(c) A stock with spot price $ is expected to pay a dividend of D int years. European call and put options on the stock with exercise price X and maturity T>t are trading at prices c and p, respectively. The continuously compounded risk-free rate ist. L Show that the following put-call parity relationship holds: cX-. Den=g45 The stock price is $5. A 12-month at-the-money European put on the stock trades at $0.40 The corresponding call trades at $0.2. The continuously compounded risk-free rate is 15%. Do these prices imply the existence of an arbitrage opportunity? Explain. (d) A house in Sydney has recently sold for $1 million. Renting an equivalent house costs $100,000 per year (paid at year-end). The risk-free rate is 7% (annually compounded). Suppose the house can either increase in price each year by 15% or decrease by 20% before rent is paid out (e. cum-dividend). For example, the price can increase from $1 million to $1.15 million, so that after $100,000 rent is paid out fue ex-dividend the house is worth $1.05 million. i. What is the price of a 2-year at-the money American call option on the house? State any assumptions you need to make. (8 marks) ii. Holding all else constant, how would each of the following affect your answer to part a decrease in the rent an increase in the price of the house an increase in the strike price of the option. In each case, state the direction of the change (e. increase the price, decrease the price, or uncertain) and provide a brief explanation of your reasoning. (6 mark (c) A stock with spot price $ is expected to pay a dividend of D int years. European call and put options on the stock with exercise price X and maturity T>t are trading at prices c and p, respectively. The continuously compounded risk-free rate ist. L Show that the following put-call parity relationship holds: cX-. Den=g45 The stock price is $5. A 12-month at-the-money European put on the stock trades at $0.40 The corresponding call trades at $0.2. The continuously compounded risk-free rate is 15%. Do these prices imply the existence of an arbitrage opportunity? Explain. (d) A house in Sydney has recently sold for $1 million. Renting an equivalent house costs $100,000 per year (paid at year-end). The risk-free rate is 7% (annually compounded). Suppose the house can either increase in price each year by 15% or decrease by 20% before rent is paid out (e. cum-dividend). For example, the price can increase from $1 million to $1.15 million, so that after $100,000 rent is paid out fue ex-dividend the house is worth $1.05 million. i. What is the price of a 2-year at-the money American call option on the house? State any assumptions you need to make. (8 marks) ii. Holding all else constant, how would each of the following affect your answer to part a decrease in the rent an increase in the price of the house an increase in the strike price of the option. In each case, state the direction of the change (e. increase the price, decrease the price, or uncertain) and provide a brief explanation of your reasoning. (6 mark
