The plot shows the volatility surface generated by the Heston stochastic volatility model Heston 1993 This is implied volatility based on the Heston price which depends on the time to expiration and on moneyness Recall that for a call option moneyness is the ratio of spot price to strike price The Heston model is described by the following stochastic differential equations SDE where and are correlated Brownian motions with The spot price follows the process with drift and variance which is itself a stochastic process defined by the second equation The second SDE is meanreverting the Cox–Ingersoll–Ross model similar to the Ornstein–Uhlenbeck process Here the longterm variance is the mean reversion or speed of reversion is and the volatility of variance is And finally there is another parameter that does not appear in the SDE the initial condition for variance evolution In this Demonstration the original volatility is used that is the square root of initial variance; volatility is used instead of variance as it is a more frequently quoted quantity The plot generation is computationally intensive so allow some time for it to regenerate