Derivatives. Forwards and Futures. Forward. Futures. Options. Initial Cost

Transcription

1 Derivaives Forwards and Fuures A derivaive securiy is a securiy whose value depends on he values of oher more basic underlying variables. Forward The mos common derivaive securiies are forward, fuures and opions. A forward conrac is an agreemen o buy or sell an asse a a fixed fuure ime for a predeermined price. Fuures A fuures conrac, like a forward conrac, is an agreemen beween wo paries o buy or sell an asse a a cerain ime in he fuure for a pre-specified price. Unlike forward conracs, fuures conracs are raded on an exchange and hey are sandardized. Opions There are wo basic ypes of opions. A call opion gives he holder he righ (bu no he obligaion) o buy he underlying asse by (or a) a cerain dae for a cerain price. A pu opion gives he holder he righ (no he obligaion) o sell he underlying asse by (or a) a cerain dae for a cerain price. Iniial Cos Forward and fuures cos o ener. For opions, you have o pay somehing up fron, which is called he premium. 1

2 Why Fuures and Forwards? The uncerainy faced by he oil producers is he fuure. The uncerainy faced by he oil consumers is also he fuure. The oil producers and oil consumers can eliminae heir risks by enering a forward or fuures conrac, which calls for he oil producers o deliver oil o oil consumers for a predeermined price a a fuure dae. Key Differences Beween Fuures and Forwards Fuures Secondary rading - liquidiy Marked o marke or pay-as-you-go Sandardized conrac unis Clearinghouse warrans performance Key Terms for Fuures Conracs Fuures price Agreed-upon price a mauriy F 0. Long posiion Agree o purchase. Shor posiion Agree o sell. Profis on posiions a mauriy Long: spo minus original fuures price (S T F 0 ) Shor: original fuures price minus spo (F 0 S T ) Types of Fuures Conracs Agriculural commodiies Meals and minerals (including energy conracs) Foreign currencies Financial fuures Ineres rae fuures Sock index fuures Trading Sraegies Speculaion Shor You believe price will Long - You believe price will Hedging Long hedge - Proecing agains a in price Shor hedge - Proecing agains a in price Suppose ha you have a long posiion in gold fuures wih a delivery dae in hree monhs. The delivery price is $300. Wha is your payoff if he gold price in hree monhs is a) $250 b) $300 c) $350 2

3 If he ending gold price is $250 If he ending gold price is $300 So when you long a fuures conrac, your payoff is higher he higher he fuure price is. If he ending gold price is $350 Payoff from Forwards & Fuures Payoff= S T F 0 Suppose ha you agree o sell an ounce of gold in hree monhs for $300. If he ending gold price is $250 If he ending gold price is $300 0 F 0 Long Posiion S T If he ending gold price is $350 So when you shor a fuures conrac, your payoff is higher he lower he fuure price is. Payoff from Forwards & Fuures Payoff= F 0 -S T 0 F 0 S T Shor Posiion 3

4 A Zero-Sum Game A Zero-Sum Game You may have noiced ha wha he long posiion wins is exacly wha he shor posiion loses and vice versa. (S T -F 0 ) + (F 0 -S T ) = 0 This is a zero-sum game. Payoff 0 Long Posiion Payoff= S T -F 0 Sum=0 F 0 Shor Posiion S T Payoff= F 0 -S T Fuures Price How do we deermine he fuures price? Is he fuures price he expeced fuure price? Should he fuures price be close o he spo price? I urns ou we can deermine he fuures price of many conracs by imposing he no arbirage condiion. Fuures Prices There are wo ways o acquire an asse for some dae in he fuure: Purchase i now and sore i. Take a long posiion in fuures. The Spo-Fuures Pariy Theorem says ha hese wo sraegies should have he same marke deermined coss. Pariy Example I Consider gold. I has basically no sorage coss Sraegy A: Buy he gold and hold i for a year. Sraegy B: Pu funds aside oday and buy a gold fuures conrac wih one year o mauriy. $400 is he curren gold price, S T is he gold price a T, which is of course unknown a. $440 is he fuures price. 10% is he risk free rae. Example I Sraegy A Acion Cash Flow a Cash Flow a T Buy gold Sraegy B Acion Cash Flow a Cash Flow a T Long gold fuures Inves $400 in TBill Toal For B Sraegy A and B have he same cash flow a and T. The key here is ha he fuures price $440 is exacly $400 (1+10%). 4

5 Pariy Example II Consider gold. I has basically no sorage coss Sraegy A: Buy he gold and hold i unil ime T. Sraegy B: Pu funds aside oday and buy a gold fuures conrac. S is he curren gold price, S T is he gold price a T, which is of course unknown a. F is he fuures price. r f is he risk free rae. Example II Sraegy A Acion Cash Flow a Cash Flow a T Buy gold -S ST Sraegy B Acion Cash Flow a Cash Flow a T Long gold fuures 0 ST F Inves F/(1+rf ) T- in TBill -F/(1+rf ) T- F Toal For B -F/(1+rf ) T- ST Pariy Theorem Sraegy A and Sraegy B give idenical payoffs a T, regardless wha he fuure gold price is. Hence hey should cos he same a. S = F = F T ( 1+ rf ) T S ( 1+ r ) f Price of Fuures wih Pariy ( ) T F = S 1+ r f This formula is also called he cos of carry formula as he fuures price is he spo price plus he cos of carry he gold. Noe ha for gold, he fuures price is always greaer han he spo price regardless of your expeced fuure gold price. Arbirage Wha if he fuures price ($420) is less han wha he cos of carry formula gives ($440)? Shor gold Long gold fuures Inves F/(1+rf ) T- in TBill Toal Arbirage Wha if he fuures price is less han wha he cos of carry formula gives? Acion Cash Flow a Cash Flow a T Shor gold S -ST Long gold fuures 0 ST F Inves F/(1+rf ) T- in TBill -F/(1+rf ) T- F Toal S-F/(1+rf ) T- 0 5

6 Fuures Pricing The cos of carry formula does no work for agriculure producs and many commodiies. Perishable High sorage coss seasonaliy 6