1. A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19 and a $1 dividend is expected in one month. Identify the arbitrage opportunity to the trader.

Consider a call option on one share of BP with a strike price of $70 and exercise time 1 quarter (3 months). Suppose the current stock price for BP is S(0) = $65 per share. Suppose further that A(0) = $100, A(1) = $102 and two possible prices for S(1) are S $74 with probability 0.5, S(1) = $66 with probability 0.5. Evaluate the expected returns E(Ks) and E(Kc) for the stock and the option.

The current stock price is $20, the risk - free interest rate is 5% per annum (consecutive compounding), and the volatility is 15% per annum. Calculate the price of a European call option with a maturity of 3 months and an exercise price of $21. However, this stock is assumed to be non - dividend.

A 6-month European call option on a dividend-paying stock is cur- rently selling for $1.75. The stock price is $58.56, the strike price is $55, and a dividend of $1.20 is expected in 2 months and 5 months. The risk-free interest rate is 3% per annum for all maturities. (a) What opportunities are there for an arbitrageur? Detail your answer. (b) In this market a European put option with same strike price and maturity is also available for trading. Derive the no-arbitrage $3. price of the put option if the call option has a price of c = %3D (c) The European put option in the above section is trading at $3. What opportunities are there for an arbitrageur? Detail your answer.

A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10% per period. Consider a six-month European put option with a strike price of $95. The risk-free interest rate is 8% per annum, compounded continuously. What is the value of the option? Question 1 options: 1.50 3.25 2.14 None of the above

Problem 1. Assume that the interest rate is 5%, continuously compounded annually, and consider call and put options of both American and European style expiring in 6 months on non-dividend paying stock. For each of the following scenarios, check if you can find an arbitrage opportunity and, if you can, describe it: (i) The strike price of a European put option is $3 and the option is traded at $4. (ii) The shares are traded at $3 and the American call option is traded at $3.20.

Use the Black-Scholes formula to find the value of the put option using the next data: Stock price: $5.03 Time to expiration: 176 days (365 days in a year) The volatility of a stock return: 65% per year Strike price: $5 Risk-free interest rate: 1% per year