A stock price is currently $36. During each three-month period
for the next six months it is expected to increase by 9% or
decrease by 8%. The risk-free interest rate is 5%. Use a two-step
tree to calculate the value of a derivative that pays off
(max[(40-ST),0])2 where ST is the stock price
in six months.
- What are the payoffs at the final nodes of the tree? [1
mark]
- Use no-arbitrage arguments (you need to show how to set up the
riskless portfolios at the different nodes of the binomial tree).
[2 mark]
- Use risk-neutral valuation. [1 mark]
- Verify whether both approaches lead to the same result.
[1 mark]
- If the derivative is of American style (ST in the
payoff function refers to the stock price when the option is
exercised), should it be exercised early? [1
mark]