Topology demands a certain kind of 'mathematical brain'.

Statistics: Posted by Cuchulainn — Yesterday, 4:50 pm

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"Born 1929" - at this age they often believe they solved the whole world.

You spoke too soon. He had that belief at an early age.

https://en.wikipedia.org/wiki/Michael_Atiyah

Statistics: Posted by Cuchulainn — Yesterday, 4:28 pm

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unfortunately the very young people often too young to understand the proofs of mature people. (but pls lets leave discussion on this for OT), lets look into the proof itself...if correct it should be simple?

Statistics: Posted by Collector — Yesterday, 2:51 pm

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Famed mathematician claims proof of 160-year-old Riemann hypothesis

https://www.newscientist.com/article/21 ... hesis/amp/

that is big (if the proof really holds).

Statistics: Posted by Collector — Yesterday, 1:05 pm

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https://www.newscientist.com/article/21 ... hesis/amp/

Statistics: Posted by Cuchulainn — Yesterday, 12:43 pm

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Working on a topic related to the vana-Volga method, i came back to the paper of Castagno and Mercurio and i have some concerns about the paper:

here is the link to the paper as i will quote some parts to expose my question

https://www.researchgate.net/profile/Fa ... lities.pdf

The Vanna-Volga is based on the idea that the price of an option is a function of the stock value S (the FX in the paper but it doesn't matter whether the underlying is a fx or not here) and the implied volatility v so that to build a locally hedged portfolio you not only need cancel Delta but also the Vega, the Vanna and the Volga components. The market products used to proceed are then the underlying S and 3 quoted options.

Very important, in page 3 of the paper just before the remark 2.1, it is clearly mentionned that the dynamics of the state variables S and v are assumed to be continuous ("under the assumptions of no jumps").

Then to pursue the objective, the authors computes the dynamic of the portfolio V assuming S and v are the only two state variables using the Ito's Lemma. They obtain a dynamic exhibiting a theta, delta, vega and gamma components as well as Volga and Vanna components. So far so good.

Then they say that to identify the hedging ratios, (the delta ratio is easily identified separately), they have to cancel the vega, the vanna and the volga components.

My main concern is that i consider this approach to be theroretically inconsistent. Why ?

As your dynamic are continuous, the only components to be stochastic here are the ones depending on dS

Apart of this, in fact, if the dynamic of V is studied at discrete times, the idea of Vanna-Volga becomes relevant as the quadratic variations are replaced by the squares and products above because you doesn't need anymore the Itô's lemma but the Taylor theorem. So in this paper, i feel the problem is ill-posed at the beginning because of this wrong application of the Itô's Lemma...

It doesn't necessarily invalidate their end results but it is annoying...

Your opinion ?

Statistics: Posted by bengourion — September 17th, 2018, 7:24 am

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I`m not sure with understanding Heston Model clearly.

1) How to derive volatility after calibrating all parameters from vanilla options in Heston Model?

Is it like putting Heston price in BS model to derive Implied vol?

2) what`s the exact meaning of volatility in volatility smile by Heston Model?

is it instantaneous volatility like local volatility at forward ?

Then how to use volatility(in smile curve) for pricing ?

i`m not sure.

3) How about SABR MODEL

What`s the meaning of volatility of SABR MODEL.

I`m quiet confusing in understanding stochastic volatility model.

IF anyone knows well, plz Help

Thanks

Statistics: Posted by juniuss — September 14th, 2018, 3:24 pm

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Cost of carry = Intrinsic Value x (1 - e^ - (Interest Rate x Days to Expiration/365))

Based on a futures price of 1617, the 1400 C is 233 and the 1400 P is 20. According to the PC parity: F-C+P-K should equal 0. However this is not the case (+4), since they apply a cost of carry component.

However, the 1100C is 517 and the 1100P = 0.5 so the PC parity works there as it should since it is an American style option.

According to Asay(1982) as described in Haug, there should NOT be any interest rate component on Margined Options on Futures.

In my opinion the CME is wrong, but need some good arguments to show them their error.

Can someone please help?

Statistics: Posted by Jerome2018 — September 13th, 2018, 3:31 pm

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if you have a matlab code to simulate asset price paths is the best

Statistics: Posted by mcbison — September 13th, 2018, 1:23 pm

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Statistics: Posted by bearish — September 13th, 2018, 2:03 am

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