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Figure 1

Short butterfly spread strategy example. Source: own elaboration.
Short butterfly spread strategy example. Source: own elaboration.

Figure 2

Example of long strip strategy. Source: own elaboration.
Example of long strip strategy. Source: own elaboration.

Figure 3

Example of long strap strategy. Source: own elaboration.
Example of long strap strategy. Source: own elaboration.

Percentage changes (MOM) of WTI crude oil prices in the construction of strategy during the period of activity of the options

Change (month on month)
Above 10%5%–10%Less than 5%
IncreaseDecreaseIncreaseDecreaseIncreaseDecrease
02.2015 (11.52%)12.201405.2015 (6.59%)08.201409.2014 (0.45%)07.2014
(–26.89%)(–5.49%)(–2.65%)
04.2015 (19.39%)01.201508.2016 (5.15%)10.201410.2015 (4.22%)06.2015
(–12.65%)(–9.62%)(–0.96%)
09.2015 (15.80%)03.201510.2016 (9.76%)11.201402.2016 (3.93%)04.2016
(–12.20%)(–6.04%)(–2.75%)
03.2016 (20.19%)07.201512.2016 (7.16%)11.201502.2017 (0.21%)06.2016
(–16.54%)(–9.62%)(–3.73%)
05.2016 (12.35%)08.201504.2017 (9.69%)07.201608.2017 (2.37%)01.2017
(–14.55%)(–6.22%)(–0.04%)
01.2018 (10.29%)12.201507.2017 (8.28%)09.201609.2017 (2.87%)05.2017
(–14.41%)(–9.52%)(–0.87%)
01.201611.2017 (7.12%)03.201710.2017 (2.73%)03.2018
(–13.33%)(–8.88%)(–0.41%)
11.201602.201812.2017 (1.86%)
(–10.18%)(–5.18%)
06.2017
(–13.67%)

The median values (USDs per barrel) achieved in crude oil price fluctuations exceeding 10% (Category 1)

StrategiesVariantUSD/barrel
Long positionShort position
Long stripATM+10% (C) + 2× ATM+10% (P)8.52
Long stripATM+5% (C) + 2× ATM+5% (P)7.09
Long stripATM (C)+ 2× ATM (P)4.35
Long strap2× ATM+10% (C) + ATM+10% (P)3.29
Long stripATM-5% (C)+ 2× ATM-5% (P)3.24
Short butterfly spread2× ATM+5%ATM-10% + ATM+10%2.87
Long strap2× ATM (C) + ATM (P)2.56
Long strap2× ATM+5% (C)+ ATM+5% (P)2.33
Short butterfly spread2× ATMATM-10% + ATM+5%1.73
Short butterfly spread2× ATMATM-10% + ATM+10%1.65
Short butterfly spread2× ATM+5%ATM-5% + ATM+10%1.52
Long stripATM-10% (C) + 2× ATM-10% (P)1.07
Short butterfly spread2× ATMATM-5% + ATM+5%0.45
Short butterfly spread2× ATM+5%ATM + ATM+10%0.40
Short butterfly spread2× ATM-5%ATM-10% + ATM0.29
Short butterfly spread2× ATMATM-5% + ATM+10%0.13
Short butterfly spread2× ATM-5%ATM-10% + ATM+5%–0.38
Short butterfly spread2× ATM-5%ATM-10% + ATM+10%–0.93
Long strap2× ATM-5% (C) + ATM-5% (P)–1.33
Long strap2× ATM-10% (C) + ATM-10% (P)–6.39

The results (USDs per barrel) and statistics for the best long strip strategy in Category 1

MonthChanges (MoM, %)Options
ATM+10%ATM+5%ATM
12.2014–26.89%40.5838.9335.08
01.2015–12.65%10.868.775.02
02.201511.52%–15.09–8.63–3.19
03.2015–12.20%8.525.932.62
04.201519.39%–8.64–2.412.74
07.2015–16.54%18.8817.0013.75
08.2015–14.55%14.1211.998.36
09.201515.80%–5.79–1.232.16
12.2015–14.41%10.969.306.74
01.2016–13.33%8.237.275.11
03.201620.19%–7.86–5.10–2.71
05.201612.35%–9.10–3.81–0.64
11.2016–10.18%8.617.094.35
06.2017–13.67%13.0811.849.50
01.201810.29%–12.02–4.152.10
Median8.527.094.35
Mean5.026.196.07
Standard deviation14.8211.829.20
Number of losses663
Number of profits9912
Pearson correlation coefficient for changes and results–0.91–0.85–0.71

The results achieved in short butterfly spread, depending on the price level of the underlying instrument on the expiry date of the option

IntervalShort call butterfly spreadShort put butterfly spread
[0;K1)c(K1 ) + 2c(K0 ) − c(K2 )K2 − 2K0 + K1p(K1 ) + 2 p(K0 ) − p(K2 )
[K1 ;K0 )K1f Tc ( K1 ) + 2 c ( K0 ) − c ( K2 )K2 + f T − 2 K0p ( K1 ) + 2 p ( K0 ) − p ( K2 )
[K0 ;K2 )2 K0f TK1c ( K1 ) + 2 c ( K0 ) − c ( K2 )K2f Tp ( K1 ) + 2 p ( K0 ) − p ( K2 )
[K2 ;∞)K2 + 2K0K1c(K1 ) + 2c(K0 ) − c(K2 )p(K1 ) + 2 p(K0 ) − p(K2 )

Median values (USDs per barrel) achieved in crude oil price changes ranging from 5% to 10% (Category 2)

StrategyVariantUSD/ barrel
Long positionnShort position
Long stripATM+10% (C) + 2× ATM+10% (P)6.25
Long stripATM+5% (C) + 2× ATM+5% (P)5.10
Long strap2× ATM+10% (C) + ATM+10% (P)2.85
Short butterfly spread2× ATM+5%ATM-10% + ATM+10%2.46
Short butterfly spread2× ATM+5%ATM-5% + ATM+10%1.76
Long strip2× ATM (P) + ATM (C)1.68
Long strap2× ATM (C) + ATM (P)1.50
Short butterfly spread2× ATMATM-10% + ATM+10%1.31
Long strap2× ATM+5% (C) + ATM+5% (P)1.21
Short butterfly spread2× ATMATM-5% + ATM+10%1.18
Short butterfly spread2× ATMATM-10% + ATM+5%0.56
Short butterfly spread2× ATMATM-5% + ATM+5%0.53
Short butterfly spread2× ATM-5%ATM-10% + ATM0.45
Short butterfly spread2× ATM +5%ATM + ATM+10%0.38
Short butterfly spread2× ATM-5%ATM-10% + ATM+5%–0.39
Short butterfly spread2× ATM-5%ATM-10% + ATM+10%–0.59
Long stripATM-5% (C) + 2× ATM-5% (P)–0.90
Long stripATM-10% (C) + 2× ATM-10% (P)–3.43
Long strap2× ATM-5% (C) + ATM-5% (P)–3.48
Long strap2× ATM-10% (C) + ATM-10% (P)–6.62

Median values (USDs per barrel) achieved in crude oil price changes below 5% (Category 3)

StrategiesVariantUSD/barrel
Long positionShort position
Short butterfly spread2× ATM-5%ATM-10% + ATM0.37
Short butterfly spread2× ATM+5%ATM + ATM+10%0.12
Short butterfly spread2× ATM-5%ATM-10% + ATM+5%–0.02
Short butterfly spread2× ATM-5%ATM-10% + ATM+10%–0.46
Long stripATM-10% (C) + 2× ATM-10% (P)–0.66
Short butterfly spread2× ATMATM-5% + ATM+5%–0.80
Short butterfly spread2× ATM+5%ATM-5% + ATM+10%–0.81
Long strap2× ATM-10% (C) + ATM-10% (P)–0.99
Short butterfly spread2× ATMATM-5% + ATM+10%–1.13
Short butterfly spread2× ATMATM-10% + ATM+5%–1.17
Long strap2× ATM+10% (C) + ATM+10% (P)–1.23
Long stripATM-5% (C) + 2× ATM-5% (P)–1.25
Short butterfly spread2× ATM+5%ATM-10% + ATM+10%–1.26
Short butterfly spread2× ATMATM-10% + ATM+10%–1.63
Long strap2× ATM-5% (C) + ATM-5% (P)–1.67
Long stripATM+10% (C) + 2× ATM+10% (P)–1.75
Long strap2× ATM+5% (C) + ATM+5% (P)–2.34
Long stripATM+5% (C) + 2× ATM+5% (P)–2.59
Long strap2× ATM (C) + ATM (P)–3.48
Long stripATM (C) + 2× ATM (P)–3.72