1. Consider a European call option when the stock price is $30, the exercise price is $25, the time to maturity is 6 months, the volatility is 35% per annum, and the risk-free rate is 5% per annum. The stock is expected to pay $1 dividend in 2 months and another $1 dividend in 5 months. Use the Black-Scholes formula to price the call option.
2. Currently, Apple stock is trading at $117.81. The 1-month $118 Apple call option is trading at $3.05. Assume the risk-free rate is 1%. Find the implied volatility.
3. VIX
a. What is the VIX index?
b. Find the current VIX value from the internet such as Yahoo Finance.
c. Is the current VIX higher or lower than the Apple implied volatility in question 2?
4. Consider a stock index currently standing at 2,100. The dividend yield on the index is 3% per annum and the risk-free rate is 1%. A 3-month European call option on the index with a strike price of 2,000 is trading at $105.91. What is the value of a 3-month European put option with a strike price of 2,000? (Hint: Use put-call parity for index options)