Option Pricing Models with HF Data - A Comparative Study - The Properties of the Black Model with Different Volatility Measures

Abstract

This paper compares option pricing models, based on the Black model (Black, 1976), with particular emphasis on volatility measures and estimators applied in the process of valuation. We calculate the Black model with historical (BHV), implied (BIV) and several different types of realized (BRV) volatility (additionally searching for the optimal interval Δ, and parameter n - the memory of the process). Our main intention is to find the best model, i.e. the model which predicts the actual market price with minimum error. We use the HF data and bid-ask quotes (instead of transactional data) to omit the problem of non-synchronous trading and to increase the number of observations. We use several error statistics (RMSE, HMAE and HRMSE) and additionally percent of price overpredictions to compare models we test. Results we have got confirm our initial intuition, that the best model is BIV, next in rank is BHV, and BRV is the last one. Models are tested separately for different class of moneyness ratio and time to maturity what enables us to observe the distinct differences among these models. Applying different volatility processes for the same pricing model suggest strongly that point-estimate, not averaged process of RV is the main reason for high errors and instability of valuation in high volatility environment. Finally, we have been able to detect “spurious outliers” and explain their effect and the reason for them thanks to the multi-dimensional comparison of the pricing error statistics.