This four question assignment guides you to determine the price of an option in a multi-period setting, that is for n>1. As discussed during the last lecture, such a multi-period model can be used to obtain the Nobel prize winning Black-Scholes formula.
For convenience, we restrict to a n=3-period setting.
A graphical description of the financial market, often called `tree' because of obvious reasons, is given by:
Suppose that S0=100, u=1.1, d=1/1.1≈0.91, and r=0 (for simplicity).
1) Determine the stock price at each `node' of the tree.
Consider a put option with strike price 100 euro that expires during the last period.
2) Suppose that the price falls in the first two periods and consider the market at the start of the third period.
Determine the price of the put at the node `d2S0'. [Hint: see Exercise 4.]
3) Also determine the price of the put at the nodes 'udS0' and `u2S0'.
4) Determine the price of the put option at each node of the tree and thus, in particular, at t=0.