Pricing Commercial Real Estate Derivatives

Abstract

The pricing of derivatives such as forwards and swaps based on financial indexes such as the Standard & Poor's (S&P) 500 stock index is relatively easy to understand due to the fact that the stocks underlying the derivative can be traded simultaneously with the derivative. This enables the construction and execution of arbitrage trading between the derivative contract and the underlying product traded in the “cash” or “spot” market. This leads to the formula for the “fair” price of futures contracts relative to their underlying assets, known as the futures-spot parity theorem. In contrast, the real estate indexes underlying real estate equity derivatives cannot be directly traded themselves, apart from the derivatives written on them. An investor cannot buy and sell each period all of the properties that comprise a real estate index. Thus, the classical arbitrage that underlies traditional futures pricing cannot be executed with real estate derivatives. Furthermore, because the index cannot itself be directly traded in a well-functioning spot market, there is no guarantee that the real estate index will always represent equilibrium values or equilibrium return expectations going forward from any time. Nevertheless, one derives what the “fair” price of a real estate index derivative should be as a function of the current underlying index value, where “fair” is defined as the equilibrium return that investors would expect in the derivative market. This price must take into consideration any lags that the index may have relative to the performance of the properties in the index. Keywords: derivative; forward; swaps; futures-spot parity theorem; equilibrium price; arbitrage; London Interbank Offered Rate (LIBOR)