1. (A) Consider a stock with a price of $140 and a standard deviation of 0.4. The stock will pay a dividend of $2 in 40 days and a second dividend of $2 in 130 days. The current risk-free rate of interest is 10 percent. An American call on this stock has an exercise price of $150 and expires in 100 days. What is the price of the call according to the pseudo-American approach?

(B) Could the exact American call pricing model be used to price the option in A?

(C) Explain why the exact American call pricing model treats the call as an option on an option.

1. In various incarnations of the black model, we saw that the role of the stock price in the black-scholes-Merton model could be played alternately by the futures price, the forward bond price, and the forward interest rate. What underlying assumptions unite these various proxies for the stock price and allow the application of the black model?
2. Explain why American and European puts on a non-dividend stock can have different values.
3. What is the GAMMA of a share if the stock price is $55 and a call on the stock with X=$50has a price c=$7 while a put with a price p=$4? EXPLAIN. (Please explain in detail, I am still not sure why it is zero)

Thank you!