$1.$ A stock price is currently $$50.$ It is known that at the end of two months it will be either $$53$ or $$48.$

The risk$-$free interest rate is $10\%$ per annum with continuous compounding. What is the value of a

two$-$month European call option with a strike price of $$49?$ What is the delta $(\backslash$Delta $)$ of the option?

$2.$ In the question above, if the stock price increases to $51$ and in two$-$months the stock will be either

$6\%$ higher or $4\%$ lower, all else being equal, what is the value of the call?