Pricing of Presale Contracts with Macroeconomic Factors and Stochastic Basis Risk

Abstract

This study analyzes the stochastic basis risk (presale price minus spot housing price) of presale housing from the viewpoint of forward pricing. We employ the modified Brownian bridge process to deal with the time-varying volatility and price convergence of presale and existing houses. The finding reveals an asymmetric effect of macroeconomic factors on the presale price in different market conditions. Such results might reflect the investors’ behaviors of overreaction and/or over-pessimism. In addition, the influence of macroeconomic variables is greater on the basis price than on the prices of existing houses, especially in a depressed housing market. Our results emphasize the importance of considering basis risk and the influence of macroeconomic factors when pricing presale houses to manage housing risk.

Keywords:

• Presale price
• basis price
• modified Brownian bridge process
• macroeconomic factors

Notes

1 Fu, Qian, and Yeung (2016) state, ‘the presale market is more attractive to short-term speculators than is the spot market for completed properties’ since the holding cost is relatively low.

2 For more discussion of the presale system, please refer to Chan, Fang, and Yang (2014).

3 Wong et al. (2006) investigate the relationship between presale prices and existing condominium prices. Yiu, Wong, and Chau (2009) studied the impact of noise traders on the volume and price dispersion of presale contracts.

4 Some studies (e.g., Grenadier, 1995, 1996; Wang and Zhou, 2006; Lai, Wang, and Yang, 2007; Buttimer, Clark, and Ott, 2008) investigate the situation where buyers have the right to buy the property at a pre-determined exercise price and to default if the spot price falls below the contract price. Using a simple two-period game theoretical model, Chan, Wang, and Yang (2012) derive a closed-form pricing equation for a presale contract that explicitly accounts for a developer’s abandonment option and a buyer’s default option. Edelstein, Liu, and Wu (2012) create a set of interrelated theoretical models for explaining how and why developers and buyers engage in presale contracts for noncompleted residential dwellings.

5 See Leung (2004) for a review of macroeconomics and housing.

6 Some studies (e.g., Chen and Leung, 2008; Jin et al., 2012) show that the real estate price fluctuations in the variability of the capital market are confirmed to be significant. However, for simplicity in providing a pricing formula, we set the house price as the dependent variable and the macroeconomic factors as explanatory variables in the regression model, ignoring the possibly bidirectional relationship.

7 Chang et al. (2011, 2012, 2013) provide evidence that the house price, among other macroeconomic variables, displays regime-switching behaviors across several markets. Hence, our existing house return model (Equation 1) can be extended to multi-regime-type models. Based on the multi-regime-type models, the variance of existing house returns could capture the behaviors of different variances under different regimes.

8 Based on the stochastic interest rate, we use the forward neutral measure, in which a zero bond is used as the numeraire. With this numeraire, the martingale property holds. That is, today’s value of an existing house is equal to the discounted expectation of its future value, taken with respect to the forward neutral measure. Hence, the price under the forward neutral measure is the fair price in a complete market. The gap between the fair price and actual price in the presale market is accompanied by the degree of imperfectness.

9 Wang and Wu (2011) use a two-factor (stochastic stock index and stochastic interest rate) model to describe the process of a futures contract.

10 For a similarly detailed derivation technique, see Klebaner (1998, p.121).