Finance - Derivative Securities
1) A stock price is currently $100. Over each of the next two six-month periods it is expected to
go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous
compounding. What is the value of a one-year European call option with a strike price of $100?
2) For the situation considered in the previous problem, what is the value of a one-year European
put option with a strike price of $100? Verify that the European call and European put prices
satisfy put–call parity.
3) If the put option in the previous problem was American, would it ever be optimal to exercise
it early at any of the nodes on the tree? Find the value of this American put option.
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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...
1. A stock price is currently $100. Over each of the next two six-month periods it...
1. A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free rate is 8% per annum with continuous compounding. (a) What is the value of a one-year European call option with a strike price of $100? (b) What is the value of a one year European put option with a strike price of $100? (c) What is the value of a one-year...
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 stock that does not pay dividend is trading at $50. A European call option with...
A stock that does not pay dividend is trading at $50. A European call option with strike price of $60 and maturing in one year is trading at $10. An American call option with strike price of $60 and maturing in one year is trading at $15. You can borrow or lend money at any time at risk-free rate of 5% per annum with continuous compounding. Devise an arbitrage strategy. So I know that usually american calls are never exercised...
Question 17 ou a) A stock price is currently $60. Over each ofthe next two three-month...
Question 17 ou a) A stock price is currently $60. Over each ofthe next two three-month periods it is expected to go up by 8% or down by 7%. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $61? (3 marks) b) Based on the information in part (a), what is the value of a six-month European put option with a strike price...
price of a non-dividend-paying stock is currently $40. periods it will go up by 5% or down with continuous com- 1. (30 points) The Over each of the next two four-month by 3%: The risk free inter...
price of a non-dividend-paying stock is currently $40. periods it will go up by 5% or down with continuous com- 1. (30 points) The Over each of the next two four-month by 3%: The risk free interest rate is 3% per annum pounding. Consider an eight-month option on the stock, with a strike price of $41. a) (5 points) What is the rick-neutral probability (P- 1-p)? b) (10 points) What is the price of the option if it is a...
A stock price is currently $100. Over each of the next two 6-month periods it is...
A stock price is currently $100. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a 1-year European call option with a strike price of $100?
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%...
10. Use DerivaGem to complete this problem where you have an option on a non-dividend paying...
10. Use DerivaGem to complete this problem where you have 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 25% per annum, and the time to maturity is four months: a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What...
You just read that a 6-month European call option on Bent Inc. with a strike price...
You just read that a 6-month European call option on Bent Inc. with a strike price of $50 is selling for $6.31. The current stock price is $52.75 and its annual volatility is 10%. The current risk free rate for all periods up to a year is 8.25% per annum with continuous compounding. What is the value of the put with the same strike and expiration? A) $1.12 B) $1.54 C) $5.19 D) $5.67 E) $6.31
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...
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...
Question 17 ou a) A stock price is currently $60. Over each ofthe next two three-month periods it is expected to go up by 8% or down by 7%. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $61? (3 marks) b) Based on the information in part (a), what is the value of a six-month European put option with a strike price...
price of a non-dividend-paying stock is currently $40. periods it will go up by 5% or down with continuous com- 1. (30 points) The Over each of the next two four-month by 3%: The risk free interest rate is 3% per annum pounding. Consider an eight-month option on the stock, with a strike price of $41. a) (5 points) What is the rick-neutral probability (P- 1-p)? b) (10 points) What is the price of the option if it is a...
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%...
10. Use DerivaGem to complete this problem where you have 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 25% per annum, and the time to maturity is four months: a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What...
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