:01 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

The model is: [$] dx(t) = [y(t) - \chi x(t)] dt + \sigma(t, x(t)) dW(t)\\ dy(t) = [\sigma(t, x(t))^2 - 2\chi y(t)] dt\\ x(0) = y(0) = 0\\ \sigma(t, x) = \alpha(t) + \beta(t)x\\ r(t) = f(0, t) + x(t) [$] Then, the pricing pde is [$] \partial_t v(t, x, y) + \frac{\sigma(t, x)^2}{2}\partial^2_x v(t, x,...
by VivienB
January 13th, 2017, 12:29 pm
Forum: Numerical Methods Forum
Topic: Cheyette Unstability in PDE
Replies: 42
Views: 10505

Re: Cheyette Unstability in PDE

Hi, I just tried on a 20y EUR swap, pay 1%, receive EURIBOR 6M, with data as if 2017-01-06, no multi curve, and got: Market swap price = 399.97bps Pde qG price (grid size = 51, time step = 50days) = 396.80bps Pde qG price, vols + 10 vol points: 397.16bps Are these bad results for you? What formula d...
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