why calibrate volatility and fix the mean reversion
$begingroup$
I have had a few experiences or chats with teammates about the Hull-White model.
The famous model has 2 parameters :
- The volatility
- The mean reversion
Very often I hear that the mean reversion has been fixed and that the calibration is only done on the volatility.
Why do that ? Why not fix the volatility and optimize on the mean reversion since both parameters have influence on the vanilla products ?
Moreover, why no optimize on both parameters simultaneously ?
Thanks a lot in advance for the context or opinions that help me to understand what are the justification of these practices.
modeling factor-models calibration hullwhite
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
$endgroup$
add a comment |
$begingroup$
I have had a few experiences or chats with teammates about the Hull-White model.
The famous model has 2 parameters :
- The volatility
- The mean reversion
Very often I hear that the mean reversion has been fixed and that the calibration is only done on the volatility.
Why do that ? Why not fix the volatility and optimize on the mean reversion since both parameters have influence on the vanilla products ?
Moreover, why no optimize on both parameters simultaneously ?
Thanks a lot in advance for the context or opinions that help me to understand what are the justification of these practices.
modeling factor-models calibration hullwhite
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
$endgroup$
add a comment |
$begingroup$
I have had a few experiences or chats with teammates about the Hull-White model.
The famous model has 2 parameters :
- The volatility
- The mean reversion
Very often I hear that the mean reversion has been fixed and that the calibration is only done on the volatility.
Why do that ? Why not fix the volatility and optimize on the mean reversion since both parameters have influence on the vanilla products ?
Moreover, why no optimize on both parameters simultaneously ?
Thanks a lot in advance for the context or opinions that help me to understand what are the justification of these practices.
modeling factor-models calibration hullwhite
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
$endgroup$
I have had a few experiences or chats with teammates about the Hull-White model.
The famous model has 2 parameters :
- The volatility
- The mean reversion
Very often I hear that the mean reversion has been fixed and that the calibration is only done on the volatility.
Why do that ? Why not fix the volatility and optimize on the mean reversion since both parameters have influence on the vanilla products ?
Moreover, why no optimize on both parameters simultaneously ?
Thanks a lot in advance for the context or opinions that help me to understand what are the justification of these practices.
modeling factor-models calibration hullwhite
modeling factor-models calibration hullwhite
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
edited Feb 14 at 14:17
Daneel Olivaw
2,9991629
2,9991629
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
asked Feb 14 at 14:01
StudentInFinanceStudentInFinance
9410
9410
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Fixing the mean reversion, and parameterizing the volatility as a step function or as a piecewise linear function, the volatility can be bootstrapped exactly to a set of vanilla options sorted by expiries. This is a very stable and fast procedure, akin to the bootstrapping of a discount curve onto rate instruments.
For instance when pricing a bermuda swaption with the HW model, a mean reversion is first choosen and the volatility is then bootstrapped on the coterminal european swaptions market prices. Hence the bermuda swaption is priced in a manner consistent with the coterminal european swaptions prices (the coterminal swaptions are also the natural hedge to the bermuda swaption). The remaining degree of freedom, the mean reversion, becomes a parameter to mark the bermuda swaption (not sure if it is still the case, but I think at some point it was even contributed to Markit's Totem).
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
$endgroup$
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Fixing the mean reversion, and parameterizing the volatility as a step function or as a piecewise linear function, the volatility can be bootstrapped exactly to a set of vanilla options sorted by expiries. This is a very stable and fast procedure, akin to the bootstrapping of a discount curve onto rate instruments.
For instance when pricing a bermuda swaption with the HW model, a mean reversion is first choosen and the volatility is then bootstrapped on the coterminal european swaptions market prices. Hence the bermuda swaption is priced in a manner consistent with the coterminal european swaptions prices (the coterminal swaptions are also the natural hedge to the bermuda swaption). The remaining degree of freedom, the mean reversion, becomes a parameter to mark the bermuda swaption (not sure if it is still the case, but I think at some point it was even contributed to Markit's Totem).
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
$endgroup$
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
add a comment |
$begingroup$
Fixing the mean reversion, and parameterizing the volatility as a step function or as a piecewise linear function, the volatility can be bootstrapped exactly to a set of vanilla options sorted by expiries. This is a very stable and fast procedure, akin to the bootstrapping of a discount curve onto rate instruments.
For instance when pricing a bermuda swaption with the HW model, a mean reversion is first choosen and the volatility is then bootstrapped on the coterminal european swaptions market prices. Hence the bermuda swaption is priced in a manner consistent with the coterminal european swaptions prices (the coterminal swaptions are also the natural hedge to the bermuda swaption). The remaining degree of freedom, the mean reversion, becomes a parameter to mark the bermuda swaption (not sure if it is still the case, but I think at some point it was even contributed to Markit's Totem).
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
$endgroup$
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
add a comment |
$begingroup$
Fixing the mean reversion, and parameterizing the volatility as a step function or as a piecewise linear function, the volatility can be bootstrapped exactly to a set of vanilla options sorted by expiries. This is a very stable and fast procedure, akin to the bootstrapping of a discount curve onto rate instruments.
For instance when pricing a bermuda swaption with the HW model, a mean reversion is first choosen and the volatility is then bootstrapped on the coterminal european swaptions market prices. Hence the bermuda swaption is priced in a manner consistent with the coterminal european swaptions prices (the coterminal swaptions are also the natural hedge to the bermuda swaption). The remaining degree of freedom, the mean reversion, becomes a parameter to mark the bermuda swaption (not sure if it is still the case, but I think at some point it was even contributed to Markit's Totem).
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
$endgroup$
Fixing the mean reversion, and parameterizing the volatility as a step function or as a piecewise linear function, the volatility can be bootstrapped exactly to a set of vanilla options sorted by expiries. This is a very stable and fast procedure, akin to the bootstrapping of a discount curve onto rate instruments.
For instance when pricing a bermuda swaption with the HW model, a mean reversion is first choosen and the volatility is then bootstrapped on the coterminal european swaptions market prices. Hence the bermuda swaption is priced in a manner consistent with the coterminal european swaptions prices (the coterminal swaptions are also the natural hedge to the bermuda swaption). The remaining degree of freedom, the mean reversion, becomes a parameter to mark the bermuda swaption (not sure if it is still the case, but I think at some point it was even contributed to Markit's Totem).
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
answered Feb 14 at 14:30
Antoine ConzeAntoine Conze
3,8401410
3,8401410
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
add a comment |
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
I understand from you answer that fixing the volatility and bootstrapping the mean reversion would be a much more complex methodology since the "inversion" of the MR is more complex than doing it for the vol... However, if I understand it right you propose to calibrate the MR at the end of the process whereas all the swpation term structure has been fitted with a fixed MR... How can it be consistent then ?
$endgroup$
– StudentInFinance
Feb 14 at 15:09
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
For a given MR $lambda$ you calibrate $sigma(t)$ to coterminal europeans and then price the bermuda. So now your bermuda price is $text{bermuda} = f(lambda, text{coterminals})$. you can then calibrate $lambda$ to quoted bermudas if there are some. If you are a market maker you can choose the $lambda$ which you believe in...
$endgroup$
– Antoine Conze
Feb 14 at 15:15
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
$begingroup$
Thanks a lot for these explanations
$endgroup$
– StudentInFinance
Feb 14 at 15:57
add a comment |
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