||Heston and SABR model are usually used on simulating implied volatility. This paper details derivation, parameter calibration and parameter meaning of both models. Then we use TXO as sample to study how the day number before expiration date and strike price affect the performance when the two models are used to simulate implied volatility. We also observe how the simulation error change when we increase or decrease parameter value 10%.|
The study shows that the difference between two models simulation error will increase when the expiration date close and the strike price is fixed. This situation will be more clear when the difference between strike price and price which is at the money increase. On the other hand, the simulation error will suddenly sharply increase and then decrease when the strike price is gradually away from at-the-money price and the day number before expiration date is fixed. The most important thing is SABR model simulation error is significantly smaller than Heston model simulation error. The sensitivity analysis shows that Heston model simulation error of call option which is out-of-the-money has significantly increase when parameter value is changed. However, SABR model simulation error is increased not more than 0.5% when we use the same kind of option. If we consider put option which is out-of-the-money, Heston model has a better performance but has no obviously difference between Heston and SABR model. In general, Heston model simulation error is bigger than SABR model simulation error when we increase or decrease parameter value.
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