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

Kokoszczyński Ryszard
Kokoszczyński Ryszard
, 
Sakowski Paweł
Sakowski Paweł
 and 
Ślepaczuk Robert
Ślepaczuk Robert
   | Apr 01, 2019
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Published Online: Apr 01, 2019
Page range: 18 - 39
DOI: https://doi.org/10.1515/ceej-2018-0010
Keywords
© 2017 R. Kokoszczyński, P. Sakowski, R. Ślepaczuk, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Index returns with the opening jump effecta The returns and index prices cover the data span between 2 January, 2008 to 30 June, 2008.
Index returns with the opening jump effecta The returns and index prices cover the data span between 2 January, 2008 to 30 June, 2008.

Fig. 2

Index returns without the opening and mid-session jump effecta The 10-second returns between the closing price from each day and the opening price from the next day have been excluded. The same was done with the mid-session jump. The returns cover the data span from 2 January, 2008 to 30 June, 2008.
Index returns without the opening and mid-session jump effecta The 10-second returns between the closing price from each day and the opening price from the next day have been excluded. The same was done with the mid-session jump. The returns cover the data span from 2 January, 2008 to 30 June, 2008.

Fig. 3

Historical and realized volatility (5m, 5m_5, 5m_10, 5m_21, 5m_63)a The volatility time series cover the data period between 2nd January, 2008 and 30th June, 2008. Vertical lines represent end of month and additionally the day of 11th January, 8th February, 14th March, 11th April, 9th May and 13th June, when the option series expired.
Historical and realized volatility (5m, 5m_5, 5m_10, 5m_21, 5m_63)a The volatility time series cover the data period between 2nd January, 2008 and 30th June, 2008. Vertical lines represent end of month and additionally the day of 11th January, 8th February, 14th March, 11th April, 9th May and 13th June, when the option series expired.

Fig. 4

Implied volatility for ATM call optionsa The volatility time series cover the data period between 2nd January, 2008 and 30th June, 2008. IV are presented for 7 series of options. Vertical lines represent end of month and additionally the day of 11th January, 8th February, 14th March, 11th April, 9th May and 13th June, when the option series expired.
Implied volatility for ATM call optionsa The volatility time series cover the data period between 2nd January, 2008 and 30th June, 2008. IV are presented for 7 series of options. Vertical lines represent end of month and additionally the day of 11th January, 8th February, 14th March, 11th April, 9th May and 13th June, when the option series expired.

Fig. 5

The number of theoretical values for call and put options with respect to TTM i MR ratioa,b
The number of theoretical values for call and put options with respect to TTM i MR ratioa,b

Fig. 6

The distribution of volume for call and put optionsa,bbthe volume for both call and put options quoted in the period between 2nd January, 2008 and 30th June, 2008.
The distribution of volume for call and put optionsa,bbthe volume for both call and put options quoted in the period between 2nd January, 2008 and 30th June, 2008.

Fig. 7

The volume of turnover for call and put optionsa
The volume of turnover for call and put optionsa

Fig. 8

MdAPE statistics for call options with respect to MR and TTM classes
MdAPE statistics for call options with respect to MR and TTM classes

Fig. 9

OP statistics for call options with respect to MR and TTM classes
OP statistics for call options with respect to MR and TTM classes

Fig. 10

MdAPE statistics for put options with respect to MR and TTM classes
MdAPE statistics for put options with respect to MR and TTM classes

Fig. 11

OP statistics for put options with respect to MR and TTM classes
OP statistics for put options with respect to MR and TTM classes

Fig. 12

The frequency of the best option pricing for Nikkei 225 index options with respect to MR based on MdAPE error statistica The charts present the data for call and put options together. On each panel, the order of the models is the same: we start with the Heston model at the top and going clockwise end up with the BIV model.
The frequency of the best option pricing for Nikkei 225 index options with respect to MR based on MdAPE error statistica The charts present the data for call and put options together. On each panel, the order of the models is the same: we start with the Heston model at the top and going clockwise end up with the BIV model.

Fig. 13

The frequency of the best option pricing for Nikkei 225 index options with respect to TTM on MdAPE error statistica The charts present the data for call and put options together. On each panel, the order of the models is the same: we start with the Heston model at the top and going clockwise end up with the BIV model.
The frequency of the best option pricing for Nikkei 225 index options with respect to TTM on MdAPE error statistica The charts present the data for call and put options together. On each panel, the order of the models is the same: we start with the Heston model at the top and going clockwise end up with the BIV model.

Fig. 14

The frequency of the best option pricing for Nikkei 225 index options with respect to the type of option on MdAPE error statisticaOn each panel, the order of the models is the same: we start with the Heston model at the top and going clockwise end up with the BIV model.
The frequency of the best option pricing for Nikkei 225 index options with respect to the type of option on MdAPE error statisticaOn each panel, the order of the models is the same: we start with the Heston model at the top and going clockwise end up with the BIV model.

Number of theoretical premiums for different classes of MR and TTM for BRV model*

optionmoneyness0–15 days16–30 days31–60 days61–90 days91+ daysTotal
CALLdeep OTM372432727089237991049466081
OTM6501116352257219567895969234
ATM819996811738512141536852774
ITM388045105373148476116008
deep ITM120519353032104413358551
total CALL2015732088754515803526917212648
PUTdeep OTM69642058044831312257768111368
OTM610981421546612674563148022
ATM802896691701412001641353125
ITM4278482674271790109619417
deep ITM2411300230981161196211634
total PUT2779046219878365885122870243566
total CALL and PUT479477830716328711688649787456214

The descriptive statistics for Nikkei 225 index returns for samples with and without opening jump effects

sample with opening jump effectssample without opening and mid-session jump effects
N67456504
Mean-0,000025394-0,000014111
Median0,0000326440,000036116
Standard Deviation0,00309070,0028429
Minimum-0,0319108-0,0319108
Maximum0,02161270,0216127
Kurtosis10,436421912,7560437
Skewness-0,62272280,7206586
Normality tests
Kolmogorov-SmirnovStatistic0,0933490,086497
Jarque-BerraStatistic30995,919544584,7971
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