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by pcaspers
April 15th, 2021, 2:39 pm
Forum: Technical Forum
Topic: time interpolation in variance vs volatility
Replies: 3
Views: 1214

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: 1214

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: 1934

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: 1934

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: 2247

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: 1542

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: 6166

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: 2247

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: 2247

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: 2247

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...
by pcaspers
December 14th, 2020, 8:40 pm
Forum: Technical Forum
Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
Replies: 11
Views: 2247

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

I have a question on the paper "A note on sufficient conditions for no arbitrage" by Carr / Madan: They say \sum_{i=1}^\infty q_{i,j} = 1. To me it seems this sums equals Q_{1,j}  = S_0 - C_{1,j} / K_1 != 1. Do we have add an additional strike, possibly K = K_0 = 0 and attach the probabili...
by pcaspers
October 29th, 2020, 8:07 am
Forum: General Forum
Topic: Illiquid swaption implied vol calculation
Replies: 4
Views: 1939

Re: Illiquid swaption implied vol calculation

For example, you might use a Hull White Model for the TRY and USD interest rate processes and a Black-Scholes Model with stochastic rates for the TRY/USD FX process (sometimes called "long term FX" model I think). Assume you have somehow fixed the mean reversions for both Hull White Models...
by pcaspers
September 11th, 2020, 4:31 pm
Forum: Programming and Software Forum
Topic: Quantlib Support
Replies: 10
Views: 2503

Re: Quantlib Support

compiles for me: clang++ check.cpp -o check --std=c++17 #include <type_traits> #include <iostream> template <typename T, typename... Ts> std::enable_if_t<!std::conjunction_v<std::is_same<T, Ts>...> > func(T, Ts...) {     std::cout << "not all types in pack are T\n"; } int main() {     // f...
by pcaspers
September 11th, 2020, 7:04 am
Forum: Programming and Software Forum
Topic: Quantlib Support
Replies: 10
Views: 2503

Re: Quantlib Support

The best way imo is to post your questions to quantlib-users@lists.sourceforge.net
by pcaspers
May 6th, 2020, 4:14 pm
Forum: Technical Forum
Topic: Zero Wide Collar Quotes
Replies: 0
Views: 5567

Zero Wide Collar Quotes

There are zero wide collar quotes available on some broker screens. How much traded volume is behind them. And what are bid-ask spreads in this "market", if this exists at all? Talking about EUR here.
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