An individual entire wealth is from one stock. The current value of the stock is $55, and the individual owns one million shares. This individual purchased puts on the stock with an exercise price of $52 to protect his wealth. He bought enough puts to protect his entire holdings of this stock. The expiration of the put is 4 years. Immediately after buying the puts he was appointed to a 4-year government position and was told that if want to stay in the government position his return over the next two years must exactly equal the risk-free rate. The risk-free rate is 10%. You have been asked to construct a spread that will provide the investor with a return over the next two years that exactly equals the return from the risk-free return on his stock holdings. You can only buy the minimum number of needed derivatives given the investors current holdings. A speculator is willing to sell or buy from you any option with any strike price with a two- year exercise.

Suppose the price of a stock is $28, the risk-free interest rate is 10%, and the price of a European call option on the stock with a one-year expiration and a strike price of $26 is $2.

Part4.

Part a.

What is the arbitrage opportunity if the stock does not pay dividends?

c max(S0 Ke^rT, 0)

2 max(28 26e ^.10(1), 0)

24.474

Needs to sell in the short position

The arbitrage opportunity is 4.474-2=$2.47

Part b.

What is the arbitrage opportunity if the stock pays $2 dividends per year? The dividends are paid at the end of the year.

c S0-D-Ke^-rT

228 2-26e ^.10(1)

22.474

Needs to sell in the short position

2.474-2=$0.47

Part 5.

Assume that the stock does not pay dividends.

Part a.

What are the arbitrage possibilities for the stock in Part 4 of this assignment when p = 3.25?

Part b.

What are the arbitrage possibilities for the stock in Part 4 of this assignment when p = 1?

Please answer 5 a and b