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Question 3 (30 points) Evaluate the profitloss of the following scenarios. 1. Short 500 shares stock...
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...
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...
Question 3 - (30 Points) (a) Assume that So = 10 EUR and r = 3%...
Question 3 - (30 Points) (a) Assume that So = 10 EUR and r = 3% continuously compounded. The price of a 9-months European put option with strike K = 8 EUR is 2 EUR. Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is...
Shares of XYZ are currently trading at $19.29 per share. You open a butterfly spread position...
Shares of XYZ are currently trading at $19.29 per share. You open a butterfly spread position because you believe the stock price will remain stable for the next month. You long a $3.40 call option with a strike price of $16.00. You short two $0.92 call options with a strike price of $19.00. You long a $0.09 call option with a strike price of $22.00. If at maturity, XYZ shares are trading at $17.00 per share, what is the final...
1. [3 points] Assume that the current stock price is 30, the stock pays dividend continuously...
1. [3 points] Assume that the current stock price is 30, the stock pays dividend continuously at a rate proportional to its price with yield 4%, and the volatility of stock is 18%. Suppose a one-year, 32-strike European call option and put option have prices 1.8779 and 2.3000. Jack sold 25 units of this cal option at time 0 and immediately used the delta hedge. After 3 months, the stock price becomes 35 and the call option price becomes 4.6345....
The current price of a stock is $31.50 per share, and six-month European call options on...
The current price of a stock is $31.50 per share, and six-month European call options on the stock with a strike price of $32.50 are currently trading at $3.60. An investor, who has $10,000 of capital to invest, believes that the price of the stock will increase by 20% over the next six months. The investor is trying to decide between two strategies - buying shares or buying call options. What return will each strategy produce after six months, if...
Question 3 (30 Points) (a) Assume that So 10 EUR and r price of a 9-months...
Question 3 (30 Points) (a) Assume that So 10 EUR and r price of a 9-months European put option with strike K 8 EUR is 2 EUR Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6...
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...
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...
1. A trader shorts 10,000 shares of non-dividend-paying stock XYZ and plans to purchase them in...
1. A trader shorts 10,000 shares of non-dividend-paying stock XYZ and plans to purchase them in one month. The trader wants to purchase some call options to hedge the risk of the increasing in the stock price. The spot price of stock XYZ is HKS2.55 per share. A 1-month call option on stock XYZ with a strike price of HKS2.75 costs HK$0.025. Each option contract consists of 100 options. (a) Suppose that the stock price increases to HK$2.7 after one...
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 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...
Question 3 - (30 Points) (a) Assume that So = 10 EUR and r = 3% continuously compounded. The price of a 9-months European put option with strike K = 8 EUR is 2 EUR. Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is...
Shares of XYZ are currently trading at $19.29 per share. You open a butterfly spread position because you believe the stock price will remain stable for the next month. You long a $3.40 call option with a strike price of $16.00. You short two $0.92 call options with a strike price of $19.00. You long a $0.09 call option with a strike price of $22.00. If at maturity, XYZ shares are trading at $17.00 per share, what is the final...
1. [3 points] Assume that the current stock price is 30, the stock pays dividend continuously at a rate proportional to its price with yield 4%, and the volatility of stock is 18%. Suppose a one-year, 32-strike European call option and put option have prices 1.8779 and 2.3000. Jack sold 25 units of this cal option at time 0 and immediately used the delta hedge. After 3 months, the stock price becomes 35 and the call option price becomes 4.6345....
The current price of a stock is $31.50 per share, and six-month European call options on the stock with a strike price of $32.50 are currently trading at $3.60. An investor, who has $10,000 of capital to invest, believes that the price of the stock will increase by 20% over the next six months. The investor is trying to decide between two strategies - buying shares or buying call options. What return will each strategy produce after six months, if...
Question 3 (30 Points) (a) Assume that So 10 EUR and r price of a 9-months European put option with strike K 8 EUR is 2 EUR Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6...
1. A trader shorts 10,000 shares of non-dividend-paying stock XYZ and plans to purchase them in one month. The trader wants to purchase some call options to hedge the risk of the increasing in the stock price. The spot price of stock XYZ is HKS2.55 per share. A 1-month call option on stock XYZ with a strike price of HKS2.75 costs HK$0.025. Each option contract consists of 100 options. (a) Suppose that the stock price increases to HK$2.7 after one...
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