Cuchulainn wrote:I heard Jim Gatheral give a talk on this at Baruch College.I think it is a good place to start.

https://arxiv.org/abs/1410.3394

can you give us directions to Baruch College then?

Across the road from the "Fighting" 69th Armory.

Statistics: Posted by Cuchulainn — August 19th, 2017, 8:02 pm

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I heard Jim Gatheral give a talk on this at Baruch College.I think it is a good place to start.

https://arxiv.org/abs/1410.3394

can you give us directions to Baruch College then?

Statistics: Posted by ppauper — August 18th, 2017, 5:33 am

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This fits the behaviour of interest rates -- if we study time series of a forward rate about particular tenor over time.

Statistics: Posted by RDiamond — August 17th, 2017, 9:33 pm

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https://arxiv.org/abs/1410.3394

Statistics: Posted by Cuchulainn — August 17th, 2017, 7:52 pm

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There is a class of distributions that keep their shape under addition, but which grow with a different rate than sqrt, the alpha stable distributions. Those are however not analytical from what I remember.

To simulate fBM I would start with discrete timesteos of your path, then compute the covariance matrix which is uniquely defined by H, then do a Cholesky and use that to correlate independent gaussians to the target covariance.?

Statistics: Posted by outrun — August 17th, 2017, 4:58 pm

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Finally found a generalisation of the Kirk's approximation for multi asset spread options (paper).

Similarly, if we have N prices

$$max(0,F_N-\sum_{k=1}^{N-1}F_k-K)$$

translates into

$$F_N N(d_1)-(\sum_{k=1}^{N-1}F_k+K)N(d_2)$$

But then what if we have [$]max(0,F_N+F_{N-1}-\sum_{k=1}^{N-2}F_k-K)[$]?

Is it right to say that it translates into $$(F_N + F_{N-1})N(d_1)-(\sum_{k=1}^{N-2}F_k+K)N(d_2)\ \ \ (1)$$

or into

$$F_N N(d_1)-(\sum_{k=1}^{N-2}F_k+K-F_{N-1})N(d_2)?\ \ \ (2)$$

Looking at the proof of the proposition for the general case, (2) seems to be true, but I am not sure for (1).

What do you think ?

Article looks like a good one. For other types of spread options you should follow the original BS idea constructing hedged portfolio with a certain delta-portions of the underling assets. It brings you a correspondent generalization of the BSE. Next you should write probabilistic representation of the solution. With some mathematical skills you can get the explicit formula.

Statistics: Posted by list1 — August 15th, 2017, 4:40 pm

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Statistics: Posted by Arthurim — August 15th, 2017, 3:59 pm

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Similarly, if we have N prices

$$max(0,F_N-\sum_{k=1}^{N-1}F_k-K)$$

translates into

$$F_N N(d_1)-(\sum_{k=1}^{N-1}F_k+K)N(d_2)$$

But then what if we have [$]max(0,F_N+F_{N-1}-\sum_{k=1}^{N-2}F_k-K)[$]?

Is it right to say that it translates into $$(F_N + F_{N-1})N(d_1)-(\sum_{k=1}^{N-2}F_k+K)N(d_2)\ \ \ (1)$$

or into

$$F_N N(d_1)-(\sum_{k=1}^{N-2}F_k+K-F_{N-1})N(d_2)?\ \ \ (2)$$

Looking at the proof of the proposition for the general case, (2) seems to be true, but I am not sure for (1).

What do you think ?

Statistics: Posted by Arthurim — August 15th, 2017, 3:48 pm

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Statistics: Posted by frolloos — August 14th, 2017, 3:20 pm

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Personally I'm a bit skeptical towards fBM, I'm not a big fan of idealized models that model things across timescales that span orders of magnitude. However, it might be a very good model in the set of models that have very little variables.

Statistics: Posted by outrun — August 14th, 2017, 2:49 pm

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Trying to grasp what the advantage would be of using fBM.

Statistics: Posted by frolloos — August 14th, 2017, 2:38 pm

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H=0.5 is classic Brownian motion H>0.5 is persistence / positive autocorrelation, H<0.5 is anti-persistence. H comes from "Hust". H<>0.5 mean that you have auto correlation across all time scales.

H is also how standard deviation scales across timesteps. With BM you have sqrt(t) = t^0.5 = t^H

What are your thoughts?

Statistics: Posted by outrun — August 14th, 2017, 2:25 pm

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what is it exactly and why is it attractive (without going into technical details)?

Statistics: Posted by frolloos — August 14th, 2017, 2:11 pm

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