# Derivatives and Black-Scholes Model

1. David is interested in purchasing a European call option on Divine Vines, Inc., a non-dividend-paying common stock, with a strike price of $30 and three months until expiration. Divine's stock is currently trading at $60 per share, and the annual variance of its continuously compounded returns is 0.36. Treasury bills that mature in three months yield a continuously compounded interest rate of 3 percent per annum.

a. Use the Black-Scholes model to calculate the price of the call option that David is interested in buying

b. What does put-call parity imply about the price of a put with a strike price of $30 and three months until expiration?

2. An investor is said to take a position in a "collar" if he buys the assets, buys an out-of-the-money put option on the asset, and sells an out-of-money call option on the asset. The two options should have the same time to expiration. Suppose Marie wishes to purchase a collar on Hollywood, Inc., a non-dividend-paying common stock, with six months until expiration. She would like the put to have a strike price of $50 and the call to have a strike price of $120.00. The current price of Hollywood's stock is $80 per share. Marie can borrow and lend at the continuously compounded risk-free rate of 10 percent per annum, and the annual variance of Hollywood's continuously compounded returns is 0.25. Use the Black-Scholes model to calculate the total cost of the collar that Marie is interested in buying

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#### Solution Summary

This solution shows step-by-step calculations and justifications using the Black-Scholes Model to determine the price of call option, put-call parity impact, and the total cost of the dollar.