Abstract:
The project deals with modelling of options implied volatility where the implied volatility is considered as a function of strike
price and time to maturity. We focus on arbitrage-free techniques where the strike arbitrage-free condition is expressed in
terms of state-price-density while the calendar arbitrage-free condition is based on the monotony of total (implied) variance.
Various statistical methods based on local smoothing with polynomial representations and kernel estimations will be
considered. One of the main goals of the project is to derive a general nonparametric model for implied volatility estimation
which will satisfy all arbitrage-free conditions, including conditions on call spread and call prices. Moreover, alternativetechniques using isotonic regression or fuzzy transform will be employed. Finally, the arbitrage-free conditions will be analyzedfrom the point of view of liquidity at the options market