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 Black model notion (Black, 1976), especially focusing on the volatility models implied in the process of pricing. We calculated 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 was to find the best model, i.e. which predicts the actual market price with minimum error. We focused on the HF data and bidask quotes (instead of transactional data) in order to omit the problem of non-synchronous trading and additionally to increase the significance of our research through numerous observations. After calculation of several error statistics (RMSE, HMAE and HRMSE) and additionally the percent of price overpredictions, the results confirmed our initial intuition that that BIV is the best model, BHV being the second best, and BRV -the least efficient of them. The division of our database into different classes of moneyness ratio and TTM enabled us to observe the distinct differences between compared pricing models. Additionally, focusing on the same pricing model with different volatility processes results in the conclusion that point-estimate, not averaged process of RV is the main reason of 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 owing to the multi-dimensional comparison of the pricing error statistics.

Which Option Pricing Model Is the Best? HF Data for Nikkei 225 Index Options

“…Such error distribution can explain higher interest of speculative investors for deep OTM and OTM options, where information noise, responsible for larger departure of transactional prices from the theoretical ones, is of greater importance. All these outcomes confirm our previous results for the Polish WIG20 index option market (Kokoszczyński 2010a).…”

“…Is it robust to large errors that are likely to emerge when analysing HF data? • Is there any substantial difference between the results for a developed (this paper) and an emerging market (Kokoszczyński et al 2010a)?…”

“…On the basis of similar studies for the Polish market (Kokoszczyński et al 2010a, Kokoszczyński et al 2010b, the realized volatility has finally been calculated on the basis of Δ equal to 5 minutes. Therefore, at this stage, we limit our selection of volatility time series only to the RV calculated for Δ = 5 minutes, with averaging parameter n = 5, 10, 21 and 63 days.…”

“…Our motivation for this paper is to check the results of Kokoszczyński et al (2010a), who conducted a similar study for emerging market HF data (WIG20 index options). 6 Their results show that the Black model with implied volatility (BIV) gives the best results, the Black model with historical volatility (BHV) is slightly worse and the Black model with realized volatility (BRV) gives clearly the worst results.…”

Which Option Pricing Model is the Best? High Frequency Data for Nikkei225 Index Options

“…Our motivation for this paper is to check the results of Kokoszczyński et al 2010a, who conducted a similar study for emerging market HF data (WIG20 index options) 2 . Their results show that the Black model with implied volatility (BIV) gives the best results, the Black model with historical volatility (BHV) is slightly worse and the Black model with realized volatility (BRV) gives clearly the worst results.…”