The Valuation of Options on Real Estate Using Laplace Transforms

Abstract

Options on real estate give the buyer the right to purchase or sell property at a specified price (exercise price) within a specific time period. Investors in real estate options are typically moderate to high risk-takers who seek to gain from rising or falling real estate prices by purchasing at bargain prices, or selling at inflated prices. This paper constructs mathematical models that value call options on real estate. We consider 3 different types of properties including real estate investment trusts (REITs), resorts, hotels, and large shopping malls. Investor sentiment for moderate risk-takers was modeled by gamma distributions, whose step function indicated a gradual increase in risk-taking propensity. Investor sentiment for risk-takers was modeled by exponential distributions with sharp upward increases in risk-taking propensity. Options were valued based on their intrinsic value and time value. The time distribution of option prices was modeled using Laplace transforms. Laplace transforms are presented as approximations of time value due to their ability to accommodate revisions in price expectations during trading. Laplace transforms of different types were considered such as the linear form, periodic summation, and the Kulback-Liebler divergence.