Statistics: Posted by Cuchulainn — Yesterday, 8:08 pm

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I have attached a more in-depth background for this question.

If I have predicted price time-horizon, trading limits and a number of constraints, what optimisation method is best? I have been told stochastic game, but not sure whether that's true.

Any help is greatly appreciated.

Kind Regards

Sam

- An_Optimisation_Problem-4.pdf

Statistics: Posted by SamHarper — Yesterday, 5:09 pm

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Hi,

I have a question on terminology regarding "basis risk".

My understanding is that "basis risk" simply means the difference between two quantities. But I don't know why in quant finance difference is called basis risk? Can someone please explain?

Thanks

The etymology is unclear, but seems to originate in US agricultural futures markets going back to the 1800s. “Your basis” represented the difference between the futures price and the cash price at your local grain elevator or mill. Basis risk would then arise from the uncertainty about this relationship in the future when hedging a (long or short) physical position with futures. From there you can see the generalization to basis risk arising when hedging one financial instrument with another.

Statistics: Posted by bearish — July 11th, 2018, 5:18 pm

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I have a question on terminology regarding "basis risk".

My understanding is that "basis risk" simply means the difference between two quantities. But I don't know why in quant finance difference is called basis risk? Can someone please explain?

Thanks

Statistics: Posted by xingwei86524 — July 11th, 2018, 1:33 am

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Just assuming a Black-Scholes world now with a deterministic term structure for the index volatility.

So, for instance, an option with price function

[$] C (S,t, T, v_{0,T} ) [$]

where

[$] v_{0,T} = \int_0^T \sigma^2 du [$]

Thanks.

Statistics: Posted by frolloos — July 3rd, 2018, 6:44 am

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And this question should be in the student forum.

Statistics: Posted by frolloos — June 25th, 2018, 9:56 am

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What is the definition of cash delta and forward delta? What does Taleb mean by transforming the future exposure into cash exposure? What is it for?

Thanks a lot

"CONFUSION: DELTA BY THE CASH OR BY THE FORWARD

The delta as expressed by the Black-Scholes-Merton formula concerns the

amount of cash the operator needs to execute to offset an option position.

For all European options, however, the real exposure lies in the forward.

Nevertheless, operators prefer to see the cash delta as they generally

hedge themselves with it. It is easier to monitor on a screen and quote in the

market. When they deal with options on futures or use the futures as a

hedge, they need to use a different delta fit to the exact period in the future.

The difference between the two is sometimes far from trivial. Operators

often must deal with questions like this one: An option that is close to the

money in the forward trades at 50% delta. What is the cash delta?

The answer is to transform the potential future exposure into a cash ex-

posure through the delta of a forward. This can be done by discounting the

forward exposure using the cash-future growth rate as a discounting factor.

Therefore, the delta of the cash will be the discounted value of that number.

The discounting method will depend on the underlying security of the op-

tion, as will be described. "

Statistics: Posted by kfp22 — June 25th, 2018, 8:14 am

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If I go back to the original equation and turn it into a 4th order equation, I find a general solution

[$]\left[c_{1}+c_{2}{\rm erf}(x)\right]M\left(\frac{n}{2}+\frac{1}{2},\frac{1}{2}.x^{2}\right)

+\left[c_{3}+c_{4}{\rm erf}(x)\right]M\left(\frac{n}{2}+1,\frac{3}{2}.x^{2}\right)[$]

some of the coefficients vanish:

2 vanish when [$]n[$] is odd and (a different) 2 vanish when [$]n[$] is even

The bad news is that while there are nice expressions for [$]M\left(m+\frac{1}{2},\frac{1}{2}.x^{2}\right)[$] and [$]M\left(m+\frac{1}{2},\frac{3}{2}.x^{2}\right)[$],

the expressions for [$]M\left(m,\frac{1}{2}.x^{2}\right)[$] and [$]M\left(m,\frac{3}{2}.x^{2}\right)[$] all seem to be lengthy and unpleasant and worse than what I had already

On a side note, a rant at maple.

I grew up using Kummer functions as my degenerate hypergeometric functions, and early versions of maple used them.

Then for no apparent reason, maple switched to Whittaker functions, including the (old old) version of maple on my laptop.

It's annoying as whenever maple spits them out as a solution to something, I have to grab Abramowitz & Stegun and convert them back to the Kummer functions that we all know and love. Maple should switch back to Kummer functions if they haven't already

j^2)+(_C2+_C4*erf(xmj))*KummerM(1+1/2*n,3/2,xmj^2)*xmj;

Statistics: Posted by ppauper — June 23rd, 2018, 6:48 am

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As ppauper states, the function [$]f(t)[$] should be qualified (e.g. is it of

If you can pose it as an ODE then you can conclude a desired positivity/maximum principle. Maybe there isn't a corresponding ODE and then I don't know.

Statistics: Posted by Cuchulainn — June 21st, 2018, 11:14 am

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[$]A=F(0)[$]

are there any conditions on [$]f(t)[$] ?

Statistics: Posted by ppauper — June 20th, 2018, 9:53 pm

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