Discounting by a Hull White object

[amar singh]

I have a doubt whether values of the parameters a and sigma would have effect on the discounting data provided by the HullWhite model. It seems that discount function value for the model exactly matches the discount function of the underlying termstructure used in creation, at each point till the maturity. It tried using different values of a and sigma, but they do not have any effect at all. Am I doing or assuming something wrong?

 

 

double a=.8;

double sigma=.5

Time t = 2.0;

HullWhite hullObject(rhTermStructure,a,sigma);

std::cout << hullObject.discount(t) << std::endl;

std::cout << rhTermStructure->discount(t) << std::endl;

 

 

 

Thanks,

Amar

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[Perissin Francesco]

Hi Amar,

if I am not wrong, it is correct that the discount value at a certain date is always equal to the discount given in termstructure. What is depending on a and sigma is the short rate in a certain point of the tree.

So, if you consider time t, you will have a set of tree points with different probabilities and different short rate levels, depending on a and sigma. When you want the discount at time t, you will somehow take a scalar product of the different discounts times their probabilities, and you will lose the dependancy of the volatility parameters.

 

Francesco

-----Original Message-----
From: amar singh [mailto:[hidden email]]
Sent: giovedì, 25 settembre 2003 09:05
To: quantlib users
Subject: [Quantlib-users] Discounting by a Hull White object

I have a doubt whether values of the parameters a and sigma would have effect on the discounting data provided by the HullWhite model. It seems that discount function value for the model exactly matches the discount function of the underlying termstructure used in creation, at each point till the maturity. It tried using different values of a and sigma, but they do not have any effect at all. Am I doing or assuming something wrong?

 

 

double a=.8;

double sigma=.5

Time t = 2.0;

HullWhite hullObject(rhTermStructure,a,sigma);

std::cout << hullObject.discount(t) << std::endl;

std::cout << rhTermStructure->discount(t) << std::endl;

 

 

 

Thanks,

Amar

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[amar singh]

Francesco,

 

Thank you very much for your help. Indeed, my assumption was wrong .( I got confused because discount depends on A(t,T) and B(t,T) functions which use 'a' and 'sigma' values for their calculation, so I thought why discount does not change.On substituting t as 0, all terms cancel and it holds for any a and sigma)

 

Regards,

Amar

Perissin Francesco <[hidden email]> wrote:

Hi Amar,

if I am not wrong, it is correct that the discount value at a certain date is always equal to the discount given in termstructure. What is depending on a and sigma is the short rate in a certain point of the tree.

So, if you consider time t, you will have a set of tree points with different probabilities and different short rate levels, depending on a and sigma. When you want the discount at time t, you will somehow take a scalar product of the different discounts times their probabilities, and you will lose the dependancy of the volatility parameters.

 

Francesco

-----Original Message-----
From: amar singh [mailto:[hidden email]]
Sent: giovedì, 25 settembre 2003 09:05
To: quantlib users
Subject: [Quantlib-users] Discounting by a Hull White object

I have a doubt whether values of the parameters a and sigma would have effect on the discounting data provided by the HullWhite model. It seems that discount function value for the model exactly matches the discount function of the underlying termstructure used in creation, at each point till the maturity. It tried using different values of a and sigma, but they do not have any effect at all. Am I doing or assuming something wrong?

 

 

double a=.8;

double sigma=.5

Time t = 2.0;

HullWhite hullObject(rhTermStructure,a,sigma);

std::cout << hullObject.discount(t) << std::endl;

std::cout << rhTermStructure->discount(t) << std::endl;

 

 

 

Thanks,

Amar

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############################### DISCLAIMER #################################

This message (including any attachments) is confidential and may be
privileged. If you have received it by mistake please notify the sender by
return e-mail and delete this message from your system. Any unauthorised
use or dissemination of this message in whole or in part is strictly
prohibited. Please note that e-mails are susceptible to change. Banca del
Gottardo (including its group companies) shall not be liable for the
improper or incomplete transmission of the information contained in this
communication nor for any delay in its receipt or damage to your system.
Banca del Gottardo (or its group companies) does not guarantee that the
integrity of this communication has been maintained nor that this
communication is free of viruses, interceptions or interference.

############################################################################

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