Problem FORW$-39$H

It is given that

$S(0)=$$$100.,$ This is the share price today $("$time $0")$ of XYZ stock.

$=5\%p.a.$ This $is$ the growth rate $of$ the number $of$ shares

under reinvestment $of$ dividends $(usinga365-$day year$).$

compounding like in

example FORW$-62$J$.$

$F(0,T)=$$$101.$ This is the forward price for delivery of $1$ share $220$ days

from now $("$time $T").$

$($a$)$ Show how synthetic lending over $220$ days can be obtained. You need to hold shares

$($long or short$)$ and one zero$-$downpayment forward contract, long or short.

$($b$)$ What is the implied annual interest rate, expressed as a continuously$-$compounded

rate $($using a $365$ day year$)?$

$($c$)$ Show how synthetic lending over $220$ days can be obtained. You need to start with a

$($long or short$)$ position in $1$ share of stock plus a $($long or short$)$ position in zero$-$

downpayment forward contracts.