I have implemented and calibrated Heston model to option prices and at the moment I try to address the issue of hedging an equity option under stochastic dynamic of volatility. So I would like to know whether did anyone know how to build a hedging strategy for an option in the case of stochastic volatility?And even if I apply the “model hedge”(delta hedging), I still have a risk of parameters changing every day, so what is the best way used in front office desks to overcome this problem?Thanks in advance

any help

check out the minimum variance hedge constructed by bakshi, cao and chen (1997) "empirical performance of alternative option pricing models" and discussed further in alexander and nogueira (2005) "a taxonomy of option pricing models"

Hi,I have read the paper of Carol Alexandre 2 months ago, the method of minimum variance hedge is in theory quite interesting but it seems to be computationally too expensive.But I heard that some desks used another way to deal with the issue of incompletness of the market: but realy i didn't understand the method very well...So let me summerize this method :-Computes “Vegas” (derivatives) of the price with respect to those parameters (stochastic volatility parameters).-Neutralizing the derivatives using liquid vanilla options ( Optimization problem on the space of options (assume Heston with parameters ->Find five options such that the overall portfolio sensitivity is minimized.)In my opinion the method was not explaned enough . Thanks in advance

I think one suitable way is to find out the best volatility model and construct the hedge strategy based on such model.

QuoteOriginally posted by: LiborForceHi,But I heard that some desks used another way to deal with the issue of incompletness of the market: but realy i didn't understand the method very well...So let me summerize this method :-Computes ?Vegas? (derivatives) of the price with respect to those parameters (stochastic volatility parameters).-Neutralizing the derivatives using liquid vanilla options ( Optimization problem on the space of options (assume Heston with parameters ->Find five options such that the overall portfolio sensitivity is minimized.)In my opinion the method was not explaned enough . Thanks in advanceSo in this hedging strategy you calculate the "TRUE" vega in the context of stochastic vol(assume this is the true process, no jumps etc..), but which vol of the vanillas should we use? Implied vol? (Notice implied vol is kind of expectation of the averaging of instantaneous ones, but the TRUE vega is based on the instantaneous vol)or should we use the same stoch. vol. model to calculate the TRUE vega of the vanillas?