A stock price is currently $$50.$ Over each of the next two $3-$month periods

it is expected to go up by $6\%$ or down by $5\%.$ The risk$-$free interest rate

is $5\%$ per annum with continuous compounding. What is the value of a $6$

$-$month European call option with a strike price of $$51?$ Use risk$-$neutral

expectation.