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List:       r-sig-finance
Subject:    Re: [R-SIG-Finance] Hull-White model calibration for Monte Carlo
From:       "Wojciech Slusarski" <wojciech.slusarski () gmail ! com>
Date:       2008-10-11 9:26:06
Message-ID: 5e64e5be0810110226o22436e29n9398ea73a3c74a70 () mail ! gmail ! com
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Thanks a lot, papers of those guys are very interesting (from time to time I
deal with energy contracts as well), though I still haven't found a solution
for H-W model. the notation you have described is correct, though I have
problems to define v(t) as it is a deterministic function of time, but it
depends on a too.

Best regards,
Wojtek

2008/10/10 Guy Yollin <guy.yollin@rotellacapital.com>

> Wojtek,
>
> If I understand your question, you would like to know how to fit the
> hull-white model parameters; using your notation:
> a = mean-reversion rate
> vol = short-rate volatility
>
> Hull (Options, Futures, and Other Derivatives) and Clewlow/Strickland
> (Implementing Derivative Models) show how to construct trinomial trees
> matched to the term structure using the Hull-White model.
>
> Further, both of these texts also show how these trees can be used to price
> fixed income derivatives.  Hence, one way to solve the parameter fitting
> problem is to find the implied tree based on the real market price of these
> derivatives.
>
> While I do not worked with interest rate trees and derivatives, I have
> worked with trinomial trees fitted to the futures curve for valuing options
> on energy futures.
>
> To estimate the mean-reversion rate and spot-volatility I simply used a
> general purpose optimization algorithm to minimize the pricing error of a
> selection of futures options (i.e. adjust a and vol to minimize the
> difference between the actual option price and option price calculated from
> the model).
>
> The main reference that I used was "Valuing Energy Options in a One Factor
> Model Fitted to Forward Prices" by Clewlow & Strickland, 1999; this paper is
> available from a variety of sources on the web.
>
> I also see that Clewlow and Strickland have a new research paper entitled
> "Calibrating Trees to the Market Price of Options" available from their
> website (www.lacimagroup.com).  Although a quick look at this paper seems
> to indicate that it specifically describes this procedure, I have not read
> this paper in detail.
>
> I hope this helps.
>
> Best,
>
> Guy
>
>
>
>
> -----Original Message-----
> From: r-sig-finance-bounces@stat.math.ethz.ch [mailto:
> r-sig-finance-bounces@stat.math.ethz.ch] On Behalf Of Wojciech Slusarski
> Sent: Friday, October 10, 2008 1:05 AM
> To: r-sig-finance@stat.math.ethz.ch
> Subject: [R-SIG-Finance] Hull-White model calibration for Monte Carlo
>
>  Hello,
>
> Does anybody could provide some hints on how to calibrate Hull-White model
> for Monte Carlo? How to fit parameters, that the model fits the initial
> term
> structure? I am interested in calibration of model in form as presented in
> 3.33 in Brigo and Mercurio (2007):
> dr(t) = [v(t) - ar(t)]dt + voldW(t)
>
> If anybody has a paper describing such calibration and description how to
> conduct such simulation, I would appreciate that a lot.
>
> Best regards,
> Wojtek
>
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>
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