Information on calls and puts

• The spot price of this share will be determined by thestudent number usingthe last digit of thestudent number. The spot price of the share will be (last digit of the student number*10+6). For example, if the last digit of the student number is 5, the spot share price will be 5*10+6=56. If the last digit of the student number is 0, please replace it with 4, i.e. the spot price will be 4*10+6=46.
• The strike price of the options will be the share price you just calculated +2. For example, if the share price calculated based on thestudent number is 56, the strike price of the options will be (56+2)=58.

Based on this spot price and this strike price as well as the fact that the risk-free interest rate is 6% per annum with continuous compounding, please undertake option valuations and answer related questions according to following instructions:

1. Use a two-step binomial tree to calculate the value of an eight-month American put option.
2. Calculate the deltas of the European put and the European call at the different nodes of the binomial three.

Note:When you use no-arbitrage arguments, need to show in detail how to set up the riskless portfolios at the different nodes of the binomial tree.

Black-Scholes-Merton model:

Using the information given above regarding the spot and strike price, risk-free rate of return and the fact that the volatility of the share price is 18%, answer following questions:

1. What is the price of an eight-month European call?
2. What is the price of an eight-month American call? What is the price of an eight-month European put?
3. How would your result from k. change if a dividend of $1 is expected in three months? How would your result from k. change if a dividend of $1 is expected in ten months?

refer to the black scholes formula below for arriving at the result