Brick by Brick

Abstract:     
Digitals are contracts that pay a fixed amount of money if at maturity the reference index is above (for a call) or below (for a put) some specific value. One can easily extend this concept
to a bivariate setting and create a contract that pays a fixed amount if both reference indices are above (for a call) or below (for a put) certain values. Using these contracts we can create what we call 'C-Bricks', i.e. contracts that pay a fixed amount if at maturity both indices are within some range. We can cut C-Bricks in half in six different ways. This gives rise to what we refer to as 'H-Bricks'. In this article we provide analytical pricing formulas for these types of contracts, assuming we live in the world of Black and Scholes (1973). In the process we also derive pricing results for equivalent contracts that, when alive at maturity, pay the value of one of the reference indices instead of a fixed amount. We refer to those as 'A-Bricks'.

JEL Classification: G13

Accepted Paper Series