Derivatives, Study Guide for Quiz 1
Derivatives, Study Guide for Quiz 1 BU.232.710.W4.SP16
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This 2 page Study Guide was uploaded by Kwan on Tuesday January 26, 2016. The Study Guide belongs to BU.232.710.W4.SP16 at Johns Hopkins University taught by Federico Bandi in Spring 2016. Since its upload, it has received 49 views. For similar materials see Derivatives in Finance at Johns Hopkins University.
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Date Created: 01/26/16
! Q1! The$spot$price$of$oil$is$$80$per$barrel$and$the$cost$of$storing$a$barrel$of$oil$for$one$year$is$$3 $to$be$paid$in$ two$semi:annual$installments$ at$the$beginning$of$each$6 :month$period.$The$risk:free$interest$rate$is$5%$ per$annum,$continuously$compounded.$What$is$a$meaningful $upper$bound$for$the$one :year$futures$ price$of$oil?$$ ! ! Q2! Today$the$spot$exchange$rate$between$the$Swiss$ Franc$and$the$U.S.$dollar$is$1.07 $($$per$Franc).$Assume$ that$ interest$ rates$ in$ the$ U.S.$ and$ Switzerland$ are$ 0.25%$ and$ 0.1%$ per$ annum,$ respectively,$ with$ continuous$compounding.$$ (a)! What$is$the$three :month$forward$exchange$rate$of$the$Swiss$Franc? $ (b)! If$the$ three:month$ forward$ exchange$ rate$were$1.06$($$per$Franc),$there$would$be$an$arbitrage$ available.$Please$provide$the$details$ of$a$suitable$arbitrage$strategy .$ $ ! ! A1:!The!present!value!of!the!storage!cost !per!barrel!is!$1.5+$1.5e =0.05×0.=!$2.963.!! The!upper!bound!for!the!one=year!futures!price!is!($80+$2.963)e 0.05×1=!$87.21.! A2:! (0.0025−0.001)×0.25! (a)!The!no=arbitrage!three=month!forward!exchange!rate!is!1.07e =!1.0704.!! (b)! (1)! Borrow!X!Swiss!Francs!at!0.1%!per!annum!(for!three!months),!(2)!convert!the!Francs!into!1.07X! US!$!to!be!invested!at!0.25%!per!annum !(for!three=month),!and!(3)!enter!into!a!three=month!forward! contract!to!buy!Xe (0.001)×0.!Swiss!Francs!at!1.06!(i.e.,!the!forward!rate).$ In!three!month,!the!arbitrageur!has!1.07Xe 0.0025×0.25=!1.070669X! US!$!from!the!investment.!Of!this,! 0.001×0.25! 0.001×0.25! ! 1.06Xe =! 1.060265X! US!$! are! used! to! purchase! ! Xe ! Francs! under! the! terms! of! the! forward! contract! and! re=pay! the! initial! loan.! The! arbitrage! profit! is,! theref ore,! ! ! (1.070669! –! 1.060265)*X. !!!!!!! !
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