Modelling the implied volatility – A case of EUR/PLN currency options

Implied volatility, quoted by market makers for Over-the-Counter foreign exchange options, constructs a volatility surface that facilitates the pricing of all vanilla contracts. This study presents a model explaining implied volatility changes in three dimensions: volatility level, slope of the volatility curve, and slope of the volatility smile. Long-term time series data from the EUR/PLN market are used to calibrate the model. The evidence demonstrates a tight interdependence between prices of option strategies, which can be leveraged to build error correction models based on cointegration of time series. In these models, At-the-Money (ATM) volatility is explained by spot returns and historical standard deviation. Additionally, the shape of the volatility curve and volatility smile are explained by the level of ATM volatility. The models exhibit significant forecasting value, quantified as a directional quality measure, with the error correction component enhancing the accuracy of forecasting decisions.