Option Pricing Models with HF Data: An Application of the Black Model to the WIG20 Index

Abstract

In this paper, we compared several Black option pricing models by applying different measures of volatility and examined the Black model with historical (BHV), implied (BIV), and several different types of realized (BRV) volatility. The main objective of the study was to find the best model; that is, the model that predicts the actual market price with the minimum error. The high frequency (HF) data and bid-ask quotes (instead of transactional data) for the Warsaw Stock Exchange (WSE) were used to omit the problem of nonsynchronous trading and to increase the number of observations. Several error statistics and the percentage of price overpredictions (OP) showed the results that confirmed the initial intuition that the BIV model is the best model, the BHV model is the second best, and the BRV is the least efficient among the models studied.