Current prices on Sterling options include the following. Sterling options £500,000 Strike price Calls March Puts March 9700 0.00 0.215 A company intends to use sterling options to hedge an exposure to the risk of a rise in the sterling interest rate above 3% before March. What should it do? A) Buy March puts B) Buy March calls C) Sell March puts D) Sell March calls
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Question 7
Current prices on Sterling options include the following.
Sterling options £500,000
Strike price Calls March Puts March
9700 0.00 0.215
A company intends to use sterling options to hedge an exposure to the risk of a rise in the sterling interest rate above 3% before March. What should it do?
A) Buy March puts
B) Buy March calls
C) Sell March puts
D) Sell March calls
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- Question 3Consider five-month European call and put options on British pounds with an exercise price of $1.1700. The current price of the put option is $0.0416. The current spot price of British pounds is $1.1706. The riskless interest rate is 4% in the U.S. and 5% in the U.K. (both of these rates are annualized and continu- ously compounded). (a) Given the price of the put option, what should be the current price of the call option? (Please report your answer to four decimal places.) (b) Suppose the current price of the call option is $0.0399. Demonstrate how you could earn costless arbitrage profits. Please be sure to clearly show the transactions you would undertake and the amount and timing of your profits.Aa.1 The current price of stock XYZ is 100. In one year, the stock price will either be 120 or 80. The annually compounded risk-free interest rate is 10%. i. Calculate the no-arbitrage price of an at-the-money European put option on XYZ expiring in one year. ii. Suppose that an equivalent call option on XYZ is also trading in the market at a price of 10. Determine if there is a mis-pricing. If there is a mis-pricing, demonstrate how you would take advantage of the arbitrage opportunity.D3 show the solution in details Use the binomial option pricing model to find the value of a call option on £10,000 with a strike price of €12,500. The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 (i.e. u = 1.6 and d = 1/u = 0.625). The current interest rates are i€ = 3% and are i£ = 4%. Choose the answer closest to yours. the answer is A) €3,275
- V7. A stock price is currently $232. It is known that at the end of seven months itwill be either $260 or $210. The risk-free interest rate is 3.5% per annum with continuouscompounding. hat is the value of a seven-month European put option with a strike priceof $240? Use no-arbitrage arguments.Q5. Consider a six-month European put option on a non- dividend-paying stock. The current stock price is $100 and the strike price is $105. The risk-free rate is 10% per annum with semiannual compounding. A lower bound for the price of the European put option is $ _ If the put option were an American put option, a lower bound would be $_ Q6. The price of a European call that expires in six months and has a strike price of $50 is $2. The current underlying stock price is $50, and a dividend of $2 is expected in three months from now. The risk-free interest rate is 10% per annum with quarterly compounding. For the same stock, what is the price of a European put option with the same maturity and strike price? $ Q7. Suppose that c1, c2, and c3 are the prices of European call options on a particular stock with strike prices K1, K2, and K3, respectively, and that p1, p2, and p3 are the prices of European put options on the same stock with strike prices K1, K2, and K3, respectively, where K…A company’s stock currently sells for $81.16. A one-year European put option on that stock with strike price of $85 sells for $16.24, and the risk free interest rate is 1.6%. The market expects the company to pay dividends during that period, and the market consensus is that present value of those dividends is $5.26. The price of a one-year European call option on that stock with strike price of $85 is $_________. (Note i: answer must be accurate to the nearest cent). (Note ii. Use annual compounding NOT exponential compounding for the purpose of this question).
- Question 5 The March 2024 S&P 500 cash index is 930 while the S&P 500 futures index is 950 and the contract value of each index point is $100. You are convinced the futures market will rise 10% by expiry. You are only prepared to buy or sell one futures contract. (i) Will you buy or sell a contract in the futures market? (2 marks) (ii) What is your profit (+) in dollars if you are correct? (2 marks) (iii) What is your profit (+)/loss (-) if the futures price on expiry is 1200? (2 marks) (iv) What is your profit (+)/loss (-) if the futures price on expiry is 700? (2 marks) (v) Explain what is meant by “initial margin” on a futures contract. (2 marks)Q1 Consider the option on currency HKD against the USD: • Current spot rate is HKD7.50 for 1 USD • Risk-free HKD rate of interest is 5% p.a. • Risk-free USD rate of interest is 2% p.a. • Volatility (σ) of the currency returns is 20% p.a. • Maturity of the option is 3 months. • Strike rate of the option is HKD8.00 for 1 USD • The currency options are European in nature Answer the following questions. (i) How much does it cost to hold (i.e., buy) a call-HKD option? Use the Garman Kohlhagen model.Q1 Consider the option on currency HKD against the USD: • Current spot rate is HKD7.50 for 1 USD • Risk-free HKD rate of interest is 5% p.a. • Risk-free USD rate of interest is 2% p.a. • Volatility (σ) of the currency returns is 20% p.a. • Maturity of the option is 3 months. • Strike rate of the option is HKD8.00 for 1 USD • The currency options are European in nature Answer the following questions. (i) How much does it cost to hold (i.e., buy) a call-HKD option? Use the Garman Kohlhagen model. (ii) What is the minimum terminal exchange rate for the holder of the call-HKD option to profit from holding the currency option? (iii) How much does it cost to hold (i.e., buy) a put-HKD option? Do not use the Garman Kohlhagen model.
- Exercise 1.A stock is worth $50 on december, 1st 2021. This price increases by 4% ou decreases by 4% every 2 months. The flat continuous rate of interest is 5% and the continuous rate of dividend is 2%.a) What is the premium of an American call on this stock with a maturity of 6 months and a strike price of $48?b) What is the premium of a European put on the stock? Maturity and strike price remain unchanged.c) In option pricing theory, what does ‘risk neutral’ probability mean? What is the probability the European put gets exercised?3. Consider a European call option on a non-dividend paying stock with exercise price 100 USD and expiration in one month. Interest rate is 1 percent and volatility of the stock is 0.4. Stock price 90 USD. Option price?? Use excel.Question 4. A stock that pays no dividends has price today of 100. In one year’s time the stock is worth 110 with probability 0.75 and 85 with probability 0.25. The one-year annually compounded interest rate is 5%. a) Calculate the forward price of the stock for a forward contract with maturity one year. b) Calculate the price of a one-year European put option with strike 100. c) Suppose you observe that the put option in part (b) has a market price of 4. Determine an arbitrage portfolio and calculate how much profit is generated at time T = 1 by this portfolio.