# Value Maximizing Decisions in the Real Estate Market: Real Options Valuation Approach

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Real Estate Projects, Uncertainty, and Valuation Frameworks

#### 2.2. The Black-Scholes Option Pricing Model

_{1}) and N(d

_{2}), and in particular explaining why they are different from each other, usually presents some difficulties. Among the major research papers, Black and Scholes (1973) did not explain or interpret N(d

_{1}) and N(d

_{2})” (Nielsen 1992, p. 1). According to Cox and Rubinstein (1985), the stock price times N(d

_{1}) is the present value of receiving the stock if the option finishes in the money, and the discounted exercise payment times N(d

_{2}) is the present value of paying the exercise price in that event.

_{1}) is the expected value of the current project and N(d

_{2}) is the risk-neutral probability that this project value at the expiration will be greater than the investment amount and the call option will be exercised at expiration. Reuer and Tong (2007) argue that there are several constraints in Black-Scholes approach usage for real options valuation as they may often differ from simple financial calls in the following ways: exercise price may be directly correlated with the value of a project instead of being a fixed amount; there might be carrying costs of holding the option open, and with financial calls, a time to maturity is a standard amount it may be difficult to identify in strategy context. That is why, recombining binomial trees, known as lattices, is perhaps one of the most practical and intuitive approaches to model uncertainty and price project managerial flexibilities for real options applications (Marques et al. 2021b).

#### 2.3. Lattice-Based Option Pricing Models

#### 2.4. Monte Carlo Simulation

^{®}) is a prerequisite for most problems. What also diminishes the appeal of the approach is that though MCS is easily applied to European-style real options; it is relatively hard to apply it to American options. Instead, MCS is commonly used to derive the value of the underlying and volatility factors (Triantis and Borison 2001; Mun 2002, pp. 223–27).

**Proposition**

**1.**

## 3. Method and Data

#### 3.1. The Input Stage: Identification of Key Points

#### 3.2. The Matching Stage: Real Options Reasoning

#### 3.3. The Decision Stage: ROV Analyses and Decision-Making

#### 3.4. Case Study Data

## 4. Case Study “Project “Sun Village”: Analysis of Results and Interpretation

## 5. Discussion and Contributions

## 6. Conclusions, Limitations, and Future Work

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Binomial underlying asset lattice for simulation and binomial option valuation lattice for decision analysis (Teoh and Sheble 2007).

**Figure 2.**Conceptual model of research: Adapted from David and David (2017); Mun (2002), and extended by the author.

**Figure 3.**Latvia house prices: average price of a standard type apartment in Riga (Euro per sq. m.). Global Property Guide (2021).

**Figure 4.**The underlying values lattice (

**upper**) and the real options valuation lattice (

**down**) of Sun Village real estate project. Source: Developed by the author.

Parameters of the Binominal Option Pricing Model | |
---|---|

Time increment (years) | $\mathsf{\delta}\mathrm{t}=\frac{\mathrm{t}}{\mathrm{N}}$ |

Up factor (u) | $\mathrm{u}={\mathrm{e}}^{\mathsf{\sigma}\surd \Delta \mathrm{T}}=\frac{1}{\mathrm{d}}$ |

Down factor (d) | $\frac{1}{\mathrm{u}}$ |

Risk-neutral probability (p) | $\mathrm{p}=\frac{{\mathrm{e}}^{\mathrm{r}\Delta \mathrm{T}}-\mathrm{d}}{\mathrm{u}-\mathrm{d}}$ |

Real Options Valuation Techniques | Strengths | Weaknesses |
---|---|---|

The Black-Scholes option-pricing model | It is the most common method for ROV analytical solutions due to its simplicity of usage | There might be carrying costs of holding the real option open; a time to maturity may be difficult to identify in a strategy context |

Lattice-based Option Pricing Models | The binomial lattices approach is the most convenient, flexible, and intuitive in valuing real options | Hard to compute since it requires many steps to produce a sufficiently accurate result |

Monte Carlo Simulation | Provide highly accurate and quick ROV results | It is easily applied to European-type real options; it is relatively hard to apply it to American options |

**Table 3.**Quarterly house prices in Latvia: average price of a standard type of apartment in Riga (Euro per sq. m.) Source: Global Property Guide (2021).

Years | Q1 | Q2 | Q3 | Q4 |
---|---|---|---|---|

2014 | 640 € | - | - | - |

2013 | 637 € | 640 € | 640 € | 641 € |

2012 | 592 € | 595 € | 595 € | 594 € |

2011 | 609 | 592 | 571 | 585 |

2010 | 612 € | 493 € | 488 € | 521 € |

2009 | 934 € | 849 € | 494 € | 576 € |

Present value of expected cash flows of the project (So) | 5,620,930.44€ |

Cost of investment or exercise price (E) | 4,912,024.43€ |

The risk-free rate of return (r) | 3.00% |

Time to expiration in years (T) | 2.0 |

The volatility of PV of FCF (σ) | 17.10% |

Option Sub-Variables | Data | Option Sub-Variables | Data |
---|---|---|---|

T = | 2.00 years | d_{1} = | 0.9265 |

S_{0}/E = | 1.1443 | N(d_{1}) = | 0.8229 |

ln(S_{0}/E) = | 0.1348 | d_{2} = | 0.6847 |

variance/2 = | 0.0146 | N(d_{2}) = | 0.7532 |

[risk-free rate + variance/2] × T = | 0.0892 | −rT = | −0.0600 |

the square root of variance = | 0.1710 | e^{−rT} = | 0.9418 |

the square root of T = | 1.4142 | S_{0 x} N(d_{1}) = | 4,625,478.72 € |

(square root of variance) × (square root of T) = | 0.2418 | K × e^{−rT} × N(d_{2}) = | 3,484,367.01 € |

Real option value: C | 1,141,111.71 € |

European Call Option | C |
---|---|

Present value of expected cash flows of the real estate project (So) | 5,620,930.44 € |

The investment required to execute the real estate project (E) | 4,912,024.33 € |

Time to expiration (T) | 2.0 years |

Real estate project uncertainty or volatility (σ) | 17.10% |

Risk-free rate (Rf) | 3.00% |

Number of steps | 6 |

Number of simulation | 1,000,000 |

European Call option price (deferral option) | 1,141,609.78 € |

time increment (years) | $\mathsf{\delta}\mathrm{t}=\frac{\mathrm{t}}{\mathrm{N}}$ = 0.33 |

up factor (u) | $\mathrm{u}={\mathrm{e}}^{\mathsf{\sigma}\surd \Delta \mathrm{T}}=\frac{1}{\mathrm{d}}$ = 1.104 |

down factor (d) | $\frac{1}{\mathrm{u}}$ = 0.906 |

risk-neutral probability (p) | $\mathrm{p}=\frac{{\mathrm{e}}^{\mathrm{r}\Delta \mathrm{T}}-\mathrm{d}}{\mathrm{u}-\mathrm{d}}$= 0.526 |

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**MDPI and ACS Style**

Čirjevskis, A.
Value Maximizing Decisions in the Real Estate Market: Real Options Valuation Approach. *J. Risk Financial Manag.* **2021**, *14*, 278.
https://doi.org/10.3390/jrfm14060278

**AMA Style**

Čirjevskis A.
Value Maximizing Decisions in the Real Estate Market: Real Options Valuation Approach. *Journal of Risk and Financial Management*. 2021; 14(6):278.
https://doi.org/10.3390/jrfm14060278

**Chicago/Turabian Style**

Čirjevskis, Andrejs.
2021. "Value Maximizing Decisions in the Real Estate Market: Real Options Valuation Approach" *Journal of Risk and Financial Management* 14, no. 6: 278.
https://doi.org/10.3390/jrfm14060278