stock S currently sells for $120. After one year it price will either increase to $132 or fall to $108. The annual risk free interest rate is 5%.

1. calculate the current value of an at-the-money European call option on stock S maturing in one year.
2. Now assume that the volatility of stock S increases so that if the stock price increases, it will still increase by 10% but when it falls, it will fall by more than 10%. Everything includes the maturity date, current stock price, exercise price, and interest rate remains the same. Show mathematically the the current value of the call option is higher than the value you get from question 1.