You think that there is an arbitrage opportunity on the market. The current stock price of Wesley corp. is $20 per share. A one- year put option on Wesley corp. with a strike price of $18 sells for $3.33, while the identical call sells for $7. The one-year risk- free interest rate is 8%. Assuming that the put option is fairly priced, compute the fair price of the call option and explain what you must do to exploit this arbitrage opportunity and what will be your gain.
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- Two investors are evaluating General Electric’s stock for possible purchase. They agree on the expected value of D1, and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stocks for 2 years and the other normally holds stocks for 10 years. On the basis of the type of analysis done in this chapter, they should both be willing to pay the same price for General Electric’s stock. True or false? Explain.You happen to be checking the newspaper and notice an arbitrage opportunity.The current stock price of Gougou is $20 per share and the one-year risk-free interestrate is 8%. A one-year put on Gougou with a strike price of $18 sells for $3.33, whilethe identical call sells for $7. Explain what you must do to exploit this arbitrageopportunityYou would like to be holding a protective put position on the stock of XYZ Co. to lock in a guaranteed minimum value of $100 at year-end. XYZ currently sells for $100. Over the next year the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on XYZ Co.a. Suppose the desired put option were traded. How much would it cost to purchase?b. What would have been the cost of the protective put portfolio?c. What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = 100? Show that the payoff to this portfolio and the cost of establishing the portfolio match those of the desired protective put.
- You would like to be holding a protective put position on the stock of XYZ Company to lock in a guaranteed minimum value of $105 at year-end. XYZ currently sells for $105. Over the next year, the stock price will increase by 9% or decrease by 9%. The T-bill rate is 7%. Unfortunately, no put options are traded on XYZ Company. Required: Suppose the desired put option were traded. How much would it cost to purchase? What would have been the cost of the protective put portfolio? What portfolio position in stock and T-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = 105? Show that the payoff to this portfolio and the cost of establishing the portfolio match those of the desired protective put.You expect the stock market to increase, but instead of acquiring stock, you decide to acquire a stock index futures contract. That index is currently 60.4, and the contract has a value that is $500 times the amount of the index. The margin requirement is $2,500. When you make the contract, how much must you put up? Round your answer to the nearest dollar. $ What is the value of the contract based on the index? Round your answer to the nearest dollar. $ If the value of the index rises 2 percent to 61.608, what is the profit on the investment? Round your answer to the nearest cent. $ What is the percentage earned on the funds you put up? Round your answer to one decimal place. % If the value of the index declines 2 percent to 59.192, what percentage of your funds will you lose? Round your answer to one decimal place. Enter your answer as a positive value. % What is the percentage you earn (or lose) if the index falls to 55.4? Round your answer to one decimal place. Enter…Consider a market where the assumptions behind the Black-Scholes model hold. A non-dividend paying share is currently priced at $300. A put option is available on the share with a strike price of $320 and one year to expiry. Volatility of 15% and the risk-free rate is 5% per annum. What would be the fair price of the put option.
- Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.As an option trader, you are constantly looking for opportunities to make an arbitrage transaction (that is, a trade in which you do not need to commit your own capital or take any risk but can still make a profit). Suppose you observe the following prices for options on DRKC Co. stock: $3.18 for a call with an exercise price of $60, and $3.38 for a put with an exercise price of $60. Both options expire in exactly six months, and the price of a six-month T-bill is $97.00 (for face value of $100). a. Using the put-call-spot parity condition, demonstrate graphically how you could synthetically re-create the payoff structure of a share of DRKC stock in six months, using a combination of puts, calls, and T-bills transacted today. b. Given the current market prices for the two options and the T-bill, calculate the no-arbitrage price of a share of DRKC stock. c. If the actual market price of DRKC stock is $60, demonstrate the arbitrage transaction you could create to…Suppose that a stock price is currently 51 dollars, and it is known that one month from now, the price will be either 6 percent higher or 6 percent lower. Find the value of an American call option on the stock that expires one month from now, and has a strike price of 49 dollars. Assume that no arbitrage opportunities exist, and a risk free interest rate of 10 percent
- Shopify, Inc common stock currently sells for $1,229.91 per share, and the standard deviation of returns is 58.67%. A call option with a strike price of $1,100 is currently trading on the market. The option expires in 0.15 years, and the risk-free rate of return is 0.9%. Shopify does not pay a dividend. What is rho (ρ) for this call option assuming a continuous model such as the Black-Scholes model? A) 104.1327 B) 107.2895 C) 57.7772 D) 107.0002Consider an American call and an American put with the same underlying stock share S paying no dividend, the same strike price K = $30 and the same expiration date T = 3 (months). Suppose that the stock price is $31, the risk-free interest rate is 10% per annum compounded continuously, the price of the American call option is $3, and the price of the American put option is $1. Using the no-arbitrage principle, prove that there exists an arbitrage opportunity then.Suppose that a stock price is currently 56 dollars, and it is known that five months from now, the price will be either 22 percent higher or 22 percent lower. Find the value of a European put option on the stock that expires five months from now, and has a strike price of 55 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 6 percent.