onsider a market defined by the initial price vector and payoff matrix

S $=$

$[95\mathrm{.}00$

$76\mathrm{.}50$

$]$

$,$ D $=$

$[100100100$

$6090120$

$]$

$($a$)$ Verify that any vector of the form

$$

$$

$0\mathrm{.}30+$ x

$0\mathrm{.}652$x

x

$$

$,$ x in R

is a state price vector.

$($b$)$ Is the market free from arbitrage?

$($c$)$ Which values of x are consistent with risk aversion?

$($d$)$ Consider a call option on the stock that is struck at $$100.$ What are the minimum

and maximum arbitrage$-$free prices for this option?