a. Calculate the prices of three-month Call(1800) and Put(1800) options on an 1800-point Dow Index if the risk-free interest rate is 8% and the annual standard deviation is 70%.
b. In New York, the Dow closed at 1800 points. The following day in Tokyo (well before the start of trading in the United States), options were traded, as follows — Call(1800) = $254, and Put(1800) = $238. What is the rate of increase/decrease that the Tokyo market expects for the Dow Index on the following day of trading in New York? What happened to the gap between these two options as compared with part (a)?
c. The Chicago Board Options Exchange Volatility Index (CBOE VIX) 68 reflects market expectations concerning short-term volatility (next 60 days). Originally, the index was measured by the average standard deviation of in-the-money put and call option pairs on the S & P 500 index, from the present month, as compared to pairs from next month. Later, the VIX was changed to include a wider range of exercise prices X and not only options which are in the money. Explain the logic behind the CBOE VIX, based on the previous sections in this question.
