Homework Answers
1.
False, value increases with time to maturity hence 1 is greater
than 2
2.
True, value increases with volatility
3.
True because of reduced volatility
4.
True because of reduced volatility
5.
False as call price decreases with strike
6.
True as put price increases with strike
P.S.: I am allowed to answer only 4 questions
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Question 2: Indicate whether the following statements are True or False: a) If time to maturity,...
Question 1 - 35 Points Consider a European put option on a non-dividend-paying stock where the...
Question 1 - 35 Points Consider a European put option on a non-dividend-paying stock where the stock price is $15, the strike price is $13, the risk-free rate is 3% per annum, the volatility is 30% per annum and the time to maturity is 9 months. Consider a three-step troc. (Hint: dt = 3 months). (a) Compute u and d. (b) Compute the European put price using a three-step binomial tree. (c) If the option in (b) is American instead...
2. The following applies to stock options. Fill in the blanks: a. As the stock’s price...
2. The following applies to stock options. Fill in the blanks: a. As the stock’s price decreases, a call option on the stock ___________ in value. b. As the stock’s price decreases, a put option on the stock ___________ in value. c. Given two call options on the same stock with the same time to expiration, the call with the greater strike price will cost ________ than the call option with the lower strike price. d. Given two put options...
Problem1 A stock is currently trading at S $40, during next 6 months stock price will increase to $44 or decrease to $32-6-month risk-free rate is rf-2%. a. [4pts) What positions in stock and T-...
Problem1 A stock is currently trading at S $40, during next 6 months stock price will increase to $44 or decrease to $32-6-month risk-free rate is rf-2%. a. [4pts) What positions in stock and T-bills will you put to replicate the pay off of a European call option with K = $38 and maturing in 6 months. b. 1pt What is the value of this European call option? Problem 2 Suppose that stock price will increase 5% and decrease 5%...
Question 15 (1 point) Which of the following statements is correct? Question 15 options: a) A...
Question 15 (1 point) Which of the following statements is correct? Question 15 options: a) A put option is out-of-the-money if spot price is more than strike price b) A call option is in-the-money if spot price is less than strike price c) A put option is in-the-money if spot price is more than strike price d) A call option is out-of-the-money if spot price is more than strike price Question 16 (1 point) Suppose the current spot rate for...
Question 1 a. A stock price is currently $30. It is known that at the end...
Question 1 a. A stock price is currently $30. It is known that at the end of two months it will be either $33 or $27. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a two-month European put option with a strike price of $31? b. What is meant by the delta of a stock option? A stock price is currently $100. Over each of the next two three-month periods it is...
On October 2, 2018, Tesla stock was trading $305.65. There are options on Tesla stock, Below...
On October 2, 2018, Tesla stock was trading $305.65. There are options on Tesla stock, Below are the yarigble inputs you require. Using the Black-Scholes-Merton model and Solyer, solve for the implied volatility that causes the option to be valued at $44.25. The appropriate risk free rate c.c. is 0.85%. These are European Options. Underlying So Call or Put Strike 306.65 Put 300.00 10/2/18 3/15/19 Today Maturity Time to Expiration Volatility Risk Free Rate 59.52% 0.85% #N/ A #N/A #N/A...
Question 3 - 20 Points Consider a European call option on a non-dividend-paying stock where the...
Question 3 - 20 Points Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option...
(a) State the Black-Scholes formulas for the prices at time 0 of a European call and put options on a non-dividend-paying stock ABC
2. (a) State the Black-Scholes formulas for the prices at time 0 of a European call and put options on a non-dividend-paying stock ABC.(b) Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 20% per annum, and the time to maturity is 5 months. What is the price of the option if it is a European call?
Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a...
Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a long position in Apple (ticker: AAPL). You want to protect your long position against losses and decide to buy a European put option on AAPL with a strike price of $180.15 and an expiration date of 1-year from today. The continuously compounded risk free interest rate is 8% and the stock pays no dividends. The current stock price for AAPL is $200 and its...
XYZ stock is trading at $120 per share, and the company will not pay any dividends...
XYZ stock is trading at $120 per share, and the company will not pay any dividends over the next year. Consider an XYZ European call option and a European put option, both having an exercise price of $124 and both maturing in exactly one year. The simple (annualized) interest rate for borrowing and lending between now and one year from now is 3% for each 6 month period (6.09% per year). Assume that there are no arbitrage opportunities. Is there...
Question 1 - 35 Points Consider a European put option on a non-dividend-paying stock where the stock price is $15, the strike price is $13, the risk-free rate is 3% per annum, the volatility is 30% per annum and the time to maturity is 9 months. Consider a three-step troc. (Hint: dt = 3 months). (a) Compute u and d. (b) Compute the European put price using a three-step binomial tree. (c) If the option in (b) is American instead...
Problem1 A stock is currently trading at S $40, during next 6 months stock price will increase to $44 or decrease to $32-6-month risk-free rate is rf-2%. a. [4pts) What positions in stock and T-bills will you put to replicate the pay off of a European call option with K = $38 and maturing in 6 months. b. 1pt What is the value of this European call option? Problem 2 Suppose that stock price will increase 5% and decrease 5%...
Question 1 a. A stock price is currently $30. It is known that at the end of two months it will be either $33 or $27. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a two-month European put option with a strike price of $31? b. What is meant by the delta of a stock option? A stock price is currently $100. Over each of the next two three-month periods it is...
On October 2, 2018, Tesla stock was trading $305.65. There are options on Tesla stock, Below are the yarigble inputs you require. Using the Black-Scholes-Merton model and Solyer, solve for the implied volatility that causes the option to be valued at $44.25. The appropriate risk free rate c.c. is 0.85%. These are European Options. Underlying So Call or Put Strike 306.65 Put 300.00 10/2/18 3/15/19 Today Maturity Time to Expiration Volatility Risk Free Rate 59.52% 0.85% #N/ A #N/A #N/A...
Question 3 - 20 Points Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option...
Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a long position in Apple (ticker: AAPL). You want to protect your long position against losses and decide to buy a European put option on AAPL with a strike price of $180.15 and an expiration date of 1-year from today. The continuously compounded risk free interest rate is 8% and the stock pays no dividends. The current stock price for AAPL is $200 and its...
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