Construct a binomial tree (left(u=frac{1}{d} ight)) with three quarters for an asset with present value ($ 100).

Construct a binomial tree \(\left(u=\frac{1}{d}\right)\) with three quarters for an asset with present value \(\$ 100\). If \(r=0.1\) and \(\sigma=0.4\), using the tree compute the prices of:

(a) A European Call option with strike 110

(b) A European Put option with strike 110

(c) A American Put option with strike 110

(d) A European Call option with strike 110, assuming that the underlying asset pays out a dividend equivalent to \(1 / 10\) of its value at the end of the second quarter

(e) An American Call option with strike 110 for an underlying as in iv)

(f) An Asian option, with strike equal to the average of the underlying asset values during the period

(g) A barrier option (for different barriers)