[R-SIG-Finance] Hull-White model calibration for Monte Carlo

[Guy Yollin]

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 at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Wojciech Slusarski
Sent: Friday, October 10, 2008 1:05 AM
To: r-sig-finance at 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

        [[alternative HTML version deleted]]

_______________________________________________
R-SIG-Finance at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-finance
-- Subscriber-posting only.
-- If you want to post, subscribe first.