OU Process Calibration

stemul · February 21st, 2011, 10:39 pm

Hello ?I would appreciate an outline of the steps involved in the calibration of an OU process ( e.g., mean reversion rate, volatility, & seasonal indices ) for the following time series: ID: Electric utility sales ( kWh ).FREQ: MonthlyNOBS: 22 * 12 = 264Note: The series exhibits both strong upward trend and seasonality.All responses deeply appreciated.Historical data available on request.THANKS,Seasoned Time Series Analyst, with NO Quantitative Finance background.

Edgey · February 22nd, 2011, 11:09 am

See Clewlow, L. & Strickland, C. (2000). Energy derivatives - Pricing and risk managementfor some step by step instructions. Note that the OU approach may not be appropriate for electricity. For example, the mean value that the process reverts to may not be constant.

tags · November 17th, 2013, 11:30 am

(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?

Cuchulainn · November 17th, 2013, 12:01 pm

A good article is by @outrun.

tags · November 17th, 2013, 12:05 pm

QuoteOriginally posted by: CuchulainnA good article is by @outrun.Yes, I am working on it

tags · November 17th, 2013, 12:10 pm

QuoteOriginally posted by: edouardQuoteOriginally posted by: CuchulainnA good article is by @outrun.Yes, I am working on itEDIT: I'm attaching a spreadsheet related to the article on OU process at sitmo, if one wants to play around.

Cuchulainn · November 17th, 2013, 12:30 pm

QuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?The reason [$]W_{t-1}[$] is that the method is explicit on RHS so t-1 is OK and standard.But your path generator is Euler-Maruyama which is komme si komme sa...Why not use the exact path as described in sitmo article? Also

tags · November 17th, 2013, 12:48 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?The reason [$]W_{t-1}[$] is that the method is explicit on RHS so t-1 is OK and standard.But your path generator is Euler-Maruyama which is komme si komme sa...Why not use the exact path as described in sitmo article? AlsoHi Cuch. Thanks for the reply.I was curious to understand.I agree the article at sitmo make the things clear.

Cuchulainn · November 17th, 2013, 3:57 pm

QuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?Euler is indeed the most simple and probably most TERRIBLE of them all.

Stale · November 18th, 2013, 10:17 am

Intuitively: Looking at the filtration generated by this process, the information at time t does not contain any uncertainty if you use W_(t-1), so the state is perfectly well know. It should be W_t as you say Eduard.This comes from the defininition of the stochastic intergral, if you like to look it up S

Cuchulainn · November 18th, 2013, 11:20 am

QuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?Hey, wait a minute!Unless I have missed something fundamental, the above formula (actually both) is very very WRONG.(BTW is "simplest updating formula" supposed to be Euler here??)

MattF · November 18th, 2013, 4:34 pm

QuoteOriginally posted by: StaleIntuitively: Looking at the filtration generated by this process, the information at time t does not contain any uncertainty if you use W_(t-1), so the state is perfectly well know. It should be W_t as you say Eduard.This comes from the defininition of the stochastic intergral, if you like to look it up Absolutely, and there's also a horrible confusion of whether t is a real-valued variable or indexing variable in the original formulation.

tags · November 18th, 2013, 7:10 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?Hey, wait a minute!Unless I have missed something fundamental, the above formula (actually both) is very very WRONG.(BTW is "simplest updating formula" supposed to be Euler here??)Ah, you! python. i noticed a typo in your snippet in "for i in xrange(1,N)", that is the letter "x" makes the whole thing bug.that's interesting how you do those things such as creating a variable for square roots.i'm posting the 'translation' of your code into R language.

Cuchulainn · November 18th, 2013, 7:16 pm

QuoteOriginally posted by: edouardQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?Hey, wait a minute!Unless I have missed something fundamental, the above formula (actually both) is very very WRONG.(BTW is "simplest updating formula" supposed to be Euler here??)Ah, you! python. i noticed a typo in your snippet in "for i in xrange(1,N)", that is the letter "x" makes the whole thing bug.that's interesting how you do those things such as creating a variable for square roots.i'm posting the 'translation' of your code into R language.Not my code: I use C++, C#, VBA and R mainly I took it from Wiki to show my question: it calls gauss(0,1) but not W_t and I don't get it. Is this scheme Euler or something else?

tags · November 18th, 2013, 8:33 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: edouardQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: edouard(Ouch! I'm sorry this is very basic)At FXpaul.wordpress.com, the author explains that "The simplest updating formula for Ornstein-Uhlenbeck process is"I don't get why [$]W_{t-1}[$] takes place in the updating of the process. I would rather write (use) [$]W_t[$], that is [$]S_t-S_{t-1}=\theta(\mu-S_{t-1})\Delta t+\sigma\sqrt{\Delta t} W_t[$].Can someone explain, please?Hey, wait a minute!Unless I have missed something fundamental, the above formula (actually both) is very very WRONG.(BTW is "simplest updating formula" supposed to be Euler here??)Ah, you! python. i noticed a typo in your snippet in "for i in xrange(1,N)", that is the letter "x" makes the whole thing bug.that's interesting how you do those things such as creating a variable for square roots.i'm posting the 'translation' of your code into R language.Not my code: I use C++, C#, VBA and R mainly I took it from Wiki to show my question: it calls gauss(0,1) but not W_t and I don't get it. Is this scheme Euler or something else?Well, I can't really anyswer. I mean I'm to OP! But, I'm looking forward to inputs that would throw the light on all this.