1. A stock is currently 1,510 with a dividend yield of 2.5%. The annual risk-free rate 4%. If the price of a 12-month American put option with a strike 1,480 is $82.50, what is the implied volatility of the index?
2. You want to have $1.5 million in real dollars in a retirement account when you retire in 40 years. The inflation rate is 2.7% and the nominal rate of return on your investment is 10%. What real amount must you deposit each year in the account to achieve your goal?
3. The price of a futures contract is $19, and the annual risk-free rate 12%. If the price of a five month European put futures option, with strike $20, is $1.64, what is the implied volatility of the futures price?