Q2. Bank BBB offers the following contract to its wealthy clients:

Deposit $1M today, t, for exactly one year that ends on date T. At T, BBB will pay back the original sum of $1M plus interest on the $1M. The interest paid will depend on the annual rate of return on the stock of BBB, denoted by RBBB. BBB does not pay dividend during the year T t.

2.1 Write down a formula for RBBB

2.2 The dollar amount of interest paid to the investor depends on RBBB in the following way: The interest rate on the $1M deposit is as follows:

it is = (.5)RBBB IF RBBB was positive during the year T - t.

it is = 0 IF RBBB was non positive during the year T - t.

Write down a formula for the dollar amount of interest paid by BBB at T as a function of RBBB and explain why this dollar amount can be viewed as the at expiration cash flow from an at-the money call on the stock of BBB.