Brick by Brick

Posted: 1 Jun 2001

See all articles by Harry M. Kat

Harry M. Kat

Independent

Ronald C. Heynen

Bank of America - Market Risk Management

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

Suggested Citation

Kat, Harry M. and Heynen, Ronald C., Brick by Brick. Risk Magazine, Vol. 9, Number 6, June 1996; Cass Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=268835

Harry M. Kat (Contact Author)

Independent

No Address Available

Ronald C. Heynen

Bank of America - Market Risk Management ( email )

1 Alie Street
London E1 8DE
United Kingdom

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