A Study on No Arbitrage Pricing Theory Using Discrete-time and Continuous-time Approaches

The real estate market is characterized by high volatility and intense competition. In particular, investment decision-making in real estate development needs to be more flexible in response to uncertain environmental changes, including legal and economic factors. No Arbitrage Pricing Theory is a framework that determines the prices of financial derivatives based on the assumption that no arbitrage opportunities exist in the financial market. This theory requires a pricing structure that eliminates risk-free opportunities for guaranteed profits across various financial products. The objective of this study is to compare the differences between discrete-time and continuous-time approaches within the No Arbitrage Pricing Theory, which is one of the pricing theories in financial engineering. Specifically, this research aims to examine the concept of no arbitrage, the Markov properties of each model, and the replicability of the payoffs of complete options from a practical perspective. By analyzing No Arbitrage Pricing Theory, this study explores methods for assessing uncertainty in real estate prices from the viewpoint of financial engineering, including methods for evaluating real estate returns, risk analysis techniques, rental derivative valuation methods, and real estate option valuation approaches. Building on this research, various analytical methods are expected to develop, and this study may play a fundamental role in that advancement.