Assume the Black-Scholes framework. Consider a 9-month at-the-money European put option on a futures contract. You are given: (i) The continuously compounded risk-free interest rate is 10%.
(ii) The strike price of the option is 20.
(iii) The price of the put option is 1.625.
If three months later the futures price is 17.7, what is the price of the put option at that time?

Anew 2-lane road is needed in a part of town that is growing. at some point the road will need 4 lanes to handle the anticipated traffic. if the city's optimistic estimate of growth is used, the expansion will be needed in 4 years and has a probability of happening of 40%. for the most likely and pessimistic estimates, the expansion will be needed in 8 and 15 years respectively. the probability of the pessimistic estimate happening is 20%. the expansion will cost $ 4.2 million and the interest rate is 8%. what is the expected pw the expansion will cost?

Which of the following services will be provided by a full-service broker but not by a discount broker? i. research of potential investment opportunities ii. purchase and sale of stock at your request iii. recommendation of investments a. i and iii b. ii only c. iii only d. i, ii, and ii

Do a swot analysis for the business idea you chose in question 2 above. describe at least 2 strengths, 2 weaknesses, 2 opportunities, and 2 threats for that company idea.