The price for the January 2020 XYZ call option with exercise price of $105 is $10.98 as of July 2019.

Use the Black-Scholes option pricing formula to check the accuracy of this pricing. Price the option as if it were July 2019 (so 6 month maturity). Use the following inputs: P = 100, K = 105, interest rate (APR) = 5%, t = 0.5 year, and sigma = 39% for the continuously compounded annual return (0.39 in decimal form). Does the Black-Scholes formula suggest a higher or lower price for this option?

Relative to the valuation, using the Black-Scholes formula, determine the call option price for the following change of assumptions:

The stock price suddenly rises to $110. Explain the economic reason for this change in value.

The exercise price changes to $110. Explain the economic reason for this change in value.

The annual interest rate falls to 4%. Explain the economic reason for this change in value.

The maturity of the call increases to 1 year. Explain the economic reason for this change in value.

The sigma changes to 30%. Explain the economic reason for this change in value.