Problem $3$

You are given the following information regarding on a stock:

One year from now the stock will sell for either $40$ or $55.$

The stock pays dividends continuously at a rate proportional to its price, with

a dividend yield of $10\%.$

The continuously compounded risk$-$free rate is $r=5\%.$

The risk$-$neutral probability of an up move is $0\mathrm{.}6.$

$($A$)$ What is the current stock price?

$($B$)$ What should be the price of an at$-$the$-$money European call?

$($C$)$ Using the put$-$call parity, what should be the price of the corresponding Euro$-$

pean put?

$($D$)$ Calculate the cost of implementing a one$-$year reversed $($i$.$e$.,$ short$)$ straddle

constructed with at$-$the$-$money options?