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 [$] \...

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)?

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.  

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 root expressio...

Not sure if this helps, here is an implementation of the C1 part for a single maturity. 

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 ...

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.

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...

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 probability 1 - Q_{...

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 and also ...

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() {     // func(1,2,3)...

The best way imo is to post your questions to quantlib-users@lists.sourceforge.net. 

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.

Shifted Lognormal with lower bound = max storage cost?

Hi Eric, I think I pretty much reproduced what they do. We are currently writing up a small note on this, I'll post a link here once this is done. In the meantime if you don't mind reading C++ code have a look here  https://github.com/lballabio/QuantLib/blob/master/test-suite/piecewiseyieldcurve.cpp...