Consider a 3-month put option. Suppose that the underlying stock price is $25, the strike $26, the interest rate is 5% p.a., stock volatility is 6% per month. Use the same data to answer questions a) h).

a) What is the level of annual volatility (compute)?

b) Define in your own words implied volatility.

c) How would you compute implied volatility? Explain (no need to compute).

d) What is the probability of stock price going down (Note: use annual volatility, number of steps in a tree is N=3)?

e) Build the binomial tree for the underlying asset (stock). Note: the tree nodes can be edited. Show computations for first up and first down nodes.

f) Compute the price of the European put option using a 3-step binomial tree. Show computations for terminal and two non-terminal nodes.

g) If the market price on the European put option is $1.5, what should be the price of the European call option of the same strike and maturity to prevent arbitrage?

h) Compute the price of the American put option using a 3-step binomial tree. Show computations for two non-terminal nodes.