New hedging techniques in energy sector using barrier options

Transcription

1 New hedging echniques in energy secor using barrier opions Monika Harčariková 1 and Michal Šolés 2 he paper is focused on he measuremen of hedging efficiency using he New 4 opion sraegy creaed by barrier opions. We aim o find he way of he risk managemen agains an underlying asse s price drop. European down and knock-in pu opions are used wih he combinaions of vanilla call and barrier call opions, where he zero-cos opion sraegy has o be me. Based on analysed hedging echniques, he imum consan selling price is secured for he case of he underlying asse s price drop. Our heoreical resuls of hedging are applied in he energy secor, i.e. Energy Selec Secor SPDR EF. All hedging echniques are analysed and compared o each oher, bu only seleced varians are presened in he paper. he findings show ha he using of barrier opions on he hedging produces very significan reducions in risk. Finally, here is necessary o develop an effecive hedging sraegy, where he srucure of he srike prices and he barrier levels plays an imporan role. According o he findings, he recommendaions of he bes ways are inroduced for poenial invesors. Keywords: hedging echnique, barrier opion, opion sraegy, Energy Selec Secor SPDR EF Inroducion Financial marke prices, mainly sock prices, commodiy prices, foreign exchanges and oher invesmen asses, have shown sriking changes in volailiy hrough ime. Each of hese kinds of he underlying asses price shows enormous unpredicable movemens from day o day or monh o monh. Due o his fac, he firms or business leaders wan o use effecive hedging sraegies, in order o avoid he disrupive consequences of heir invesmens. Financial derivaives are an ineresing opporuniy o proec agains marke risks. Mainly barrier opions inroduce effecive and flexible ools used in he risk managemen. Over he years, many financial sudies are dealing wih he risk managemen using financial derivaives. Many sudies deal wih he solving problem in he risk managemen. Brown (2001), Guay and Kohari (2003) sudy he managing of risk hrough derivaives. Hankins (2011) invesigae how he firms manage risk by exaing he ineracions beween financial and operaional hedging. Loss (2012) presens he opimal hedging sraegies, and ichý (2009) focuses on currency hedging of he nonfinancial insiuion. o our bes knowledge, our risk managemen using barrier opions appears o be unique in his field. Hence, comparing he various risk managemen varians using New 4 opion sraegy creaed by barrier opions fills a noiceable gap in his opic. Our heoreical resuls will be useful no only for financial insiuions bu also for academic and research communiy. Hedging aims o reduce any subsanial losses from he operaions in fuure, where i is possible o hedge he values of energy, precious meals, foreign currency, and ineres rae flucuaions. I is valid ha he loss in spo marke posiion is compensaed by he gain in fuures marke posiion and vice versa. In our case, hedger inends o sell an underlying asse in fuure and wishes o eliae he downside risk. he purpose of he paper is o hedge agains price drop using New 4 opion sraegy. We do no avoid a price drop, bu we wan o secure only he imum accepable selling price. he mehodology of he paper is based on opion sraegies, inroduced in he papers such as Hull (2012) and aleb (1997). Mainly barrier opions inroduce a new ool in he risk managemen. hese ools are paricularly aracive o hedgers in he financial marke. In essence, here are four ypes of barrier opions, i.e. UI, UO, DI, DO call/pu opions. Where he righ o exercise eiher appears (IN) or disappears (OU) on some barrier level. he barrier level can be se above (UP) or below (DOWN) he underlying asse price a he ime he opion is creaed. he barrier level mus be se above (for UP opions) and below (for DOWN opions) he acual spo price, because oherwise, he opions would be worhless. Barrier opions are generally cheaper han sandard opions due o he underlying asse has o cross a cerain barrier level. As we will see laer, DI pu opions wih he combinaions of vanilla/barrier call opions are he bes for hedging agains a price drop. More deailed characerisics of barrier opions are presened by ichý (2004) and Zhang (1998). In he paper, we discuss only European opions in any deail. However, he nex approach can be oriened on American opions. We aim o hedge he imum selling price for our porfolio hrough New 4 opion sraegy using barrier opions. here are 124 possibiliies creaion of his sraegy using barrier and vanilla opions in oal. For full 1 2 Monika Harčariková, echnical Universiy of Košice, Faculy of Economics, Deparmen of Finance, Němcovej 32, Košice, Slovakia, monika.harcarikova@uke.sk Michal Šolés, echnical Universiy of Košice, Faculy of Economics, Deparmen of Banking and Invesmen, Němcovej 32, Košice, Slovakia, michal.soles@uke.sk 386

2 proecion agains price drop, here have o be used DI pu opions wih he smalles srike price and oher ypes of opions. Our research shows ha 16 ypes using only barrier opions and 9 ypes using vanilla and barrier opions are suiable for our analysis. We have presened seleced hedging varians wih he bes resuls of he secured selling price because oher ways are secured only parially. he resuls of our approach are applied in he energy secor, specifically, Energy Selec Secor SPDR EF. I is a fund allocaed o oil gas and consumable fuels companies. However, his approach can be applied for various underlying asses. Based on individual componens of replicaing porfolio, he hedging echniques on hese shares are proposed and compared o each oher wih he unsecured posiion. In he end, he bes hedging echniques are presened in differen underlying asse s price developmen wih he recommendaions for poenial insiuions. Research mehodology Our approach is based on opion sraegies and heir using in risk managemen. he significan par of financial engineering are opions and opion sraegies. hese ools are also used on he new innovaive financial produc s creaion as i is proved by Hull (2012). herefore, he mehodology of he paper is based on hese ools by which he significan role plays a valuaion. Undersanding of he New 4 opion sraegy creaion is needed for is use in risk managemen. New 4 opion sraegy can be creaed in 3 ways. he firs way is creaed as he buying n pu opions wih a srike price X 1, he premium p 1N per opion, simulaneously by selling n pu opions wih a higher srike price X 2 he premium p 2S per opion and by buying n pu opions wih he highes srike price X 3 he premium p 3B per opion. he second way is similar o he previous one wih he same parameers bu is creaed by buying call opions and a he same ime by selling call opions and by buying pu opions. However, hese wo ways are no possible o creae wihou iniial coss. he las way fulfils he zero coss, which is creaed by buying n pu opions and a he same ime by selling n call opions and by buying n call opions, where he srike prices should be se as X 1 < X 2 < X 3. herefore, we will consider only wih his way for hedging. Also, European-syle of opions is used for he same underlying asse and wih he same expiraion ime. he New 4 opion sraegy using only sandard vanilla opions was designed by Šolés (2011). he New 1 opion sraegy formed by barrier opions and is using in risk managemen was discussed by Šolés and Harčariková (2015). Shor Call Ladder sraegy creaed by vanilla opions and is using on hedging is deal by Amaiiek e al. (2010). Also, Rusnáková and Šolés (2012), Rusnáková (2015), Šolés and Rusnáková, (2012; 2013) analyse he hedging agains a price increase or drop by means of differen opions sraegies using vanilla and barrier opions. According o he sudies menioned, we analyse all possible ways of New 4 opion sraegy creaion using barrier opions wih he aim o hedge agains a price drop. Valuaion he analysis consiss of all ways of New 4 opion sraegy creaion using barrier opions in risk managemen. here is possible o creae 124 ways of New 4 opion sraegies using barrier opions. However, only seleced varians are presened in his paper. Using DI pu opions wih he smalles srike price are suiable for full hedging agains a price drop. All combinaions of DI pu opions ogeher wih 2 various call/call barrier opions are analysed, i.e. 9 ways wih he vanilla opions and 16 ways only wih barrier opions. Choosing of secured varians have o mee he zero-cos condiions. Our heoreical resuls are applied o he Energy Selec Secor SPDR EF (XLE), where he evaluaion of he hedger s profiabiliy a he mauriy dae is presened. Based on comparaive analysis of he proposed hedging varians, he recommendaions for invesors are given. he approach is based on he value of European vanilla and barrier opions on he Energy Selec Secor SPDR EF wih he various srike prices and he barrier levels. Real vanilla opions are gained from European barrier opion prices are no publicly accessible. hen, we have o calculae barrier opion premiums. Auhors Black and Scholes (1973) inroduced basic, generally used, opion pricing model and heir work are considered as a significan added value in financial engineering heory and pracice. However, his model canno be used for he pricing of he barrier opions. Meron (1973) modified classic version of his model for European down and knock-ou call opion. Formulas for eigh ypes of he barrier opions were derived by Rubinsein and Reiner (1991). Moreover, finally, Haug (2007) applied valuaion formulas on all 16 ypes of he European syle of he barrier opions. Based on Haug model (2007) we compue heoreical prices of sandard European barrier call/pu opions, where he following inpu parameers are considered: he acual underlying spo price S 0, he barrier level B, he srike price X, compensaion K, he risk-free ineres rae r (derived from governmen bonds yields U.S. reasury rae, source: 387

3 Monika Harčariková and Michal Šolés: New hedging echniques in energy secor using barrier opions he implied volailiy σ (we used hisorical volailiy), dividend yield q, he ime o mauriy of he opion. All derived relaions of barrier call opions can be found in Iacus (2011). Our calculaions of seleced barrier opions were processed in he saisical program R. Hedging echniques wih using of barrier opions Suppose ha he firm decides o hedge by using New 4 opion sraegy. herefore, we analyse various hedging echniques using given opion sraegy by barrier opions. he used way is creaed by buying n pu opions and a he same ime by selling n call opions and by buying n call opions, where he srike prices should be se as X1 < X 2 < X3. In he analysis of hedging echniques we can consider differen levels of call barrier opions. Where barrier condiions for paricular call barrier opions wih premium c 2S or c 3B are in able 1. For easier undersanding, we will consider he same level of lower D and upper U barriers for used barrier opions. ab. 1. Call barrier opions. ype of call barrier opion Barriers up and knock-in (UI) up and knock-ou (UO) U > X U > S0 down and knock-in (DI) D < X 2 D < X3 D = X 2 D = X 3 down and knock-ou (DO) D > X 2 D > X3 Noes: X srike price, D lower barrier, U upper barrier. D < S 0 Le s consider he selling n pieces of he underlying asse from our porfolio. However, we are afraid of is price flucuaion o he drop in he marke. he income from he sale of he unsecured posiion in he amoun of n pieces a ime is n, where is he underlying spo price a ime. A firs, le us consruc New 4 opion sraegy by buying n down and knock-in pu opions wih a srike price X 1, he premium p 1BDI per opion, he barrier level D and a he same ime by selling he same amoun of n call opions wih he srike price X 2, he premium c 2S per opion and by buying n call opions wih he srike price X 3, he premium c 3B per opion. All relaions for analyical expressions of vanilla and barrier opions used in our analysis are derived and presened by Rusnáková (2012). For simplificaions, we have assumed he same level of lower D (for DI and DO barrier opions) and upper U (for UI and UO barrier opions) barriers for invesigaed hedging echniques in our research analysis. I is valid, ha D < X1and U > X 3, simulaneously D < S0 and U > S 0 should be se, where S 0 is he acual underlying spo price a he ime of issue. In case of DI/DO call opions, he barrier D can be se lower, equal or higher han he srike price. For UI/UO call opions, he barrier U should be se higher han he srike price. Oherwise, i is classical corresponden vanilla call opions. able 2 shows he final selling price of New 4 opion sraegy_1 as a sum he cash marke price and he fuure marke payoff. ab. 2. Final selling prices using New 4 opion sraegy_1. Price scenarios of energy Cash marke Fuure marke payoff fund price ( S ) >D < X1 n n ( p1 BDI c2s + c3b ) ) D < X1 S X1 < X 2 X 2 < X 3 S X 3 Final selling price ( S p + c c ) n 1BDI 2S 3B n ( S X + p c c ) ( X p + c c ) n 1 1BDI 2S + 3B n 1 1BDI 2S 3B n n ( p1 BDI c2s + c3b ) n ( B ) n S n ( X2 + p1bdi c2s + c3b ) n ( X 2 B ) n S ( X X p + c c ) ( S + X X p + c c ) n 2 3 1BDI 2S 3B n 2 3 1BDI 2S 3B In comparison o he classical vanilla opions, he barrier opion premiums are always cheaper for he uncerainy of he barrier opion price in he fuure. In every ime his New 4 opion sraegy is creaed wihou any iniial coss, i.e. he zero-cos sraegy is fulfilled by relaion (1): c n p c (1) ( ) n + 2 S 1BDI 3B his hedging echnique is he bes due o higher selling call opion premium. he higher srike price is, he lower call opion premiums and he higher pu opion premiums are. 388

4 he comparison of cash marke price and final selling price as i is shown by income funcion in able 1, we can conclude: he expecaions of reaching he lower barrier D by underlying asse during he ime o mauriy and S < X 1 a he mauriy dae are desired. For our purpose, he incomes of final selling price are sill consan in amoun of n ( X1 c 3B ). By comparing wih he cash marke price (he unsecured posiion), he incomes will be higher wih he given hedging sraegy if ( + ) n X1 p1bdi c2s c 3B. On he oher side, if he lower barrier is no reached during ime o mauriy and S < X1 or X1 < X 2, he incomes from he final selling price are n ( c 3B ). In his case we hedged a consan profi in amoun of ( ) n c2s p1bdi c 3B. If he underlying asse s spo price a he mauriy dae is a an inerval X2 < X3, hen he incomes of n X 2 c 3B. And he hedged sraegy will be he hedged sraegy will be consan in amoun of ( ) beer han unsecured posiion for case S n ( X p + c c ). 2 1BDI 2S 3B If he price X3, he secured incomes will always be lower han he incomes from unsecured posiion in amoun of ( + + ) n S X X p c c BDI 2S 3B Le us consider wih hedging opion s creaion as buying n down and knock-in pu opions wih a srike price X 1, he premium p 1BDI per opion, he barrier level D and a he same ime by selling he same amoun of n call opions wih he srike price X 2, he premium c 2S per opion and by buying n call barrier opions wih he srike price X 3, where he call barrier opions can be: 2A) up and knock-in call opions wih he barrier level U, i.e. U > X3 and premium c 3SUI per opion. 2B) up and knock-ou call opions wih he barrier level U, i.e. U > X3 and premium c 3SUO per opion. 2C) down and knock-in call opions wih he barrier level D, i.e. D < X3 and premium c 3SDI per opion. 2D) down and knock-ou call opions wih he barrier level D, i.e. D < X3 and premium c 3SDO per opion. he expiraion period has o be same for all used opions. he final selling prices of New 4 opion sraegy_2 for used call barrier opions are presened in able 3. Price scenarios of energy fund S > D S < X 0 ( ) 1 ) D < X 1 X < ab. 3. Final selling prices using New 4 opion sraegy_2. Final selling price_2a Final selling price_2b Final selling price_2c Final selling price_2d p1 BDI BDI BDO X1 p1 BDI X1 X1 BDI X1 BDO 1 S X 2 p1 BDI BDI BDO X < 2 S X 3 X 2 p1 BDI X 2 X 2 BDI X 2 BDO ) U X 3 + X 2 X3 BU X 2 p1bdi - - ) < U X 3 ) D X 3 ) > D X 3 X 2 p1 BDI X 2 X3 BU X 2 X 3 B - - X 2 p1bdi BDI + X 2 BDO + X 2 X3 BD Now, le s creae a hedging hrough Nova 1 sraegy using only barrier opions. he bes possibiliies are by buying n down and knock-in pu opions wih a srike price X 1, he premium p 1BDI per opion, he barrier level D and a he same ime by selling he same amoun of n down and knock-ou call opions wih he srike price X 2, he premium c 2SDO per opion, he barrier level D and by buying n 3A) up and knock-in call opions wih he srike price X 3, he premium c 3BUI per opion and barrier level U. 3B) up and knock-ou call opions wih he srike price X 3, he premium c 3 per opion and barrier level U. he final selling prices of New 4 opion sraegy_3 are presened in able

5 Monika Harčariková and Michal Šolés: New hedging echniques in energy secor using barrier opions ab. 4. Final selling prices using New 4 opion sraegy_3. Price scenarios of energy fund Final selling price_3a Final selling price_3b ) > D < X1 p1bdi DO DO ) D < X1 X1 DO X1 DO X1 < X 2 DO DO ) > D X 2 < X3 ) D X 2 < X3 ) U ) > D X3 ) U ) D X3 ) < U ) > D X3 ) < U ) D X3 X 2 DO X 2 DO DO DO + X 2 X3 DO X 2 DO 2 X3 DO DO X 2 DO + X 2 X3 DO DO 2 X3 DO For righ invesor s decision, i is necessary o choose call barrier opions (UI, UO, DI, DO) depends on he ype of expecaions of underlying asse s developmen. We can predic rapid/slowly increase or rapid/slowly drop of he underlying asse. According o his, he call barrier opions are chosen for he hedging. Some opions secure he final selling price only parially, oher ypes fully. Finally, i may no be a perfec hedge, bu i should remove much of he risk, and he hedger has o make a final decision. Pracical applicaion o he energy secor In his par, our proposed hedging varians are applied in energy secor using exchange-raded funds (EFs), specifically Energy Selec Secor SPDR EF (referred XLE). EFs provide an ineresing way how o inves in energy sources such as oil, gas, coal or elecriciy. XLE fund is chosen due o is size in his caegory. Now, le us suppose ha in he fuure (January 2018) we are planning o sell 100 socks of XLE. We are afraid a downwards price movemen over he period. In his ime, we aim o hedge using above menioned New 4 opion sraegy creaed by vanilla and barrier opions. Using his opion sraegy, we wan o hedge he imum selling price in January raded amoun of shares are 100 pieces, while he zero-cos opion sraegy has o be fulfilled according o relaion (1). Oherwise hedging varians are excluded from our observaions. For easier way, we do no consider any ransacion coss and rading consrains. Nex par shows some hedging varians, which mee he above-saed requiremens. Daa descripion he shares of XLE are raded a USD per share on 13 h informaion are presened in able 5. Sepember Basic key hedging ab. 5. Key hedging informaion. Underlying asse Energy Selec Secor SPDR EF (XLE) Issue dae 13 h Sepember 2016 Issue price USD Mauriy dae 19 h January 2018 Muliplier 1:1 Dividend yield 3.54 % Source: finance.yahoo.com Vanilla opions are in real raded in he marke, where he daase is obained from finance.yahoo.com. European barrier opions are calculaed according o Haug model (2007) in saisical program R wih he inpu parameers as he spo price of he underlying asse (68.38 USD), imes o mauriy (494 days, i.e. hedging period from 13 h Sepember 2016 o 19 h January 2018), ineres rae 0.67 % (gained from reasury.gov), dividend yield 3.54 % (gained from google.com/finance) and hisorical volailiy % (analysed for period 8 h May h Sepember 2016). Seleced European call/pu opion premiums for classic vanilla and barrier opions (barriers 40 and 90 USD) are presened in able

6 ab. 6. European call/pu/call barrier/pu barrier opion premiums wih barrier levels 40 and 90 on 13 h Sepember Implied volailiy Call UI Call UO Call DI Call DO Pu Call Srike Pu DI [%] (90) (90) (40) (40) (40) Noes: Opion premiums are in USD. Source: finance.yahoo.com, own calculaions in saisical program R. he daase for our analysis consiss of 39 vanilla call/pu opions, 128 UI/UO/DI/DO call opions and 12 DI pu opions. he used currency of an underlying asse and opion premiums is in USD. he srike prices of a real vanilla call opions are considered in he range of he barrier levels are seleced by auhors, where for lower barriers of DI/DO call/pu opions in he range of and for upper barriers of UI/UO call opions in he range of , all in muliples of 10. Based on he daase, here are analysed hedging echniques wih he srike prices: 1. X 1 = 50, X 2 = 60 and X 3 = 75, 2. X 1 = 45, X 2 = 58 and X 3 = 73, 3. X 1 = 50, X 2 = 55 and X 3 = 70, and considered lower barrier of he level 30, 40, 50 and 60, and he upper barrier of he level 80, 90, 100 and 110. oally, 2601 hedging varians are proposed and analysed. However, only seleced varians fulfilling zerocos opion sraegy are presened in his paper. Also for easier way o showing resuls, he same barrier for UI/UO opions (he level 90 USD) and DI/DO opions (he level 40 USD) are used. Resuls and discussion Given hedging echniques have secured us a imum accepable selling price of he underlying asse, where he zero-cos opion condiions are preferred. he XLE acual spo price is USD, and we expec XLE price drop in January According o he firs hedging echnique, we will buy 100 DI pu opions wih he srike price 50, he barrier level 40, he premium 1.39 per opion and simulaneously, we will sell 100 call opions wih he srike price 55, he premium per opion and buy 100 call opions wih he srike price 70 and he premium 5.95 per opion. his hedging echnique is he simples of all varian. In his example, able 7 liss he final selling prices in USD for a case of various fuure XLE price scenarios. Price scenarios of XLE ( S ) > 40 S < 50 ( S ) 40 S < 50 ab. 7. Final selling prices using New 4 opion sraegy_1. Final selling price of Final selling price of Cash marke Final XLE selling XLE per share hedging per share price price 100 S < 55 S 55 < 70 S 100 S 100 S , S , S S here is compared cash marke price wih final selling price a various XLE price developmen during he ime o mauriy and a he mauriy dae, where he following conclusions are formulaed: If he spo price of XLE shares during he ime o mauriy does no reach or reaches he barrier 40 USD and is lower han USD, hen he hedged varian 1 is sill beer han he unsecured posiion. Hedged posiion secures consan selling price in he amoun of USD per share for he case of reaching he barrier 40 USD during he ime o mauriy and XLE price lower han 50 USD, and he higher consan selling price USD per share in inerval <55, 70> of XLE spo price a he mauriy dae. Anoher hedging varians are creaed as combinaions of barrier opions. he second varian can be creaed by buying 100 DI pu opions wih he srike price 50, he barrier level 40, he premium 1.39 per opion and a he same ime by selling 100 call opions wih he srike price 55 and he premium per opion and by buying 100 2A) UI call opions wih a srike price 70, he barrier level 90, he premium 5.56 per opion, 391

7 Monika Harčariková and Michal Šolés: New hedging echniques in energy secor using barrier opions 2B) UO call opions wih a srike price 70, he barrier level 90, he premium 0.77 per opion, 2C) DI call opions wih a srike price 70, he barrier level 40, he premium 0.00 per opion, 2D) DO call opions wih a srike price 70, he barrier level 40 and he premium 6.32 per opion. he las (he hird) varian of New 4 opion sraegy creaion is by buying 100 DI pu opions wih he srike price 50, he barrier level 40, he premium 1.39 per opion and a he same ime by selling 100 DO call opions wih he srike price 55, he barrier 40, he premium per opion and by buying 100 3A) UI call opions wih a srike price 70, he barrier level 90, he premium 5.56 per opion. 3B) UO call opions wih a srike price 70, he barrier level 90 and he premium 0.77 per opion. he comparison of all analysed hedging echniques a various XLE price developmen during he ime o mauriy and a he mauriy dae are shown in able 8 wih a provided more deailed illusraion of seleced hedging varians. he resuls from able 8 shows ha he bes hedging echnique is varian 2C securing he highes selling price in he amoun of USD per share. Also, varian 2B is ineresing for hedgers, where he selling price is in he amoun of USD. ab. 8. Comparison of he hedging echniques 2A 2D and 3A 3B. Price scenarios of energy Final selling Final selling Final selling Final selling fund price_2a price_2b price_2c price_2d ) > 40 < , , S ( S ) 40 S < 50 Final selling price_3a Final selling price_3b S , , , , , , , S < S , , S , S < 70 6, , , , ( S ) > S < , , ( S ) S < , ( S ) 90 S , ( S ) < 90 S 70 6, ( S ) 40 S 70 S S , ( S ) > 40 S , ( S ) 90 ( S ) > 40 S S 6, ( S ) 90 ( S ) 40 S , , ( S ) < 90 ( S ) > 40 S , S ( ) < 90 ( S ) 40 S 70 S Graphical comparison of seleced varians is illusraed below in Figure 1. S 200 5,

8 Barrier D was, reached, and barrier U was no reached Barrier D and U were reached Barrier D was no reached, and barrier U was reached Barrier D and U were no reached Fig. 1. Comparison of he seleced analysed hedging echniques. Le us look a able 8 and Figure 1, where he following conclusions are valid: If he XLE spo price during he ime o mauriy drops under lower barrier 20 USD and does no grow above upper barrier 90 USD and is lower han USD a he mauriy dae, hen he varian 2C is sill beer han oherwise hedging varians. Oherwise, he varian 3C is beer. If we compare only varians 2C and 3A, he hedging varian 2C generaes us he beer income up o XLE price of USD. If he boh of barrier levels are reached, he varian 2C is beer up o spo price USD, hen he varian 3C from he inerval <58.52, 74.79>, oherwise he varian 3B. hese hree varians secure he higher selling price han he unsecured posiion. For he hird case, if he lower barrier is no reached and he upper barrier is reached during he ime o mauriy, he varian 2C secures higher income in inerval <40, 70.21>. Oherwise, he unsecured posiion is beer up o he endlessly. In he las case, he boh of barrier levels are no reached during he ime o mauriy; hen he resuls are he same as in he hird case. However, he income from he unsecured posiion is limied up o upper barrier 90 USD. Finally, we will recommend he hedging varian 2C as one way o secure he higher imum selling price for hedgers. All hedging echniques creaions using barrier opions are very ineresing in a price drop. Barrier opion premium is always cheaper han classic vanilla opion premiums according o aleb (1997). In our expeced XLE price scenario, i.e. he lower barrier D is reached during he ime o mauriy, and he XLE spo price a he mauriy dae is lower han 50, he varian 2C is he bes in comparison o ohers, where he imum selling price in he value of USD per share is secured. However, he resuls of our analysis reveal ha he hedger s choice of he barrier opions in he hedging echniques depends on he expecaions of he underlying asse s price developmen. Hedgers can choose beween knock-in and knock-ou barrier opions based on zero-cos opion sraegy. If here is expeced srong drop/increase, he knock-in opions are chosen. In his case, he opion 393

9 Monika Harčariková and Michal Šolés: New hedging echniques in energy secor using barrier opions is acivaed afer reaching he barrier level. Oherwise, if here is expeced only moderaely drop/increase, he knock-ou opions are chosen, when hey are deacivaed afer reaching he barrier level. Finally, all designed hedging varians are beer as he unsecured posiion for our expeced XLE price drop. herefore, he final decision is a hedger s expecaions and willingness o ake risks. If he hedger s expecaions do no mee, hey could gain a loss in comparison o he unsecured posiion. Conclusion High volailiy scares invesors, firms and ohers marke paricipans and fear can impac he marke iself. Due o susained drops in he marke, he risk managemen appears as an ineresing way of solving his problem. he paper aimed o inroduce he hedging analysis agains underlying asse s price drop using New 4 opion sraegy creaed by barrier opions. In he beginning, he paper presened he overview of he lieraure and he research mehodology. o he bes of our knowledge, he only lile research has invesigaed he hedging echniques using barrier opions. he main purpose of his approach is o joinly analyse and compare various ways of New 4 opion sraegy creaion using barrier opions and heir applicaion in he energy secor, i.e. Energy Selec Secor SPDR EF. he primary aim is o choose hedging varians, which mee he requiremens of zero-coss. Our resuls show ha using he barrier opions indicae he more alernaives for hedging, where all varians are analysed. Following he menioned assumpions, he only bes hedging echniques are inroduced in deailed descripion as well. Also, numerical examples on given hedging echniques are presened, where he varian 2C, i.e. creaed wih DI pu, call and DI call opions ensure he highes income a expeced inervals of he XLE shares spo price a he mauriy dae. Ohers varians are no excluded from our observaions because heir income is ineresing oo. However, hey are no presened in he paper. However, he final decision, wha combinaions of he srike prices, he lower and he upper barrier levels and ype of opions, is on he hedger and his expecaions abou underlying asse s price developmen and he willingness o ake a risk. Our resuls can be imporan for praciioners, individual invesors, firms, ohers marke paricipans and he general public. he main conribuion of he paper is o highligh he one ype of derivaive conracs, i.e. barrier opions, whose payoff srucures produces a beer hedging resuls agains downside risk. References Amaiiek, O. F. S., Bálin,., Rešovský, M.: he Shor Call Ladder sraegy and is applicaion in rading and hedging. Aca Monanisica Slovaca, 15(3), , Black, F., Scholes, M.: Pricing of Opions and he Corporae Liabiliies. Journal of Poliical Economy, 81(3), , Brown, G.W.: Managing foreign exchange risk wih derivaives. J. Financial Economics, 60(2-3), , Guay W., Kohari S. P.: How much do firms hedge wih derivaives? Journal of Financial Economics, 70(3), , Hankins, K.W.: How Do Financial Firms Manage Risk? Unraveling he Ineracion of Financial and Operaional Hedging. Managemen Science, 57(12), , Haug, E. G.: he Complee Guide o Opion Pricing Formulas, second ed., Hardcover: McGraw-Hill, Hull, J. C.: Opions, Fuures and Oher Derivaives, Prenice-Hall, New Jersey, Iacus, S.M.: Opion Pricing and Esimaion of Financial Models wih R, firs ed., John Wiley & Sons, Ld., Unied Kingdom, Loss, F.: Opimal Hedging Sraegies and Ineracions beween firms. Journal of economics & managemen sraegy, 21(1) , Meron, R.C.: heory of raional opion pricing. Journal of Economics and Managemen Science, 4(1), , Rubinsein, M., Reiner, E.: Breaking Down he Barriers. Journal of Risk, 4(8), 28-35, Rusnáková, M.: Bariérové opcie a ich využiie na hedging. Dizeračná práca. Košice: echnická univerzia v Košiciach, Ekonomická fakula, Rusnáková, M., Šolés, V.: Long srangle sraegy using barrier opions and is applicaion in hedging. Acual Problems of Economics, 134(8), , Rusnáková, M.: Commodiy price risk managemen using opion sraegies. Agriculural Economics, 61(4), , Šoles, M.: Opčne sraégie a ich využiie na finančných rhoch. Habiliačná práca. Košice: echnická univerzia v Košiciach, Ekonomická fakula,

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