Question 2. What is the price of a European call option on a non-dividend paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months?

Problem 1. Assume that the interest rate is 5%, contimuously 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.

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.

Give typing answer with explanation and conclusion  5. A European call option on Home Depot stock has a strike price of $160 and expires in 0.9 years. Home Depot stock has a current market price of $165.99 and the risk-free rate is 4%.   What must be the minimum price of the option?