Q$.6(10$ points$)$

Consider a three date environment, $t=0,1,2,t=0$ is now, $t=1$ is one year from now and $t=2$ is

two years from now.

The price of Asset X at each date is presented in the table below.

The cash flows above are all known for sure at $t=0$ without uncertainty.

Investors can borrow and lend for one year from $t=0$ to $t=1,$ and from $t=1$ to $t=2,$ but cannot

directly borrow nor lend for two years from $t=0$ to $t=2.$

The annual risk free interest rate that investors can borrow and lend:

$($i$)$ from $t=0$ to $t=1$ is $10\%($cc$).$

$($ii$)$ from $t=1$ to $t=2$ is $12\%($cc$).$

The rates above are known for sure at $t=0.$

Does an arbitrage opportunity exist? If no$,$ explain why not. If yes, specify the arbitrage strategy

and verify that it is any arbitrage strategy.