Question

2. Using our market assumptions (particularly the assumption of "no arbitrage") prove that the value f(c) of a long futures/forward contract for an asset with price S(t), delivery date T, and delivery price K, satisfies the equation f(t) = S(t) - Ke- (7-6).

Answer 1

for Passible Synamics of thu Basis fituses Contradt: Price fu hures Price Basis Spet Price Time the pecofion The assemption that interest afes coe nat may time nown and Constant over be Too Severe fot Shoat tem contracts

ard Contrart tine t that Callsor delivy of /Onit of He Commodity ot time T fo) Price of a futures contadt at diliveary The Price of a at The that calls at time t Leel time Ts Fa) The basis at dato 6(0) 50)-f(0) the b0)uhure Valuing forwasd Contods tra des who at Consides a ongpostion in Joreward Conthat, wth ilment dat TRecall that tho's Pce i the Fime 0 enters into o a Stablished do Ahat the value d Ze1o. Conthart i

at time 0 of this Contract. Tharn Vo O Oves time the valuu at this conract eoi) change. Let be i value Coatraet whre os t T the ddilmant dati Tthe alue the be the differuna beteun onad the time Zero et Yo . contret wl) and Scttlemant Price, That i ADe livery et at Pric Po), Snu the Spo Price is s), the valus must be the dnce th Contradt

i the underly ing Commo dity provida Shong chuges Ceuy change just efu the opportunty cost 0ends an d FOCO))+ ALCoT) S0)RT (aah Hows and enure no then He T the tinme to delivey, Tis mansured 7 other than dlay, then the be espresred in years abeu Jorwerd Price Can Folo)- slo)e T as Stovege charges inurred are Cantinuaualy and a Pop otional to the the commodity hen the tcassy Price incuard frem ast T-t and the Jati Con FO (O)=SA-KET

i the underly ing Commo dity provida Shong chuges Ceuy change just efu the opportunty cost 0ends an d FOCO))+ ALCoT) S0)RT (aah Hows and enure no then He T the tinme to delivey, Tis mansured 7 other than dlay, then the be espresred in years abeu Jorwerd Price Can Folo)- slo)e T as Stovege charges inurred are Cantinuaualy and a Pop otional to the the commodity hen the tcassy Price incuard frem ast T-t and the Jati Con FO (O)=SA-KET

finally,if the undulying commodity Con tinuous dividlund idld at Pays calry Tale T the nt cost Tate educe d rom to t) equahior Po Co)- So)-te (T-t) to at the eguation ie, henu it prored -Y