1. Consider an up and in European barrier call option on the same underlying stock.

With an up and in barrier option the buyer gets an option that becomes active if and when the underlying hits a given barrier value. If the underlying never reaches this value, the option will expire without a value.

What would be the price of an up and in European barrier call option on the same stock with a barrier at $12? Why?

Note: The same assumptions as before the stock goes up/down by +/- 10% each period, strike of $8, risk free rate of 5% p.a. and time to maturity of three months.

Hint: You are not required to draw another binomial tree.