Serving the Quantitative Finance Community

 
User avatar
quantobe
Topic Author
Posts: 5
Joined: May 13th, 2009, 10:27 am

test and verify/validate local volatility surface

January 19th, 2016, 1:06 pm

Hi All,What approaches can I take to test, verify and validate a local volatility surface quantitatively?Thanks
 
User avatar
quantobe
Topic Author
Posts: 5
Joined: May 13th, 2009, 10:27 am

test and verify/validate local volatility surface

January 19th, 2016, 6:45 pm

Given the implied vol surface from which we built the local vol surface what sort of validation can be done? C'mmon gentelmen, and ladies.
 
User avatar
Alan
Posts: 2958
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

test and verify/validate local volatility surface

January 19th, 2016, 7:44 pm

What type of assets and options? What have you done so far?
 
User avatar
quantobe
Topic Author
Posts: 5
Joined: May 13th, 2009, 10:27 am

test and verify/validate local volatility surface

January 20th, 2016, 8:41 am

QuoteOriginally posted by: AlanWhat type of assets and options? What have you done so far?Its FX. I guess one test would be that ATM vol should be the same as what is on the implied vol surface.
 
User avatar
Alan
Posts: 2958
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

test and verify/validate local volatility surface

January 20th, 2016, 1:41 pm

Yes -- not my market, but there is a general effect in all markets that there is a saw-tooth pattern in the implied vols as one crossesimportant dates. In fx, I guess this is central bank announcements, but perhaps jobs reports also -- certainly for equities.So, I would make sure this behavior is finely resolved and correctly reproduced.
 
User avatar
mutley
Posts: 20
Joined: February 9th, 2005, 3:51 pm

test and verify/validate local volatility surface

January 20th, 2016, 9:21 pm

simulate many paths & ensure your local vol MC manages to recover the European option prices / vols that were used to construct the LV surface from the IV surfacethat is one of the easiest ways to validate it - and it that doesn't work, you have bugs somewhere!
 
User avatar
list1
Posts: 827
Joined: July 22nd, 2015, 2:12 pm

test and verify/validate local volatility surface

January 20th, 2016, 9:52 pm

QuoteOriginally posted by: quantobeHi All,What approaches can I take to test, verify and validate a local volatility surface quantitatively?ThanksSorry for might be naive question. Assume we get a local volatility surface. What does it mean to 1) test, 2) verify and 3) validate it quantitatively?
Last edited by list1 on January 19th, 2016, 11:00 pm, edited 1 time in total.
 
User avatar
mutley
Posts: 20
Joined: February 9th, 2005, 3:51 pm

test and verify/validate local volatility surface

January 21st, 2016, 6:49 am

QuoteOriginally posted by: list1Sorry for might be naive question. Assume we get a local volatility surface. What does it mean to 1) test, 2) verify and 3) validate it quantitatively?I wouldn't say that was a naive question; it's certainly a list1 question though.
 
User avatar
quantobe
Topic Author
Posts: 5
Joined: May 13th, 2009, 10:27 am

test and verify/validate local volatility surface

January 21st, 2016, 8:08 am

Thanks Alan, mutley for your suggestions.@list1 it means that given an implied vol surface how can one distinguish between a LV which is correctly built using a Dupire type formula from a LV with nonsensical numbers. What properties the LV surface should have, i.e. to recover market prices, to prevent arbitrage that sort of things.
 
User avatar
list1
Posts: 827
Joined: July 22nd, 2015, 2:12 pm

test and verify/validate local volatility surface

January 21st, 2016, 3:51 pm

QuoteOriginally posted by: quantobeThanks Alan, mutley for your suggestions.@list1 it means that given an implied vol surface how can one distinguish between a LV which is correctly built using a Dupire type formula from a LV with nonsensical numbers. What properties the LV surface should have, i.e. to recover market prices, to prevent arbitrage that sort of things.I think that Dupire formula for LV dealing with the same prices of the option. The LV concept shows that BS option price C ( t , S ; T , K ) , t [$]\in[$] [ 0 , T ] as a function of variables t , S when T , K are fixed can be interpreted with the help of heuristic diffusion process K ( T ) , when variable T [$]\in[$] [ t , - [$] \infty [$] ) and t , S are fixed . Diffusion coefficient of K ( T ) is the LV. Hence the first observation of the LV concept does not present refining of the option price. It looks like alternative point on the same price.
Last edited by list1 on January 20th, 2016, 11:00 pm, edited 1 time in total.
 
User avatar
quantobe
Topic Author
Posts: 5
Joined: May 13th, 2009, 10:27 am

test and verify/validate local volatility surface

January 21st, 2016, 9:38 pm

QuoteOriginally posted by: list1QuoteOriginally posted by: quantobeThanks Alan, mutley for your suggestions.@list1 it means that given an implied vol surface how can one distinguish between a LV which is correctly built using a Dupire type formula from a LV with nonsensical numbers. What properties the LV surface should have, i.e. to recover market prices, to prevent arbitrage that sort of things.I think that Dupire formula for LV dealing with the same prices of the option. The LV concept shows that BS option price C ( t , S ; T , K ) , t [$]\in[$] [ 0 , T ] as a function of variables t , S when T , K are fixed can be interpreted with the help of heuristic diffusion process K ( T ) , when variable T [$]\in[$] [ t , - [$] \infty [$] ) and t , S are fixed . Diffusion coefficient of K ( T ) is the LV. Hence the first observation of the LV concept does not present refining of the option price. It looks like alternative point on the same price.I'm not sure I follow. Are you saying that whatever method I would use to validate IV surface should be used to validate LV??
 
User avatar
list1
Posts: 827
Joined: July 22nd, 2015, 2:12 pm

test and verify/validate local volatility surface

January 21st, 2016, 9:57 pm

It seems to me that original question was about LV and I did not talk about IV and I talked about theoretical aspect of the option price. If option price is defined by BS formula then there exists alternative probabilistic representation of the option price. That is there no new option price there is other representation of the BSE solution.