- April 15th, 2021, 2:39 pm
- Forum: Technical Forum
- Topic: time interpolation in variance vs volatility
- Replies:
**3** - Views:
**819**

Good idea, thanks Alan. I'll try that.

- April 3rd, 2021, 6:12 pm
- Forum: Technical Forum
- Topic: time interpolation in variance vs volatility
- Replies:
**3** - Views:
**819**

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...

- December 24th, 2020, 9:44 am
- Forum: Technical Forum
- Topic: N-VOL -> LN-VOL Hagan?
- Replies:
**4** - Views:
**1539**

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 [$] \...

- December 23rd, 2020, 3:40 pm
- Forum: Technical Forum
- Topic: N-VOL -> LN-VOL Hagan?
- Replies:
**4** - Views:
**1539**

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)?

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)?

- December 22nd, 2020, 4:01 pm
- Forum: Technical Forum
- Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
- Replies:
**11** - Views:
**1833**

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.

- December 20th, 2020, 3:16 pm
- Forum: Technical Forum
- Topic: Normal Free Boundary SABR
- Replies:
**0** - Views:
**1184**

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...

- December 20th, 2020, 12:04 pm
- Forum: Technical Forum
- Topic: Nabil Kahale's Smile Interpolation Paper
- Replies:
**3** - Views:
**5804**

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

- December 17th, 2020, 8:11 am
- Forum: Technical Forum
- Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
- Replies:
**11** - Views:
**1833**

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 ...

- December 16th, 2020, 11:36 am
- Forum: Technical Forum
- Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
- Replies:
**11** - Views:
**1833**

It does. I am setting up an arbitrage-checker on a discrete grid though and want some theoretical foundation for that.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?

- December 16th, 2020, 11:28 am
- Forum: Technical Forum
- Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
- Replies:
**11** - Views:
**1833**

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...

- December 14th, 2020, 8:40 pm
- Forum: Technical Forum
- Topic: Carr / Madan: A note on sufficient conditions for no arbitrage
- Replies:
**11** - Views:
**1833**

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...

- October 29th, 2020, 8:07 am
- Forum: General Forum
- Topic: Illiquid swaption implied vol calculation
- Replies:
**4** - Views:
**1718**

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...

- September 11th, 2020, 4:31 pm
- Forum: Programming and Software Forum
- Topic: Quantlib Support
- Replies:
**10** - Views:
**2128**

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...

- September 11th, 2020, 7:04 am
- Forum: Programming and Software Forum
- Topic: Quantlib Support
- Replies:
**10** - Views:
**2128**

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

- May 6th, 2020, 4:14 pm
- Forum: Technical Forum
- Topic: Zero Wide Collar Quotes
- Replies:
**0** - Views:
**5338**

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.