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

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Kokoszczyński R., Sakowski P., Ślepaczuk R.
Central European Economic Journal
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2017
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vol. 4
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issue 51
EN
In this study, we analyse the performance of option pricing models using 5-minutes transactional data for the Japanese Nikkei 225 index options. We compare 6 different option pricing models: the Black (1976) model with different assumptions about the volatility process (realized volatility with and without smoothing, historical volatility and implied volatility), the stochastic volatility model of Heston (1993) and the GARCH(1,1) model. To assess the model performance, we use median absolute percentage error based on differences between theoretical and transactional options prices. We present our results with respect to 5 classes of option moneyness, 5 classes of option time to maturity and 2 option types (calls and puts). The Black model with implied volatility (BIV) comes as the best and the GARCH(1,1) as the worst one. For both call and put options, we observe the clear relation between average pricing errors and option moneyness: high error values for deep OTM options and the best fit for deep ITM options. Pricing errors also depend on time to maturity, although this relationship depend on option moneyness. For low value options (deep OTM and OTM), we obtained lower errors for longer maturities. On the other hand, for high value options (ITM and deep ITM) pricing errors are lower for short times to maturity. We obtained similar average pricing errors for call and put options. Moreover, we do not see any advantage of much complex and time-consuming models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare the results we obtain here with a detailed study for Polish emerging option market (Kokoszczyński et al. 2010b).
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Midquotes or transactional prices? Evaluation of Black model on high-frequency data

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Kokoszczyński R., Sakowski P., Ślepaczuk R.
Studia Ekonomiczne
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2018
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vol. 366
43-58
EN
The main idea of this research is to check the efficiency of the Black option pricing model on the basis of high frequency emerging market data. However, liquidity constraints – a typical feature of an emerging derivatives market – put severe limits for conducting such a study [Kokoszczyński et al., 2010]. This is the reason we focus on midquotes instead of transactional data being aware that midquotes might not be a proper representation of market prices as probably transactional data are. We compare in this paper our results with the research conducted on high-frequency transactional and midquotes data. This comparison shows that the results do not differ significantly between these two approaches and that Black model with implied volatility (BIV) significantly outperforms other models, especially the Black model with realized volatility (BRV) with the latter producing the worst results.
PL
Głównym celem artykułu jest weryfikacja efektywności modelu Blacka wyceny opcji na podstawie danych wysokiej częstotliwości dla rynku rozwijającego się. Ograniczenia dotyczące płynności opcji – typowa charakterystyka instrumentów pochodnych na rynkach rozwijających się – stanowią jednak istotne ograniczenie dla takiego badania [Kokoszczyński et al., 2010]. Niska płynność jest jedną z przyczyn, dla których wykorzystuje się kwotowania mid zamiast danych transakcyjnych ze świadomością, że dane transakcyjne mogą być lepszą reprezentacją aktualnego stanu rynku na danym instrumencie finansowym. W badaniu porównano obliczenia przeprowadzone na danych wysokiej częstotliwości dla cen transakcyjnych i kwotowań mid. Porównanie to pokazuje, że rezultaty praktycznie nie różnią się dla tych dwóch różnych danych wejściowych i model Blacka ze zmiennością implikowaną (BIV) osiąga znacznie lepsze wyniki od pozostałych modeli, szczególnie w porównaniu z modelem Blacka ze zmiennością zrealizowaną (BRV).
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