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by pcaspers
August 25th, 2023, 2:21 pm
Forum: Technical Forum
Topic: Which expiry interpolation method for cap surfaces
Replies: 5
Views: 4469

Re: Which expiry interpolation method for cap surfaces

Sorry, I confused myself w.r.t. the linear in sigma^2 T interpolation.

As for the objective criterion. Maybe the total variation of the caplet volatility curve should be minimal?
by pcaspers
July 26th, 2023, 6:31 pm
Forum: Technical Forum
Topic: LGM Multifactor Model / Reversion Parameter
Replies: 2
Views: 4274

Re: LGM Multifactor Model / Reversion Parameter

Thanks. And yes, the example in the note is simplified, in reality I use e.g. sigma = 0.0030 and kappa = 0.50 for one of the factors, but the instability remains.  In the meantime I think the issue is quite obvious. When you develop the multi factor Hull-White model from the HJM equation you natural...
by pcaspers
July 19th, 2023, 6:42 pm
Forum: Technical Forum
Topic: Which expiry interpolation method for cap surfaces
Replies: 5
Views: 4469

Re: Which expiry interpolation method for cap surfaces

Hi,  is "left-continuous" the same as  "piecewise constant" / "backward flat"? And the interpolation variable is implied volatility, at least initially? And later on you talk about interpolation in variance, is that sigma^2 T, because I guess linear interpolation would ...
by pcaspers
January 9th, 2023, 4:39 pm
Forum: Technical Forum
Topic: LGM Multifactor Model / Reversion Parameter
Replies: 2
Views: 4274

LGM Multifactor Model / Reversion Parameter

I am running into some numerical issues when trying to generalize the LGM (linear Gauss-Markov) model to multiple factors and associate a "high" mean reversion value to one of the factors. See here  https://ssrn.com/abstract=4317184 . Is there a simple way out that I am missing oder is the...
by pcaspers
December 25th, 2022, 7:26 pm
Forum: Technical Forum
Topic: Two-factor Interest Rates model: intuitive parameters ?
Replies: 16
Views: 10615

Re: Two-factor Interest Rates model: intuitive parameters ?

Piterbarg / Andersen "Interest Rate Modeling" has a chapter 12.1.5 "Multi-Factor Statistical Gaussian Model" that explores the relation between principal components of rate curve movements and the Gaussian model parameters (there is also a reference to the original paper underlyi...
by pcaspers
April 15th, 2021, 2:39 pm
Forum: Technical Forum
Topic: time interpolation in variance vs volatility
Replies: 3
Views: 4546

Re: time interpolation in variance vs volatility

Good idea, thanks Alan. I'll try that.
by pcaspers
April 3rd, 2021, 6:12 pm
Forum: Technical Forum
Topic: time interpolation in variance vs volatility
Replies: 3
Views: 4546

time interpolation in variance vs volatility

For equity and fx vol surfaces you'd generally prefer to interpolate linearly in [$]\sigma^2t[$] over [$]\sigma[$] (keeping the forward moneyness constant) to avoid calendar arbitrage. For swaption or caplet vol interpolation it's not so clear why [$]\sigma^2t[$] is the better choice, since the unde...
by pcaspers
December 24th, 2020, 9:44 am
Forum: Technical Forum
Topic: N-VOL -> LN-VOL Hagan?
Replies: 4
Views: 4921

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

On 1: I meant looking at (1.7) [$]f(b) := \frac{n\cdot        (b^{2}\cdot t         +24       )       }{       \sqrt{fk}\cdot        (ln         (\frac{f}{                 k}         )         +24       )       } [$] we can solve for b and take this as the guess, i.e. the first expression here [$] \...
by pcaspers
December 23rd, 2020, 3:40 pm
Forum: Technical Forum
Topic: N-VOL -> LN-VOL Hagan?
Replies: 4
Views: 4921

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

I did not know this paper, thanks for posting.

As for your question #1: Can you just view (1.7) as a quadratic equation in [$]\sigma_B[$] and solve this in closed form?

As for your question #2: Did he maybe mean to say [$]H'(\sigma_B) = \sqrt{fK}[$] (looking at 1.4a)?
by pcaspers
December 22nd, 2020, 4:01 pm
Forum: Technical Forum
Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
Replies: 11
Views: 5498

Re: Carr / Madan: A note on sufficient conditions for no arbitrage

On 5 I believe it's because they have a specific goal in mind, namely showing that the conditions they state are sufficient for no-arbitrage. The discrete model they construct is the most parsimonious and natural way to do that.  
by pcaspers
December 20th, 2020, 3:16 pm
Forum: Technical Forum
Topic: Normal Free Boundary SABR
Replies: 0
Views: 4350

Normal Free Boundary SABR

Implementing the normal free boundary SABR model by Antonov et al. using the approximation for G(t,s) as outlined in "SABR spreads it wings", formulas (11), (12), (13) involves the bit "...  In computation, R(t,s) is replaced by its fourth-order expansion for small s, as is the square...
by pcaspers
December 20th, 2020, 12:04 pm
Forum: Technical Forum
Topic: Nabil Kahale's Smile Interpolation Paper
Replies: 3
Views: 8715

Re: Nabil Kahale's Smile Interpolation Paper

Not sure if this helps, here is an implementation of the C1 part for a single maturity. 
by pcaspers
December 17th, 2020, 8:11 am
Forum: Technical Forum
Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
Replies: 11
Views: 5498

Re: Carr / Madan: A note on sufficient conditions for no arbitrage

That makes sense. Actually, in the paper, they start without making any model assumptions, they just impose some no-arbitrage conditions on a discrete set of observed option prices. From that, they construct a discrete probability distribution for [$]S_{T_j}[$] at each maturity [$]T_j[$] compatible ...
by pcaspers
December 16th, 2020, 11:36 am
Forum: Technical Forum
Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
Replies: 11
Views: 5498

Re: Carr / Madan: A note on sufficient conditions for no arbitrage

And I quote

[$]\frac{\partial C}{\partial K}  \le 0[$]

[$]\frac{\partial^2 C}{\partial K^2} \ge 0[$]

[$]\frac{\partial C}{\partial \tau}  \ge 0[$]

Does this make sense?
It does. I am setting up an arbitrage-checker on a discrete grid though and want some theoretical foundation for that.
by pcaspers
December 16th, 2020, 11:28 am
Forum: Technical Forum
Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
Replies: 11
Views: 5498

Re: Carr / Madan: A note on sufficient conditions for no arbitrage

In the Carr-Madan lattice version this would be the condition that [$] 1 = \frac{C_0 - C_1}{K_1 - K_0} = \frac{S_0 - C_1}{K_1}[$]. So you need to assume that [$]C_1 = S_0 - K_1[$] as the lattice version of (*).  Thanks. I am a bit reluctant to make this assumption, since [$]K_1 > 0[$], so this woul...
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