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.