European plain vanilla call options with strikes 30 and 35 on the same non- dividend paying asset with spot price $ 35 are trading for $ 11.50 and $ 7, respectively. Does arbitrage exist, and if so, how do you take advantage of it?
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European plain vanilla call options with strikes 30 and 35 on the same non- dividend paying asset with spot price $ 35 are trading for $ 11.50 and $ 7, respectively. Does arbitrage exist, and if so, how do you take advantage of it?
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- 1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?The price of a one-year European call option on a non-dividend-paying stock is $6. The price of a one-year European put option on the same stock is $1. The strike price for both the call and the put is $50. The stock price today is $51 and the continuously compounded risk-free rate is 6% per annum. Use the put-call parity to suggest an arbitrage strategy to earn risk-free profits. Specifically, describe the various short and long positions you need to take in the underlying assets and show all the relevant cash flows from this strategy at both origination and expiration. Use a TABLE to show all of your work.
- Suppose there is also a 1-year European put option on the same stock as in Question 3 with exercise price $30. The current stock price is also $25 and the stock price, in 1 year, will be either $35 (up by 40%) or $20 (down by 20%). The interest rate is 8%. This stock does not pay dividend. What is the value of the put option? Please use risk neutral probability method and assume discrete discounting. (2) What is put-call parity in option pricing? What needs to be true in order for put-call parity to hold?In this problem, we derive the put-call parity relationship for European options on stocks that pay dividends before option expiration. For simplicity, assume that the stock makes one dividend payment of $D per share at the expiration date of the option.a. What is the value of a stock-plus-put position on the expiration date of the option?b. Now consider a portfolio comprising a call option and a zero-coupon bond with the same maturity date as the option and with face value (X + D). What is the value of this portfolio on the option expiration date? You should find that its value equals that of the stock-plus-put portfolio regardless of the stock price.c. What is the cost of establishing the two portfolios in parts (a) and (b)? Equate the costs of these portfolios, and you will derive the put-call parity relationship.Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held untilmaturity. Under what circumstances will the holder of the option make a profit? Underwhat circumstances will the option be exercised? Draw a diagram illustrating how the profitfrom a long position in the option depends on the stock price at maturity of the option. Suppose that a European put option to sell a share for $60 costs $8 and is held untilmaturity. Under what circumstances will the seller of the option (the party with the shortposition) make a profit? Under what circumstances will the option be exercised? Draw adiagram illustrating how the profit from a short position in the option depends on thestock price at maturity of the option.
- In a financial market a stock is traded with a current price of 50. Next period the price of the stock can either go up with 30 per cent or go down with 25 per cent. Risk-free debt is available with an interest rate of 8 per cent. Also traded are European options on the stock with an exercise price of 45 and a time to maturity of 1, i.e. they mature next period. Does put-call parity hold? Explain.1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.77. and put option value is 1.99 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. explainc. What would be the extent of your profit in (a) depend on? explain1. Suppose you have the following information concerning a particular options.Stock price, S = RM 21Exercise price, K = RM 20Interest rate, r = 0.08Maturity, T = 180 days = 0.5Standard deviation, � = 0.5 The Call option value is 3.7739. and put option value is 1.8101 Suppose a European put options has a price higher than that dictated by the putcall parity. a. Outline the appropriate arbitrage strategy and graphically prove that the arbitrage is riskless. Note: Use the call and put options prices above)b. Name the options/stock strategy used to proof the put-call parity. c. What would be the extent of your profit in (a) depend on?
- An investor buys a European call option at a price of 7.6 yuan. The stock price is 52 yuan and the strike price is 55 yuan. Under what circumstances will the investor make a profit ? Under what circumstances will the option be executed ? Draw a diagram of the relationship between investor profitability and stock price at maturity.Consider a 11-period binomial model with R=1.02, S0 = 100, and u= 1.05. Compute the value of a European call option on the stock with strike K = 102. The stock does not pay dividends.Let there exist a non-dividend-paying stock, A, which has a current price of $80. Let there exist another stock, B, which has a current price of $100. Stock B will continuously pay dividends at a dividend yield of x. A one-year European exchange call option with underlying asset A and strike asset B is sold for $5, while a one-year European exchange put option with underlying asset A and strike asset B is sold for $15. 12% is the continuously compounded, risk-free interest rate. Calculate the value of stock B's dividend yield, x.