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.