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Cuchulainn
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### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

On page 319, the 2nd formula has the magic number 0.25. This comes from the fact that p1 = p2 = 1/2.
The formula can be generalized? Then I don't see how puu, pud, pdu, pdd relate to it.
Step over the gap, not into it. Watch the space between platform and train.
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Collector
Posts: 4734
Joined: August 21st, 2001, 12:37 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

On page 319, the 2nd formula has the magic number 0.25. This comes from the fact that p1 = p2 = 1/2.
The formula can be generalized? Then I don't see how puu, pud, pdu, pdd relate to it.
are you thinking of generalizing to more assets or other stochastic processes?

Cuchulainn
Posts: 62961
Joined: July 16th, 2004, 7:38 am
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### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

On page 319, the 2nd formula has the magic number 0.25. This comes from the fact that p1 = p2 = 1/2.
The formula can be generalized? Then I don't see how puu, pud, pdu, pdd relate to it.
are you thinking of generalizing to more assets or other stochastic processes?
In principle, it should be possible (1d, OK, 2d OK), just use induction, yes? And these days we don't need to be scared of factorials and multiple loops.
What is your source for 319 formula?

Can use page 316 for all that p, u, d stuff?
Last edited by Cuchulainn on October 3rd, 2016, 8:46 pm, edited 1 time in total.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

trackstar
Posts: 27505
Joined: August 28th, 2008, 1:53 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Just an aside, but before p. 282, there are some Jump Diffusion Models (p. 253-258) and Stochastic Volatility Models (p. 258-271).

Some interesting work still being done in those areas, perhaps.
Last edited by trackstar on October 4th, 2016, 12:23 am, edited 2 times in total.

Cuchulainn
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### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

They are still reasonably good for American options in 1 factor.
For more factors, LSM, stochastic mesh, regression etc. is touted but at the end of the day they are not so accurate and also suffer from curse of dimensionality.  The main bottleneck is multivariate orthogonal polynomials.
Binomial can be used as 'option price 2nd opinion' and for other reasons.

I am the proud owner of a signed copy of the Collector's book .. March 2 2007. Tempus fugit. Tempus neminem manet.
Last edited by Cuchulainn on October 3rd, 2016, 8:56 pm, edited 2 times in total.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

trackstar
Posts: 27505
Joined: August 28th, 2008, 1:53 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Have you ordered this one yet?

The Volatility Smile - Emanuel Derman September 2016

On my shelf for the holiday break.
Last edited by trackstar on October 4th, 2016, 12:28 am, edited 2 times in total.

Collector
Posts: 4734
Joined: August 21st, 2001, 12:37 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

On page 319, the 2nd formula has the magic number 0.25. This comes from the fact that p1 = p2 = 1/2.
The formula can be generalized? Then I don't see how puu, pud, pdu, pdd relate to it.
are you thinking of generalizing to more assets or other stochastic processes?
In principle, it should be possible (1d, OK, 2d OK), just use induction, yes? And these days we don't need to be scared of factorials and multiple loops.
What is your source for 319 formula?

Can use page 316 for all that p, u, d stuff?
I suspect possibly my book is the source to this formula, and I was likely inspired by the Rubinstein binomial for 2 assets (Return to OZ, Risk Mag) for American style, but he did not have (at least not in that paper) the compact neat algorithm/formula for European 2 asset.  I knew for European we only need end scenario (no roll back). But then the compact European style form was so simple one did not need to derive it, one could just take it straight out of the æther like the Wizard of OZ would have done.

Rubinstein also refer to one of his papers Somewhere over the Rainbow 1991 for European style, but as I remember that is just about closed form solutions, cannot find it now. Would like to know.

I would be happy to be informed if someone know of potential earlier sources dealing with same, good to have if I should get time to update my book.

The plain 1D case I think possibly go back to CRR or Rendleman and Bartter paper?  Me and my brother did some more complex 1D cases in our: Resetting Strikes, Barrier and Time 2001 article. One could likely combine some of this with 2 assets and get something interesting

Cuchulainn
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### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Let's go back to the 1 factor case page 282. It is really an example of a Bernstein polynomial, in this case in terms of the payoff at discrete mesh points. Normally the function is scaled to [0,1] to fit into the discussion but I don't think it is essential.
Computing the discrete mesh points (as in page 319 for S1 and S2) is not obvious but my guess it is using Cholesky decomposition. Anyway, it works very well
Step over the gap, not into it. Watch the space between platform and train.
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http://www.datasim.nl

Cuchulainn
Posts: 62961
Joined: July 16th, 2004, 7:38 am
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### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Resetting Strikes, Barrier and Time 2001 article.

Where can I find it? had a look at Articles but is a bit fubar.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

Collector
Posts: 4734
Joined: August 21st, 2001, 12:37 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Resetting Strikes, Barrier and Time 2001 article.

Where can I find it? had a look at Articles but is a bit fubar.
W Magazine 2001, or Models on Models p. 157-164 (2007, basically same as 2001), it covers what we could call weak path dependence 1 asset case, same could easily be done for weak path dependent 2 asset case.

Cuchulainn
Posts: 62961
Joined: July 16th, 2004, 7:38 am
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### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Resetting Strikes, Barrier and Time 2001 article.

Where can I find it? had a look at Articles but is a bit fubar.
W Magazine 2001, or Models on Models p. 157-164 (2007, basically same as 2001), it covers what we could call weak path dependence 1 asset case, same could easily be done for weak path dependent 2 asset case.
Are you saying that equation 7.3 can be used with let's say (to begin with to make it easy) for a barrier option by choosing g() as in 7.7 as some kind of modification of the payoff, e.g. checking the barrier reached and hence V = 0 for that term. Since we agreed that 7.7 is the same as binomial method and the latter works for barriers then 7.7 should be OK with barriers, yes? A bit like page 280 when you just take ITM values in the formula.
Not sure how you would do strike resets because where do you put reset dates into the formula?

What about formula #3 on page 306?
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

Collector
Posts: 4734
Joined: August 21st, 2001, 12:37 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Resetting Strikes, Barrier and Time 2001 article.

Where can I find it? had a look at Articles but is a bit fubar.
W Magazine 2001, or Models on Models p. 157-164 (2007, basically same as 2001), it covers what we could call weak path dependence 1 asset case, same could easily be done for weak path dependent 2 asset case.
Are you saying that equation 7.3 can be used with let's say (to begin with to make it easy) for a barrier option by choosing g() as in 7.7 as some kind of modification of the payoff, e.g. checking the barrier reached and hence V = 0 for that term. Since we agreed that 7.7 is the same as binomial method and the latter works for barriers then 7.7 should be OK with barriers, yes? A bit like page 280 when you just take ITM values in the formula.
Not sure how you would do strike resets because where do you put reset dates into the formula?

What about formula #3 on page 306?
yes formula #3 on page 306 can be used for barriers (I guess a simplification of the H & H 2001 slightly more complex version of reset strike barriers, p. 310 ), but I would double check it against other models, like closed forms, long time since I we did this one. But method is very flexible as one can easily add many features to it, and price many type of strange barrier options and even include other path dependent properties by small modifications. The method is very flexible.
7.7 I don't think is okay with barriers without doing what is done on page 306 in addition, but combined one get long series of barrier option, for example Sinus barrier options

also send u a PM
Last edited by Collector on October 4th, 2016, 8:31 pm, edited 3 times in total.

Collector
Posts: 4734
Joined: August 21st, 2001, 12:37 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

using Cholesky decomposition
yes, or alternatively Chu Shih-chien extended philosophy

Collector
Posts: 4734
Joined: August 21st, 2001, 12:37 pm

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Have you ordered this one yet?

The Volatility Smile - Emanuel Derman September 2016

On my shelf for the holiday break.
I have ordered it, but not got it yet, looks very interesting!

Cuchulainn
Posts: 62961
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: New 2nd Edition - The Complete Guide to Option Pricing Formulas + CD-ROM by Espen Gaarder Haug

Question on section 3.3 and typos

There is a mismatch between the maths and the VBA code that gives me some discrepancies in my C++ solution.

page 106
1. types in e3 (T -> t1), f3 (I2^2 -> I1^2).
2. rho -> sqrt(t1/T)

3. page 108, function ksi() ==> kappa has a funny 2s*b in it.
4. lambda in phi() has a *T at the end.

For S = X = 100
r = 0.1, b = 0.001
sig = .20
T = 0.1

I get C = 2.49695
You get 2.5057

Any ideas on how to resolve the dilemma?

tusen takk

// The main conundrum is

1. there is an error in my C++ code (for whatever reason)
2. The Genz VBA code does not produce the same results as the Genz C code.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

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