Volatility Models in Option Pricing

10/18/2018

Volatility is one of the most important subjects in all of quantitative finance, due not only to its impact on the prices of options but also to its elusiveness. In this thesis we study some of the models most used to forecast this variable, namely Dupire's local volatility as well as Heston and Static/Dynamic SABR stochastic volatility models. We train these models with some options' implied volatility data, making them able to replicate real market behavior. We find that, when dealing with options with a single maturity, the Static SABR model is the one that best fits the data, while with multiple maturities, the Heston model outperforms Dynamic SABR. All these models vastly outperform the constant volatility model, assumed in Black-Scholes. We then use these trained models to price European and Barrier options with the Monte Carlo numerical pricing method, which is able to accurately predict implied volatilities for near-the-money options, failing for deep in-the-money European call options.

Authors in the community:

• 

  M

  Miguel Ângelo Maia Ribeiro

  ist179013

Supervisors of this institution:

• 

  C

  Cláudia Rita Ribeiro Coelho Nunes Philippart

  ist12953

• 

  R

  Rui Manuel Agostinho Dilão

  ist12028

physical-sciences - Physical sciences

eng - English

Instituto Superior Técnico