Please assist with these questions! Must show all work!

Homework 7 1. Consider a European call option when the stock price is $28, the exercise price is $25, the time to maturity is 7 months, the volatility is 30% per annum, and the risk-free rate is 10% per annum. The stock is expected to pay $0.20 dividend in 2 months and another $0.20 dividend in 5 months. Use the Black-Scholes formula to price the call option. 2. Currently, Apple stock is trading at $132.54. The 1-month $130 Apple call option is trading at $4.55. Assume the risk-free rate is 0.15% (not 15%). Find the impli 3. What is the VIX index? Find the current VIX value from the internet such as Yahoo Finance. Is it higher or lower than your answer to Q2. Discuss (explain why). 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: put-call parity for index options) mplied volatility. y)