1. An exchange rate is currently $0.8500 per unit of the foreign currency. The volatility of the exchange rate is 15%. Interest rate in $ is 5% while the interest rate in the foreign currency is 2%. Both rates are quoted per annum on a continuously compounded basis. Using the lognormal assumption, estimate the probability that the exchange rate in four months will be: a. less than or equal to $0.800, b. between $0.800 and $0.900, and c. greater than $0.900.
2. Suppose that the result of a major lawsuit affecting a company is due to be announced in the next few seconds. The company’s stock price is currently $500 per share. If the ruling is favorable to the company, the stock price per share is expected to jump to $650. If it is unfavorable, the stock is expected to drop to $300 per share.
a. What is probability of a favorable ruling implied by the stock price and the two possible outcomes after the announcement?
b. Assuming that the volatility of the company’s stock after the ruling will be 20% for six months if the ruling is favorable and 40% if it is unfavorable, calculate the prices of six-month European call options with strike prices of $500, and $600. Finally calculate the implied volatilities corresponding to these two option prices. Assume that the company does not pay dividends and that the six-month risk-free rate is 5% on a continuously compounded basis.