Hi,
I came across an old exam question regarding the value of options, and I’m having a bit of trouble solving it.
Here is the question:
The spot price of zink is currently 17 SEK per kilogram, and each months of the next three months it is expected to either increase by 2% or dexrease by 3%. Assume that the risk-free rate of interest is 4.75%. Use a three step binomial tree model to calculate the value of a three-month American option contract written on 900 kilograms of zink that pays of
(St)(15 - St)^2 per kilogram of zink, where St denotes the spot price of zink on the maturity date of the option contract.
How would your answer change if the contract payoff at maturity was max ((19 - min(S)), 0), where min(S) in the payoff formula denotes the minimum spot price of zink realized during the life of the option contract?
Can someone give me a hint? How can I calculate the minimum spot price?
Thanks in advance