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Re-pricing a Call | Taylor Series
Please see attached screenshot. Can anyone please explain the reason for this strange coincidence? What if we hadn't taken the average and instead took some weighted sum ... that would then no longer lead to an equation that closely resembles the second-order Taylor approximation?
Re: Re-pricing a Call | Taylor Series
What weighted sum other than a simple average would you use, and why would you use it?
If I'm not missing something and if I have interpreted your symbols correctly, you are effectively DOING a second order Taylor Series approximation; it's not really a coincidence at all that your answer "closely resembles" a second order Taylor Series approximation. You've done the simple integration a little differently from what is normally done, but ultimately it's the same thing.
If I'm not missing something and if I have interpreted your symbols correctly, you are effectively DOING a second order Taylor Series approximation; it's not really a coincidence at all that your answer "closely resembles" a second order Taylor Series approximation. You've done the simple integration a little differently from what is normally done, but ultimately it's the same thing.
Re: Re-pricing a Call | Taylor Series
Okay thanks Marsden. The average was the simplest operation, but if we were to consider some weighting, then we could weight the old delta less than the new one. For instance, an arbitrary 25% and 75%. Only in the special case that those weights are 50% and 50% (i.e. the computation is the average) does the final equation above resemble the Taylor series approximation. Hence I was wondering.
Re: Re-pricing a Call | Taylor Series
Off the top of my head, if you decide for some reason to use 25% and 75% weighting on your delta, isn't that basically saying that you don't really believe your gamma? Why not just use a different gamma?
Re: Re-pricing a Call | Taylor Series
Thanks Marsden. But couldn't we use that same argument (that we don't really believe our gamma) when using even the 50% and 50% weights?
Re: Re-pricing a Call | Taylor Series
I'm speculating, but it seems likely that your original screenshot was contemplating the instantaneous case, where you are either working with an Ito or a Kolmogorov integral; the way the equations were laid out is sort of half way between the two ... but really Ito, when all is said and done.
And in either, I think you must believe in your gamma. The only "good" reason not to believe in your gamma is because you're not really contemplating the instantaneous case, which means you need to go beyond the second order in your Taylor series approximation.
And in either, I think you must believe in your gamma. The only "good" reason not to believe in your gamma is because you're not really contemplating the instantaneous case, which means you need to go beyond the second order in your Taylor series approximation.
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- katastrofa
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Re: Re-pricing a Call | Taylor Series
Thinking sensitivity analysis, couldn't weighted average mean e.g. attributing more importance to more recent market conditions by putting higher weight on the new Delta or, to the contrary - damping random fluctuations by giving higher weight to older, long-term average than the recent value?Off the top of my head, if you decide for some reason to use 25% and 75% weighting on your delta, isn't that basically saying that you don't really believe your gamma? Why not just use a different gamma?
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- Cuchulainn
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Re: Re-pricing a Call | Taylor Series
I once heard from a Scottish quant that it should be called a Maclaurin series.
Re: Re-pricing a Call | Taylor Series
I have seen it called MacLaurin.
I think there was a distinction -- Taylor began at 0 and used x, and MacLaurin began at a and used (x-a). Or vice versa.
Prof. Murray MacBeth may have had something to do with that.
I think there was a distinction -- Taylor began at 0 and used x, and MacLaurin began at a and used (x-a). Or vice versa.
Prof. Murray MacBeth may have had something to do with that.
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- katastrofa
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Re: Re-pricing a Call | Taylor Series
Vice versa 
MacLaurin is Taylor around 0. I was trained to use the distinction in my maths courses at the Institute of Mathematics in Poland. We were taught to respect historical and social aspects of science. MacLaurine's work was decades after Taylor. Hard to imagine, but possibly if is wasn't for his extensive use of this particular case of Taylor series, it wouldn't be so popular today.
MacLaurin is Taylor around 0. I was trained to use the distinction in my maths courses at the Institute of Mathematics in Poland. We were taught to respect historical and social aspects of science. MacLaurine's work was decades after Taylor. Hard to imagine, but possibly if is wasn't for his extensive use of this particular case of Taylor series, it wouldn't be so popular today.-
- Cuchulainn
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Re: Re-pricing a Call | Taylor Series
The current crop of liberal arts data science STEM graduare are drifting. Some think gradient descent was invented by Marvin Minsky.Vice versa
We also learn things like Cauchy–Bunyakovsky–Schwarz Inequality.
Chancers..
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- Cuchulainn
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Re: Re-pricing a Call | Taylor Series
A howler from someone on Wilmott.
UAT thread.
"Gradient descent are much older than 1990s. Peter Debye did it 1909!"
UAT thread.
"Gradient descent are much older than 1990s. Peter Debye did it 1909!"
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- riskneutralprob
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Re: Re-pricing a Call | Taylor Series
what about Delta Decay (ie d_Delta / dt ). Seems like your average is combining the shock in time and the shock in underlying level. Maybe should be expressed as a regrouping of a subset of the Taylor terms?