A financial company wants to sell to a customer a put option on 1,000 shares of Apple stock with a strike price of $120 per share and a maturity of 6 months. The company believes that Apple does not pay any dividend in the lifetime of the option, and that the price of Apple stock follows a geometric Brownian motion with volatility 30%. The current price of Apple's stock is $124 and the continuously compounded risk-free rate is 3%. (a) Find the Black-Scholes price of the put option. (b) Suppose the company wants to dynamically hedge the risk arising from selling the option. How many shares of Apple stock does the company have to hold or short-sell at the beginning? (c) Suppose that after 1 month, Apple stock price becomes $120. How many shares of Apple stock should the company hold or short-sell then? A financial company wants to sell to a customer a put option on 1,000 shares of Apple stock with a strike price of $120 per share and a maturity of 6 months. The company believes that Apple does not pay any dividend in the lifetime of the option, and that the price of Apple stock follows a geometric Brownian motion with volatility 30%. The current price of Apple's stock is $124 and the continuously compounded risk-free rate is 3%. (a) Find the Black-Scholes price of the put option. (b) Suppose the company wants to dynamically hedge the risk arising from selling the option. How many shares of Apple stock does the company have to hold or short-sell at the beginning? (c) Suppose that after 1 month, Apple stock price becomes $120. How many shares of Apple stock should the company hold or short-sell then