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Paul
Posts: 7596
Joined: July 20th, 2001, 3:28 pm

Re: Why changing measure is necessary?

May 18th, 2017, 4:05 pm

I rather sympathize with list1 on this occasion! If you start from a certain set of assumptions then the option-valuation problem becomes like a certain type of maths, called change of measure. If you had a different set of assumptions and you changed measured willy-nilly then it might not make any sense. So the word 'necessary' in the title of the thread is a bit misleading. 

So do you have to change measure? No. You don't need to know anything about this. (And I suspect that list1 does know quite a lot of the theory.)

Does it have any advantages? Yes. Some people find this way of thinking helpful.

Does it have any disadvantages? Yes. If you think every model turns into a change of measure, or if being tied to this concept limits new ideas.
 
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list1
Posts: 1668
Joined: July 22nd, 2015, 2:12 pm

Re: Why changing measure is necessary?

May 18th, 2017, 4:39 pm

Change measure does not alternative to BS approach. It is mathematical illustration not even interpretation of the BS pricing. BS teaches us formal financing thinking. Measure change does not teach anything. The question ' why' the answer should be referred to as it is implied by BSE.

PS whether my suctions 'do not have permission to answer' on any other wilmott's forums somewhat connected to the Crimea or Donbass war? Of course, it will be o'k for me. How does timing condition is established?
 
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frolloos
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Location: Netherlands

Re: Why changing measure is necessary?

May 18th, 2017, 5:05 pm

Until you run into a problem that can't be solved by PDE methods..

Or can *all* pricing questions be solved by PDE methods and hence true that no measure change necessary at all?

And doesn't the PDE already say change the measure please (Feynman-Kac)? I don't see how it's *not* necessary to change the measure. 
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Re: Why changing measure is necessary?

May 18th, 2017, 5:33 pm

To do this topic justice you need to talk about:

1. The different assumptions you can make

2. The modelling tools or framework used

3. The analytical methods available

4. Numerical methods you can use to get the answer

And probably a lot more!

It is complicated by 99% of people only knowing one route from one set of assumptions to one answer. (Change of this and that, then hit with Monte Carlo.) However there is a wider world out there with different assumptions, different tools, different models, etc. And it's a wonderful world with beautiful women (and men), the sun is shining and everyone is drinking Pina Coladas. (The 99% world is full of French and Russians and no one is beautiful.)
 
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list1
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Joined: July 22nd, 2015, 2:12 pm

Re: Why changing measure is necessary?

May 18th, 2017, 5:40 pm

frolloos wrote:
Until you run into a problem that can't be solved by PDE methods..

Or can *all* pricing questions be solved by PDE methods and hence true that no measure change necessary at all?

And doesn't the PDE already say change the measure please (Feynman-Kac)? I don't see how it's *not* necessary to change the measure. 

Advantage of the BS approach that it uses synthetic pricing in construction of the (hedged) portfolio. PDE is the final outcome of this approach and PDE does not actually a method. The pricing is reduced to PDE.
 
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Alan
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Re: Why changing measure is necessary?

May 19th, 2017, 2:01 pm

frolloos wrote:
Until you run into a problem that can't be solved by PDE methods..

Or can *all* pricing questions be solved by PDE methods and hence true that no measure change necessary at all?

Suppose we live in a discrete-time world where stock prices only change in a trinomial way: up, down, or unchanged. Then, what can you say about option prices? 

I believe it was these kinds of questions that got people thinking, post-Black-Scholes paper --  what is the more general theory that BS have partially discovered in a very specific model (GBM)?    

Of course, pre-Black-Scholes, there was a lot of general theory about options and the best thinking used the notion of "util-probs" (Samuelson-Merton, 1969). Post-BS, this morphed into "measure change", a trivial change in nomenclature but accompanied by a deeper theory. 

Can we have a general theory of option/securities valuation without mentioning util-probs/measure change? I doubt it because fundamentally:

- investors are risk-averse, and
- markets are not complete.  
 
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snufkin
Posts: 40
Joined: January 25th, 2017, 9:05 am
Location: Cambridge

Re: Why changing measure is necessary?

May 20th, 2017, 10:07 pm

Paul wrote:
To do this topic justice you need to talk about:

1. The different assumptions you can make

2. The modelling tools or framework used

3. The analytical methods available

4. Numerical methods you can use to get the answer

And probably a lot more!

It is complicated by 99% of people only knowing one route from one set of assumptions to one answer. (Change of this and that, then hit with Monte Carlo.) However there is a wider world out there with different assumptions, different tools, different models, etc. And it's a wonderful world with beautiful women (and men), the sun is shining and everyone is drinking Pina Coladas. (The 99% world is full of French and Russians and no one is beautiful.)

Well, now I'm offended! 
 
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Paul
Posts: 7596
Joined: July 20th, 2001, 3:28 pm

Re: Why changing measure is necessary?

May 21st, 2017, 7:07 am

Nothing personal, I offend everyone!

Alan's example is very good. He nails it. (Although I think sometimes people are risk seeking.)
 
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Cuchulainn
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Location: Amsterdam
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Re: Why changing measure is necessary?

May 21st, 2017, 6:44 pm

snufkin wrote:
Paul wrote:
To do this topic justice you need to talk about:

1. The different assumptions you can make

2. The modelling tools or framework used

3. The analytical methods available

4. Numerical methods you can use to get the answer

And probably a lot more!

It is complicated by 99% of people only knowing one route from one set of assumptions to one answer. (Change of this and that, then hit with Monte Carlo.) However there is a wider world out there with different assumptions, different tools, different models, etc. And it's a wonderful world with beautiful women (and men), the sun is shining and everyone is drinking Pina Coladas. (The 99% world is full of French and Russians and no one is beautiful.)

Well, now I'm offended! 

Which part(s) did you not like? The Monte Carlo?

5. Check output; GOTO 1 if necessary.

?
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