Suppose we're in a standard N-period binomial pricing model with risk-free interest rate r, and let K be a positive number and 1 · m < N. Consider the following two securities:

Security A: our security will act as either a European put or a European call, with strike K, but we don't make the choice as to which one until time m (this object is called a chooser option).

Security B: we just purchase a K-strike European put, expiring at time N, and a European call with strike K (1+r)N¡m , expiring at time m, and lump them together.

Now it's possible to use some fairly sophisticated mathematics to prove that the two securities have the same premium, but we can do better and prove that one replicates the other. Explain how the choice of whether or not to exercise the call in Security B effectively does the same thing as the making the choice in Security A.