with current European option prices is known as the local volatility func- tion. It is unlikely that Dupire, Derman and Kani ever thought of local volatil-. So by construction, the local volatility model matches the market prices of all European options since the market exhibits a strike-dependent implied volatility. Local Volatility means that the value of the vol depends on time (and spot) The Dupire Local Vol is a “non-parametric” model which means that it does not.
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I am reading about Dupire local volatility model and have a rough idea volatiloty the derivation. But I can’t reconcile the local volatility surface to pricing using geometric brownian motion process. How does my model know that I changed my strike?
If I have a matrix of option prices by strikes volatilty maturities then I should fit some 3D function to this data. I did the latter.
If they have exactly the same diffusion, the probability density function will be the same and hence the realized volatility will be exactly the same for all bolatility, but market data differentiate volatility between strike and option price. If I have realized volatility different than implied, there is no way I should get the same option prices as the market. Could you guys clarify? Ok guys, I think I understand it now.
I performed MC simulation and got the correct numbers. In fact the pdf will be tlhe same but it will allow to replicate implied vol surface. Thanks for the explanation, it was helpful. Dupre idea behind this is as follows: The payoff of a European contingent claim only depends on the asset price at maturity.
Consequently any two models whose implied probability densities agree for the maturity of interest agree on the prices of all European contingent claims. So by construction, the local volatility model matches the market prices of all Volatiility contingent claims without the model dynamics depending on what strike or payoff function you are interested in.
Here is how I understand your first edit: You write that since there is only one price process, there is one fixed implied standard deviation per maturity. You then argue that consequently, we can’t replicate the prices of all European options since the market exhibits a strike-dependent implied volatility.
Home Questions Tags Users Unanswered. I’m still not sure if I understand that correctly. LocalVolatility 5, 3 13 Gordon – thanks I agree. I thought I could get away with it.
Local volatility – Wikipedia
LocalVolatility I added a comment to my original post. Could you look at volatillty Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.
options – pricing using dupire local volatility model – Quantitative Finance Stack Exchange