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juniuss
Topic Author
Posts: 3
Joined: August 16th, 2018, 9:28 am

How to derive vol from Heston Model

September 14th, 2018, 3:24 pm

Hi

I`m not sure with understanding Heston Model clearly.

1) How to derive volatility after calibrating all parameters from vanilla options in Heston Model? 
    Is it like putting Heston price in BS model to derive Implied vol? 

 2)  what`s the exact meaning of volatility in volatility smile by Heston Model?  
   is it instantaneous volatility like local volatility at forward ?  
   Then how to use volatility(in smile curve) for pricing ? 
   i`m not sure.

3) How about SABR MODEL
    What`s the meaning of volatility of SABR MODEL.

I`m quiet confusing in understanding stochastic volatility model. 
IF anyone knows well, plz Help

Thanks :) 
 
User avatar
andcoo01
Posts: 63
Joined: January 7th, 2008, 9:49 am

Re: How to derive vol from Heston Model

September 30th, 2018, 7:33 pm

1. Yes if the vol you want to derive is for the Black Scholes model. In that case you will find the BS vol that gives the same price of the option as the Heston model would calculate.
2. So the Heston model is made up from two stochastic processes, one for the asset price and the other for the volatility that is used in the SDE of the asset price. So the volatility is itself a stochastic process with its own volatility parameter. The Heston model "models" the smile. You can see this by backing out (as in 1) the implied black vol for different strikes on the same expiry. In this sense the Heston model calibrates to the smile and prices back more closely options at different strikes
3. The sabr model is also another model that models the volatility of the asset price as its own SDE. Typically used more for interest rates.
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