WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be eiher buying he underlying asse or selling he underlying asse. In he world of oions he underlying asse, generally, is a comany share (sock oion) or a foreign currency (currency oion). Thus, he holder of a sock oion reserves he righ o eiher buy or sell a aricular share, he underlying asse. Likewise he holder of a currency oion reserves he righ o buy or sell a foreign currency, he underlying asse. The righ also secifies he rice a which he asse can be bough or sold. This is called he Srike rice of he oion. I also secifies he dae ill when he righ can be exercised and i is called he Mauriy dae or Exiry dae. The rice aid o buy he righ is called he remium or simly, he rice of he oion. obligaion o buy i. The holder has o ay a rice (remium) o buy his righ. In he same manner an invesor can buy he righ o sell an underlying asse, say a comany share, a a cerain rice by a aricular dae in he fuure by aying some remium. Such an oion is called a u oion. A u oion gives he holder he righ o sell he underlying asse a a cerain rice a a cerain fuure dae wihou an obligaion o sell i. The holder has o ay a rice (remium) o buy his righ. Having made i clear ha he holder of an oion has he righ o eiher buy or sell he underlying asse bu no obligaion o do so, i is hen necessary o lay down he circumsances under which he would exercise he righ and when he would no. The assumion is ha he invesor would exercise his righ if i is rofiable o him and ha he would le go his righ if by exercising i he would incur a loss. An invesor can buy he righ o buy a When would a Call oion be exercised? aricular share a a aricular rice by a aricular dae by aying some The holder of a call oion has he righ o remium. Such an oion is called a Call buy an underlying asse bu no obligaion. oion. Le us ake he case of an invesor who has bough a call oion where he underlying A Call oion gives he holder he righ o asse is a comany share. The siuaion buy he underlying asse a a cerain can be exlained bes wih a diagram. rice a a cerain fuure dae wihou an SIBM, une 2010 30
S Fig. 1: rofi from a Call Oion = rofi; S = Terminal Sock rice; = remium; = Srike rice Referring o he Fig 1 we can make following buy he oion. saemens; The holder of he call oion has aid a Siuaion 2: Sock rice Rs. 40 rice '' o buy he oion i.e. o buy he The holder will no exercise his righ righ o buy he underlying asse (share) because by exercising his righ he will be a some fuure dae (exiry dae). aying Rs. 50 for he share which hen The rice a which he share will be could be sold in he sock marke for Rs. 40 bough is ''; he srike rice. hereby incurring a oal loss of Rs. 15 (Rs. The x-axis gives he sock rice in he 10 on he exercising of oion and Rs. 5 on sock marke. he remium.) The y-axis gives he rofi made by he By no exercising he righ he holder will holder. incur a loss of Rs. 5 only which is on accoun of he remium aid. Now le us ake a numerical examle. Imagine ha he invesor (he holder of he Siuaion 3: Sock rice Rs. 53 oion) has aid Rs. 5 for he call oion The holder can exercise his righ and buy where he srike rice is Rs. 50. he share a Rs. 50 Sell he share in he sock marke for Rs. 53 Now le us imagine following siuaions: and make a rofi of Rs. 3 on he share. This is done o reduce he loss incurred on Siuaion 1: Sock rice Rs. 60 aying he remium. The oal loss will The holder can exercise his righ o buy now be Rs. 2. he share a Rs. 50. If he had no exercised his righ he loss Sell he share in he sock marke for Rs. would have been Rs. 5. 60 ocke he rofi of Rs. 5 afer deducing The hree siuaions menioned above give us he remium aid in he beginning o an imoran rule for he Call oion. I is ha: SIBM, une 2010 31
A Call oion mus be exercised if he sock rice exceeds he srike rice. This is so because when he sock rice exceeds he srike rice i will eiher lead o a ne osiive cash flow if he sock rice exceeds he sum of srike rice and he remium aid. If he sock rice exceeds only he srike rice bu no he sum of he srike rice and he remium aid i will a leas reduce he negaive cash flow. When would a u oion be exercised? The holder of a u oion has he righ o sell an underlying asse bu no obligaion. Le us ake he case of an invesor who has bough a u oion where he underlying asse is a comany share. The siuaion can be exlained bes wih a diagram. S Fig. 2: rofi from a u Oion = rofi; S = Terminal Sock rice; = remium; = Srike rice Referring o he Fig 2 we can make following saemens; The holder of he u oion has aid a rice '' o buy he oion i.e. o buy he righ o sell he underlying asse (share) a some fuure dae (exiry dae). The rice a which he share will be sold is ''; he srike rice. The x-axis gives he sock rice in he sock marke. The y-axis gives he rofi made by he holder. Now le us ake a numerical examle. Imagine ha he invesor (he holder of he oion) has aid Rs. 5 for he u oion and ha he srike rice is Rs. 50. Now le us imagine following siuaions: Siuaion 1: Sock rice Rs. 40 The holder can exercise his righ o sell he share a Rs. 50. Buy he share back in he sock marke for Rs. 40 ocke he rofi of Rs. 5 afer deducing he remium aid in he beginning o buy SIBM, une 2010 32
he oion. Siuaion 2: Sock rice Rs. 60 The holder will no exercise his righ because by exercising his righ he will be buying he share a Rs. 60 in he sock marke and selling i a Rs. 50 while exercising he oion, hereby incurring a oal loss of Rs. 15 (Rs. 10 on he exercising he oion and Rs. 5 on he remium.) By no exercising he righ he holder will incur a loss of Rs. 5 only which is on accoun of he remium aid. remium aid i will a leas reduce he negaive cash flow. Two yes of oions on he basis of when hey can be exercised If an oion, eiher Call or u, can be exercised on any day before he exiry dae i is called an American oion. If an oion, eiher Call or u, can be exercised only on he dae of exiry, i is called a Euroean oion. Thus on he above basis we have four yes: An American Call oion An American u oion A Euroean Call oion Siuaion 3: Sock rice Rs. 47 The holder can exercise his righ by buying he share in he marke for Rs. 47 and selling i a Rs. 50 as ar of he A Euroean u oion oion conrac. He will hen make a rofi of Rs. 3 on he share. This is done o reduce he loss incurred on aying he remium. The oal loss will now be Rs. 2. If he had no exercised his righ he loss would have been Rs. 5. The hree siuaions menioned above give us an imoran rule for he u oion. I is ha: A u oion mus be exercised if he sock rice is less han he srike rice. This is so because when he sock rice is less han he srike rice i will eiher lead o a ne osiive cash flow if he sock rice is less han he difference beween he srike rice and he remium aid. If he sock rice is only less han he srike rice bu no he difference of srike rice and he Though he above argumens for Call and u oions are he same for boh yes he difference becomes aaren when cerain oher roeries are sudied. These will be aken u in fuure chaers. The wo sides of an oion conrac There are wo sides o every oion conrac. On one side is he invesor who has aken he long osiion (i.e. has bough he oion). On he oher side is he invesor who has aken a shor osiion (i.e. has sold an oion or 'wrien' an oion.) The above saemen needs furher clarificaion. An invesor, when he buys a Call oion, buys he righ o buy he underlying asse bu his righ has no meaning unless here is someone who agrees o sell he underlying asse if he firs invesor decides o SIBM, une 2010 33
exercise his righ. Similarly an invesor, when he buys a u oion, buys he righ o sell he underlying asse bu his righ has no meaning unless here is anoher invesor who agrees o buy he underlying asse if he firs invesor decides o exercise his righ. In oion rading following erms are used: Invesor who buys an oion is said o have a Long osiion and he is called he buyer or he holder. Invesor who sells an oion is said o have a Shor osiion and he is called he seller or he wrier. This gives rise o four osiions which are as follows: A long osiion in a Call oion: Long Call (osiion of he buyer of a Call oion) A shor osiion in a Call oion: Shor Call (osiion of he wrier of a Call oion) A long osiion in a u oion: Long u (osiion of he buyer of a u oion) A shor osiion in a u oion: Shor u (osiion of he wrier of a u oion) Figures 1 and 2 show he rofi in a long call and a long u resecively. Fig. 3 shows he rofi from wriing a Call oion (a shor call). S Fig. 3: rofi from wriing a Call Oion = rofi; S = Terminal Sock rice; = remium; = Srike rice The wrier of a Call oion has sold he righ Call oions and refer Fig 1.) o he holder o buy he underlying asse bu When holder exercises he righ he he holder has no obligaion o do so. wrier will have o rocure a share from Consider following oins: he marke a he sock rice and sell i The holder will exercise he righ only o he holder a he srike rice. The if he sock rice exceeds he srike wrier will incur a loss equal o he rice (recall he argumens made for rofi of he holder. SIBM, une 2010 34
If he holder does no exercise his righ hen he wrier kees he remium aid. In his case his rofi (he remium received) is equal o he loss of he holder (he remium aid). In he same manner we can examine he case of a shor u. The wrier of a u oion has a shor u osiion and has given he righ o sell he underlying asse o he holder of he u oion (long u osiion). Fig. 4 shows he rofi from a shor u osiion. S Fig. 4: rofi from wriing a u Oion = rofi; S = Terminal Sock rice; = remium; = Srike rice The wrier of a u oion has sold he righ I is ofen useful o characerize he oion o he holder o sell he underlying asse bu osiions in erms of he erminal sock rice he holder has no obligaion o do so. (S ) or he ayoff o he invesor on mauriy. Consider following oins: The iniial cos (remium) is hen no included The holder will exercise he righ only in he calculaion. If, hen, he srike rice is if he sock rice is less han he srike and he erminal sock rice is S hen ayoffs rice (recall he argumens made for for he four osiions are as given below: u oions and refer Fig 2.) When holder exercises he righ he For long call osiion: max (S, 0). This wrier will have o buy he share from means ha he oion will be exercised if S > he holder a he srike rice and and will no be exercised if S < or S =. resell i in he marke a a lower rice. The wrier will incur a loss equal o For shor call osiion: min ( S, 0); he rofi of he holder. If he holder does no exercise his For long u osiion: max ( S, 0). This righ hen he wrier kees he means ha he oion will be exercised if S < remium aid. In his case his rofi (he remium received) is equal o he loss of he holder (he remium aid). and will no be exercised if S > or S = For shor u osiion: min (S, 0) SIBM, une 2010 35
We mus undersand ha an oion once bough or sold (wrien) can no be raded again. However, we can neuralize he osiion by going ino he oosie direcion. So he holder of an oion conrac can neuralize or offse his osiion by wriing an oion conrac or vice versa. Thus a long call can be neuralized by a shor call and vice versa and a long u can be neuralized by a shor u and vice versa. I is very imoran o remember ha a Call oion canno be neuralized by a u oion. Imagine ha an invesor has bough a Call oion wih a srike rice of Rs. 50 by aying a remium of Rs. 5 and he wishes o cancel ou his osiion. To cancel ou he will now have o wrie he same Call oion. Now, he srike rice may have remained he same bu he remium may have changed. Since we know ha he rofi of a holder is he same as he loss of he wrier our invesor's gain and loss will cancel ou. However he may eiher make a small rofi or loss on he differen rices aid and received for buying and wriing a differen ime. Same argumen is alicable o u oions. So, if we do no consider he remium and if he sock rice is higher han he srike rice he gain in long call will be he loss in shor call. If he oion is no exercised hen i is zero. Noe ha he remiums aid a differen imes are overlooked in his argumen. When invesors offse heir osiions i affecs wha is ermed 'Oen Ineres'. Oen Ineres is he number of ousanding osiions in a aricular oion of eiher he long or he shor ye. If, when an oion conrac is raded neiher invesor is offseing his exising osiion hen he Oen Ineres increases by one conrac. If one invesor is offseing an exising osiion bu he oher is no hen he Oen Ineres remains he same. If boh are offseing heir exising osiions hen he Oen Ineres goes down by one conrac. SIBM, une 2010 36