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Consider an economy with two dates (t=0,1) and at t=1 there are three states. The following...
1. Draw payoff diagrams for the following option trading strategies. Assume all options have the same...
1. Draw payoff diagrams for the following option trading strategies. Assume all options have the same expiration date. a. Buy a share and write a call on the stock b. Buy a call with exercise price X1 and write a call with an exercise price X2 on the same stock, with X1 < X2. c. Buy a call with exercise price X1, sell two calls with exercise price X2 and buy a call with exercise price X3 with X1 X2...
Exercise 7.3. There are three assets in the economy, stock, money, and call option. The stock...
Exercise 7.3. There are three assets in the economy, stock, money, and call option. The stock price tomorrow can be either 5 or 15 depending on the economy's performance. The money price tomorrow is 1 independent of the economy's performance. The call option has a strike price of 10 (if you oun one unit of the call option, you are entitled to purchase a share of stock tomorrow at the strike price). Suppose today's prices for a share of stock...
You are considering buying three stocks whose prices at time t are given by P1(t), P2(t),...
You are considering buying three stocks whose prices at time t are given by P1(t), P2(t), and P3(t) . You know that dP1 dt is near zero, dP2 dt is a large negative number, and dP3 dt is a large positive number. Which stock will you buy? P1(t)P2(t) P3(t) Explain your answer. Since dP1 dt is near zero, the price of the first stock ---Select--- is increasing is decreasing remains relatively constant . Since dP2 dt is a large negative number, then...
8- Suppose that you noticed the following prices: C=$12; S=$60; X=$50, for a one year European...
8- Suppose that you noticed the following prices: C=$12; S=$60; X=$50, for a one year European call option. The simple risk-free interest rate is 10% per year. Is there an arbitrage profit opportunity here? Yes or no? If yes, how would you exploit it? If no, explain why not. PS: In all questions above X denotes the exercise price of the options, C=call premium, P=put premium, and S=stock price.
Consider European call and pit on a non dividend paying stock; both for T=1yr. The stock...
Consider European call and pit on a non dividend paying stock; both for T=1yr. The stock price is $45/share and k=$45/share for both options. The call premium is equal to the put premium c=p= $7/share. The annual risk-free rate is 10%. Use the put-call parity and show that there exist an arbitrage opportunity. Also, show the complete table of cash flows and P/L at the options expiration of a strategy that will create the arbitrage profit in Q2.
3. Consider two European put options with the same expiration dates and the same strike prices....
3. Consider two European put options with the same expiration dates and the same strike prices. The underlying assets of the two options are different. One option is for stock A whose current price is $50 and has the volatility of 30%. The other is for stock B whose current price is $45 and has the volatility of 25%. Both stock A and B will pay no dividends. The price of put A is always higher than the price of...
Question 7: 1. Both a call option and a put option are currently traded on stock...
Question 7:
1. Both a call option and a put option are currently traded on stock AXT. Both options have a strike price of $90 and maturity (T) of three months. The call premium (Co) is $2.75, the put premium (Po) is $4.12, and the underlying stock price (So) is $89.50. Assume that you trade one contract that has 100 shares when you calculate profit or loss. What will be your profit (or loss) if you take a long position...
10 Answer the following a. Suppose data are collected for a certain stock: Stock price Call...
10 Answer the following a. Suppose data are collected for a certain stock: Stock price Call price (1-year expiration, E $105) Put price (1-year expiration, E 105) $110 $17 $5 5% per year Risk-free interest rate Is there a mispricing of the call and put? If yes, can you exploit this mispricing to create arbitrage proft? b. Design a portfolio using only call options and the underlying stock with the following payoff at expiration: 0 10 20 30 40 S0...
Consider three call options on the same underlying stock and same expiration date. You buy the...
Consider three call options on the same underlying stock and same expiration date. You buy the call with X=40, buy the call with X=30, and sell two calls with X=35. What is the payoff from your position if the stock prices ends at $32? What is the highest payoff from this position? What is the lowest payoff from this position? For you to engage in such a position, what are your expectations about the stock price? PS: In all questions...
9. Put-call parity and the value of a put option Aa Aa E Consider two portfolios...
9. Put-call parity and the value of a put option Aa Aa E Consider two portfolios A and B. At the expiration date, t, both portfolios have identical payoffs. Portfolio A consists of a put option and one share of stock. Portfolio B has a call option (with the same strike price and expiration date as the put option) and cash in the amount equal to the present value (PV) of the strike price discounted at the continuously compounded risk-free...
1. Draw payoff diagrams for the following option trading strategies. Assume all options have the same expiration date. a. Buy a share and write a call on the stock b. Buy a call with exercise price X1 and write a call with an exercise price X2 on the same stock, with X1 < X2. c. Buy a call with exercise price X1, sell two calls with exercise price X2 and buy a call with exercise price X3 with X1 X2...
Exercise 7.3. There are three assets in the economy, stock, money, and call option. The stock price tomorrow can be either 5 or 15 depending on the economy's performance. The money price tomorrow is 1 independent of the economy's performance. The call option has a strike price of 10 (if you oun one unit of the call option, you are entitled to purchase a share of stock tomorrow at the strike price). Suppose today's prices for a share of stock...
8- Suppose that you noticed the following prices: C=$12; S=$60; X=$50, for a one year European call option. The simple risk-free interest rate is 10% per year. Is there an arbitrage profit opportunity here? Yes or no? If yes, how would you exploit it? If no, explain why not. PS: In all questions above X denotes the exercise price of the options, C=call premium, P=put premium, and S=stock price.
Question 7:
1. Both a call option and a put option are currently traded on stock AXT. Both options have a strike price of $90 and maturity (T) of three months. The call premium (Co) is $2.75, the put premium (Po) is $4.12, and the underlying stock price (So) is $89.50. Assume that you trade one contract that has 100 shares when you calculate profit or loss. What will be your profit (or loss) if you take a long position...
10 Answer the following a. Suppose data are collected for a certain stock: Stock price Call price (1-year expiration, E $105) Put price (1-year expiration, E 105) $110 $17 $5 5% per year Risk-free interest rate Is there a mispricing of the call and put? If yes, can you exploit this mispricing to create arbitrage proft? b. Design a portfolio using only call options and the underlying stock with the following payoff at expiration: 0 10 20 30 40 S0...
Consider three call options on the same underlying stock and same expiration date. You buy the call with X=40, buy the call with X=30, and sell two calls with X=35. What is the payoff from your position if the stock prices ends at $32? What is the highest payoff from this position? What is the lowest payoff from this position? For you to engage in such a position, what are your expectations about the stock price? PS: In all questions...
9. Put-call parity and the value of a put option Aa Aa E Consider two portfolios A and B. At the expiration date, t, both portfolios have identical payoffs. Portfolio A consists of a put option and one share of stock. Portfolio B has a call option (with the same strike price and expiration date as the put option) and cash in the amount equal to the present value (PV) of the strike price discounted at the continuously compounded risk-free...
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