1. What is the delta of a nine-month at the money European call option on a non-dividend paying stock when the risk-free interest rate is 12% per annum, and the volatility of the stock is 18% per annum?

2. A portfolio is worth $90 million. To protect against market downturns the manager of the portfolio requires a six-month European put option contracts on the S&P 500 with a strike price of $10. The S&P 500 index stands at 900. The risk-free rate is 9% per annum, the dividend yield is 6% per annum, and the volatility of the portfolio is 25% per annum.

if the manager buys traded European put options, how much would the insurance cost?

If the manager decides to provide insurance by keeping part of the portfolio in risk-free securities, how much portion of the portfolio should be initially sold and invested in risk-free securities?

3. Consider a call option on a non-dividend paying stock where the stock price is $49, the strike price is $50, the risk free rate is 5%, the time to maturity is 20 weeks (~0.3846 years), and the volatility is 20%

Calculate the delta

Calculate the theta

Calculate the gamma

Calculate the Vega

Calculate the rho