Set the global evaluation date to January 3, 2006.
Construct a binomial tree approximating a Black-Scholes process with an initial value of 100, a risk-free rate of 10% and a constant volatility of 40%. We will assume that no dividend is paid. Build the tree by subdividing the time period 0..0.6 into 1000 equal time steps.
Consider a European call option with a strike price of 90 that matures in 6 months.
Calculate the price of this option using the tree constructed above. Use the risk-free rate as the discount rate.
Consider a European call option with a strike price of 110 that matures in 6 months.
Calculate the price of this option using the tree constructed above. Use the risk-free rate as the discount rate.
Finally, consider a call option with a strike price of 100 maturing in 6 months.
Calculate the price of this option using the tree constructed above. Use the risk-free rate as the discount rate.
Consider a more complicated payoff function.
Calculate the price of this option using the tree constructed above. Use the risk-free rate as the discount rate.
Note that the payoff of the options E8 and E7 can be replicated using the payoffs of the options E1, E2, E3, E4, E5, and E6.
This means that the prices should also match.