The market price of a 1000-share European put option contract is $6200. The expiration date of the put option is one year from today. On that date, the price of the underlying stock will be either $50 or $32. The two states are equally likely to occur. Currently, the stock sells for $40; its strike price is $42. Suppose you are able to borrow money at 10% annual rate. Is there an arbitrage chance? How can you earn risk-free profit?

The market price of a 1000-share European put option contract is $6200. The expiration date of the put option is one year from today. On that date, the price of the underlying stock will be either $50 or $32. The two states are equally likely to occur. Currently, the stock sells for $40; its strike price is $42. Suppose you are able to borrow money at 10% annual rate. Is there an arbitrage chance? How can you earn risk-free profit?

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter5: Currency Derivatives

Section: Chapter Questions

Problem 4ST

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The stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 20% or down by 20%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? 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.
A speculator is considering the purchase of a 6-month Swiss franc call option on 50,000 francs with a strike price of $1.0885/SFr The premium is $0.0075/Sfr. The spot price is $1.0822/Sfr and the 60-day forward rate is $1.0880/SFr. The speculator believes the Franc will appreciate to $1.0994/Sfr over the next six months. What is the profit or loss if the franc appreciates only to the forward rate at the end of the 6 months? A. $170 B. -$235 C. $450 D -$375
The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. Risk-free interest rates (all maturities) are 10% per annum with continuous compounding. What is the price of a European put option that expires in six months, and has a strike price of $30 and the same underlying asset?
Consider a six-month European call option on the spot price of gold, that is, an option to buy oneounce of gold in the spot market in six months. The strike price is $1, 200, the six-month futuresprice of gold is $1, 240, the risk-free rate of interest is 5% per annum, and the volatility of thefutures price is 20%. The option is the same as a six-month European option on the six-monthfutures price. Calculate the value of this option.
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? 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.
Melbourne Capital Ltd considers selling European call options on ANZ Bank Ltd for$1.50 per option. The current market price is $17.70 on 28th September 2020, theexercise price is $20, and the maturity of each call option is 6 months. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised? How many call options should the investor sell to raise a total capital of$1,260,000?
Suppose that you trade a forward contract today that matures after one year. The forward price is $105 and the simple interest rate is 7 percent per year. If after six months from today, the spot price is going to be $125 and the value of the forward contract is $20, the arbitrage profit that you can make today by trading one forward contract and other securities is?
. A European put option written on a non-dividend paying stock that is currently worth ₺100 in the stockmarket has a strike price of ₺100 and exactly five months left until its expiration date. If the continuouslycompounded annual risk-free rate is observed as 20% per year across all maturities and the put option iscurrently priced at ₺3.20 in the option market, what should be the theoretical price of a European call optionwritten on the same stock that has the same strike price and expiration date as the put option described?
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