# Profit Distribution in Guaranteed Savings Contracts: Determination Based on the Collar Option Model

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. An ESCO’s Business Structure in a Guaranteed Savings Contract

Term | Definition |
---|---|

Energy savings | Energy reductions from the installation of the energy reduction system |

Target savings | The maximum energy savings that the ESCO calculates through an energy usage diagnosis or other methods to guarantee a level of performance |

Performance guarantee | The act of guaranteeing an energy reduction value from installing the energy reduction system. The ESCO provides this guarantee to the energy user |

Guaranteed savings | The amount of guaranteed energy reductions that the ESCO provides to the user, which must be more than 80% of the target reduction value |

Performance guarantee period | The period to recover the entire project investment amount through the guaranteed energy savings |

Profit distribution | The distribution of profits resulting from surpassing the target reduction value between the energy user and the ESCO |

#### 2.2. Literature Review

#### 2.3. Real Options

Financial Options | Real Options |
---|---|

Stock price | Present value of expected incomes |

Exercise price | Costs of irreversible follow-on investment |

Time to maturity | Time until the investment opportunity disappears |

Volatility of stock return | Variability of project value |

Risk-free rate of return | Risk-free rate of return |

Methods | Advantages | Disadvantages |
---|---|---|

BSOPM | Simple to calculate the option value. | Only applicable to European options; Only works with normal distributions; Require advanced financial knowledge; Required assumptions limit the use of the model (price, volatility, duration); Able to deal with only one factor of uncertainty. |

BOPM | Effective when dealing with one factor of uncertainty; Provides project managers with an appropriate evolution of the underlying asset; Estimates the value of several option futures. | Requires advanced financial knowledge; Able to deal with only one factor of uncertainty. |

RADT | Allows mapping complex problems; Able to deal with multiple uncertainties; Enables decision makers to develop insights into ROs; Useful in the case of a possible drastic change in systems. | Does not provide the true value of the project; If the number of branches is high, it becomes too complicated and unclear. |

MCS | Demonstrates graphically the analysis results; Able to deal with multiple uncertainties; Not required to understand financial theory; Helpful for problems with path-dependency; User-friendly multiple document interface. | Lacks transparency; Hard methodology to implement with American options. |

HROs | Able to deal with multiple uncertainties; Combining the best of decision analysis and options analysis; Independent handling of technical and financial parts. | Hard methodology to implement (it requires highly sophisticated mathematical modeling skills). |

## 3. Research Methodology

#### 3.1. Profit Distribution Framework Using the Collar Option Model

_{0}, S

_{0}rests between the exercise price of put option (X

_{p}), the guaranteed savings, and the exercise price of the call option (X

_{c}), the target savings.

_{p}), the energy user can receive the difference from the guaranteed savings, and the value of the guarantee is positive. However, if S is larger than X

_{p}, the value of the guarantee from the energy user’s perspective is equivalent to 0. Therefore, depending on the change in S, the value of the guarantee is represented by the graph, which demonstrates the change of value of the put option.

_{c}), the ESCO can obtain a certain portion of the difference between the energy savings and the target savings as profit. However, if S is less than X

_{c}, there is no profit. Therefore, based on X

_{c}and the corresponding changes to S, the ESCO obtains the right to profit. The change in the value of the right to profit is shown in a graph that demonstrates the value of the call option.

**Figure 4.**Change in the value of the Energy Services Company’s (ESCO) right to profit according to fluctuation in the energy savings.

_{p}), and the ESCO has a call option where the target savings value is the exercise price (X

_{c}). As the guaranteed savings contract is a bilateral agreement between both parties, if one profits, the other faces a loss. Therefore, the value of the option possessed by each side must be equal. If the target and guaranteed savings are set contractually between the ESCO and the energy user, the value of the put option owned by the energy user is determined. Therefore, the profit distribution ratio (K) in Zone B, where the value of the call option is determined, can be modified to change the slope by using Equation (1) such that the value of the energy user’s guarantee and the ESCO’s right to profit are equal.

#### 3.2. Binomial Lattice Model to Calculate the Option Value

_{uu}node is obtained by calculating the expected value using the OV

_{uuu}node, and the OV

_{uud}node. In this way, the binomial tree in Figure 6 displays the process of repeated calculations on the present node after calculating the value of the call or put option using the equation at the final stage. Risk-neutral probabilities (p) are determined using Equation (5).

## 4. Applications

#### 4.1. Data Collection

^{2}and has been over 20 years since the completion of construction.

Category | Details | |
---|---|---|

Year Built | 1994 (20 years since completion) | |

Site area | 97,140.28 m^{2} | |

Principal use | Office space | |

Building size | 1 floor underground, 7 floors aboveground | |

Building area | 17,512.66 m^{2} | |

Total floor area | 30,147.63 m^{2} | |

Equipment | Absorption chiller-heater, steam boiler | |

Total project cost | Heat insulation | 317,570 USD |

Windows | 298,010 USD | |

Total | 615,580 USD |

Category | Estimated Value |
---|---|

Target savings | 88,200 USD/year |

Guaranteed savings | 70,560 USD/year |

Expected savings | 77,616 USD/year |

Performance guarantee period | 9 years |

Year | Interest Rate | Inflation Rate | Real Discount Rate | Average Discount Rate |
---|---|---|---|---|

2004 | 3.75 | 3.6 | 0.14 | 0.96 |

2005 | 3.57 | 2.8 | 0.74 | |

2006 | 4.36 | 2.2 | 2.11 | |

2007 | 5.01 | 2.5 | 2.45 | |

2008 | 5.67 | 4.7 | 0.93 | |

2009 | 3.23 | 2.8 | 0.42 | |

2010 | 3.18 | 3.0 | 0.17 | |

2011 | 3.69 | 3.6 | 0.09 | |

2012 | 3.43 | 2.2 | 1.20 | |

2013 | 2.70 | 1.3 | 1.38 |

Time | Investment Cost | Guaranteed Savings (Constant) | Guaranteed Savings (Discounted) | Guaranteed Savings (Discounted) Accumulated Sum |
---|---|---|---|---|

0 | 615,580 | |||

1 | 70,560 | 69,889 | 69,889 | |

2 | 70,560 | 69,225 | 139,114 | |

3 | 70,560 | 68,566 | 207,680 | |

4 | 70,560 | 67,914 | 275,594 | |

5 | 70,560 | 67,269 | 342,863 | |

6 | 70,560 | 66,629 | 409,492 | |

7 | 70,560 | 65,995 | 475,487 | |

8 | 70,560 | 65,368 | 540,855 | |

9 | 70,560 | 64,746 | 605,601 | |

10 | 70,560 | 64,131 | 669,731 |

#### 4.2. Results

_{p}) in Zone A is USD 607,416, which is the present value of the annual guaranteed savings. The exercise price of the call option (X

_{c}) in Zone B is USD 759,270, which is the present value of the annual target savings.

Year | Gas | Electricity | Energy Cost (USD) | Change Rate | Volatility | ||
---|---|---|---|---|---|---|---|

Used Amount (Nm^{3}) | Unit Price (USD/Nm^{3}) | Used Amount (KWh) | Unit Price (USD/KWh) | ||||

2004 | 58,717 | 0.925 | 2,575,682 | 0.127 | 381,425 | 10.00 | |

2005 | 74,759 | 0.925 | 2,743,321 | 0.127 | 417,554 | 9.05 | |

2006 | 47,324 | 0.925 | 2,442,482 | 0.127 | 353,970 | −16.52 | |

2007 | 48,783 | 0.925 | 2,649,536 | 0.127 | 381,615 | 7.52 | |

2008 | 42,286 | 0.925 | 2,526,969 | 0.127 | 360,039 | −5.82 | |

2009 | 65,515 | 0.925 | 2,637,817 | 0.127 | 395,604 | 9.42 | |

2010 | 51,018 | 0.925 | 2,520,640 | 0.127 | 367,313 | −7.42 | |

2011 | 82,245 | 0.925 | 2,661,946 | 0.127 | 414,144 | 12.00 | |

2012 | 69,083 | 0.925 | 2,629,320 | 0.127 | 397,825 | −4.02 | |

2013 | 50,736 | 0.925 | 2,544,804 | 0.127 | 370,121 | −7.22 |

_{f}) was set at 2% based on the 3-year government bond rate, and the unit of time is in years. Based on this, the rise rate (u), fall rate (d), and the risk-neutral probabilities (p) were calculated using Equations (2), (3), and (5); Table 9 reports the results.

Variables | Estimated Value |
---|---|

Underlying asset (S) | 668,158 USD |

Put option exercise price (X_{p}) | 607,416 USD |

Call option exercise price (X_{c}) | 759,270 USD |

Volatility(σ) | 10.0% |

Risk-free rate (r_{f}) | 2.00% |

Time interval | 1 year |

Rise Rates (u) | 1.105 |

Fall Rates (d) | 0.905 |

Risk-neutral probability (p) | 0.576 |

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

668,158 | 738,429 | 816,090 | 901,919 | 996,775 | 1,101,606 | 1,217,463 | 1,345,505 | 1,487,013 | 1,643,403 |

604,574 | 668,158 | 738,429 | 816,090 | 901,919 | 996,775 | 1,101,606 | 1,217,463 | 1,345,505 | |

547,041 | 604,574 | 668,158 | 738,429 | 816,090 | 901,919 | 996,775 | 1,101,606 | ||

494,984 | 547,041 | 604,574 | 668,158 | 738,429 | 816,090 | 901,919 | |||

447,880 | 494,984 | 547,041 | 604,574 | 668,158 | 738,429 | ||||

405,258 | 447,880 | 494,984 | 547,041 | 604,574 | |||||

366,693 | 405,258 | 447,880 | 494,984 | ||||||

331,797 | 366,693 | 405,258 | |||||||

300,223 | 331,797 | ||||||||

271,653 |

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

15,601 | 7752 | 2968 | 701 | 35 | 0 | 0 | 0 | 0 | 0 |

26,993 | 14,614 | 6186 | 1638 | 85 | 0 | 0 | 0 | 0 | |

45,073 | 26,745 | 12,654 | 3823 | 204 | 0 | 0 | 0 | ||

72,083 | 47,139 | 25,240 | 8916 | 491 | 0 | 0 | |||

109,348 | 79,094 | 48,592 | 20,775 | 1182 | 0 | ||||

155,580 | 124,237 | 88,651 | 48,357 | 2842 | |||||

205,472 | 178,411 | 147,538 | 112,433 | ||||||

251,901 | 228,741 | 202,158 | |||||||

295,224 | 275,619 | ||||||||

335,764 |

_{p}), target savings (X

_{c}), and volatility were selected as major variables for the sensitivity analysis. Guaranteed savings and target savings are the points where guaranteed value and right to profit are created. When each one changes, there is an impact on the guaranteed value and the right to profit. As volatility is an index that indicates the extent of energy savings uncertainty, it is likely to have a great influence on the ESCO profit distribution ratio.

_{p}) increases. Since the increased guaranteed savings (X

_{p}) means that a relatively high business safety of the ESCO is provided to the energy user through the guarantee, the ESCO profit distribution ratio increases. We also confirmed that the ESCO profit distribution ratio increases as the target savings (X

_{c}) increase. Since the increased target savings (X

_{c}) means that acquiring profit becomes relatively difficult following excessive performance, the right to profit decreases. As the guaranteed value that is calculated under the condition of fixed guaranteed savings (X

_{p}) and the volatility are identical, the ESCO profit distribution ratio increases relatively. Finally, we confirmed that the ESCO profit distribution ratio increases as volatility increases. An increase in volatility means greater uncertainty for energy savings, which eventually increases the ESCO profit distribution ratio.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

94,651 | 131,390 | 179,186 | 239,637 | 313,746 | 401,651 | 502,707 | 616,249 | 742,924 | 884,133 |

49,234 | 72,693 | 105,559 | 150,319 | 209,192 | 283,386 | 372,254 | 473,321 | 586,235 | |

19,704 | 31,498 | 49,766 | 77,475 | 118,322 | 176,092 | 252,589 | 342,336 | ||

4619 | 8182 | 14,492 | 25,669 | 45,467 | 80,535 | 142,649 | |||

0 | 0 | 0 | 0 | 0 | 0 | ||||

0 | 0 | 0 | 0 | 0 | |||||

0 | 0 | 0 | 0 | ||||||

0 | 0 | 0 | |||||||

0 | 0 | ||||||||

0 |

Category | Estimated Value |
---|---|

Value of guarantee | 15,601 USD |

Value of right to profit | 94,651 USD |

ESCO Profit distribution ratio | 16.5% |

X_{c} (USD) | Volatility (%) | X_{p} (USD) | |||||
---|---|---|---|---|---|---|---|

560,000 | 580,000 | 600,000 | 620,000 | 640,000 | 668,158 | ||

668,158 | 5% | 0.17% | 0.34% | 0.77% | 1.21% | 1.92% | 4.21% |

10% | 7.07% | 8.58% | 10.10% | 13.34% | 17.10% | 22.39% | |

15% | 16.64% | 19.07% | 23.15% | 27.24% | 31.32% | 37.07% | |

680,000 | 5% | 0.19% | 0.37% | 0.84% | 1.31% | 2.07% | 4.56% |

10% | 7.42% | 9.01% | 10.60% | 14.01% | 17.95% | 23.51% | |

15% | 17.19% | 19.71% | 23.93% | 28.15% | 32.37% | 38.31% | |

710,000 | 5% | 0.24% | 0.46% | 1.05% | 1.64% | 2.59% | 5.69% |

10% | 8.49% | 10.32% | 12.14% | 16.04% | 20.5% | 26.91% | |

15% | 18.78% | 21.54% | 26.15% | 30.76% | 35.37% | 41.86% | |

740,000 | 5% | 0.30% | 0.58% | 1.33% | 2.07% | 3.27% | 7.19% |

10% | 9.90% | 12.02% | 14.14% | 18.68% | 23.94% | 31.35% | |

15% | 20.70% | 23.74% | 28.82% | 33.90% | 38.98% | 46.13% | |

770,000 | 5% | 0.40% | 0.79% | 1.80% | 2.81% | 4.43% | 9.74% |

10% | 11.05% | 13.42% | 15.79% | 20.87% | 26.74% | 35.01% | |

15% | 23.06% | 26.44% | 32.09% | 37.75% | 43.41% | 51.38% | |

800,000 | 5% | 0.54% | 1.05% | 2.39% | 3.73% | 5.89% | 12.95% |

10% | 12.51% | 15.20% | 17.88% | 23.63% | 30.28% | 39.64% | |

15% | 24.88% | 28.53% | 34.63% | 40.74% | 46.85% | 55.44% |

## 5. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Pachauri, R.; Reisinger, A. IPCC Fourth Assessment Report; IPCC: Geneva, Switzerland, 2007. [Google Scholar]
- Pachauri, R.; Meyer, L. IPCC Fifth Assessment Report; IPCC: Copenhagen, Denmark, 2014. [Google Scholar]
- International Energy Agency (IEA). Energy Technology Perspectives 2010; IEA: Paris, France, 2010. [Google Scholar]
- Li, X.; Yang, F.; Zhu, Y.; Gao, Y. An assessment framework for analyzing the embodied carbon impacts of residential buildings in China. Energy Build.
**2014**, 85, 400–409. [Google Scholar] [CrossRef] - Zabaneh, G. Zero net house: Preliminary assessment of suitability for Alberta. Renew. Sustain. Energy Rev.
**2011**, 15, 3237–3242. [Google Scholar] [CrossRef] - Ionescu, C.; Baracu, T.; Vlad, G.; Necula, H.; Badea, A. The historical evolution of the energy efficient buildings. Renew. Sustain. Energy Rev.
**2015**, 49, 243–253. [Google Scholar] [CrossRef] - Pfeiffer, A.; Koschenz, M.; Wokaun, A. Energy and building technology for the 2000 W society-potential of residential buildings in Switzerland. Energy Build.
**2005**, 37, 1158–1174. [Google Scholar] [CrossRef] - Cellura, M.; Guarino, F.; Longo, S.; Mistretta, M. Different energy balances for the redesign of nearly net zero energy buildings: An Italian case study. Renew. Sustain. Energy Rev.
**2015**, 45, 100–112. [Google Scholar] [CrossRef] - Ministry of Land Infrastructure and Transport (MOLIT). Available online: http://www.molit.go.kr/USR/NEWS/m_71/dtl.jsp?id=95072458 (accessed on 2 July 2015).
- DeCanio, S.J. The Efficiency Paradox: Bureaucratic and Organizational Barriers to Profitable Energy-Saving Investments. Energy Policy
**1998**, 26, 441–454. [Google Scholar] [CrossRef] - Jaffe, A.B.; Stavins, R.N. The Energy-Efficiency Gap-What Does it Mean. Energy Policy
**1994**, 22, 804–810. [Google Scholar] [CrossRef] - Goldman, C.A.; Hopper, N.C.; Osborn, J.G. Review of US ESCO industry market trends: An empirical analysis of project data. Energy Policy
**2005**, 33, 387–405. [Google Scholar] [CrossRef] - Xu, P.; Chan, E.H.; Qian, Q.K. Success factors of energy performance contracting (EPC) for sustainable building energy efficiency retrofit (BEER) of hotel buildings in China. Energy Policy
**2011**, 39, 7389–7398. [Google Scholar] [CrossRef] - Larsen, P.; Goldman, C.; Satchwell, A. Evolution of the U.S. energy service company industry: Market size and project performance from 1990–2008. Energy Policy
**2012**, 50, 802–820. [Google Scholar] [CrossRef] - Painuly, J.; Park, H.; Lee, M.; Noh, J. Promoting energy efficiency financing and ESCOs in developing countries: Mechanisms and barriers. J. Clean. Prod.
**2003**, 11, 659–665. [Google Scholar] [CrossRef] - Patari, S.; Sinkkonen, K. Energy Service Companies and Energy Performance Contracting: Is there a need to renew the business model? Insights from a Delphi study. J. Clean. Prod.
**2014**, 66, 264–271. [Google Scholar] [CrossRef] - De T’Serclaes, P. Financing Energy Efficient Homes: Existing Policy Responses to Financial Barriers; International Energy Agency: Paris, France, 2007. [Google Scholar]
- Golove, W.H.; Eto, J.H. Market Barriers to Energy Efficiency: A Critical Reappraisal of the Rationale for Public Policies to Promote Energy Efficiency; Lawrence Berkeley National Laboratory: Berkeley, CA, USA, 1996.
- Brown, M.A. Market failure and barriers as a basis for clean energy policies. Energy Policy
**2001**, 29, 1197–1207. [Google Scholar] [CrossRef] - Du, P.; Zheng, L.Q.; Xie, B.C.; Mahalingam, A. Barriers to the adoption of energy-saving technologies in the building sector: A survey study of Jing-jin-tang, China. Energy Policy
**2014**, 75, 206–216. [Google Scholar] [CrossRef] - Zhang, X.; Platten, A.; Shen, L. Green property development practice in China: Costs and barriers. Build. Environ.
**2011**, 46, 2153–2160. [Google Scholar] [CrossRef] - Shi, Q.; Zuo, J.; Huang, R.; Huang, J.; Pullen, S. Identifying the critical factors for green construction—An empirical study in China. Habitat Int.
**2013**, 40, 1–8. [Google Scholar] [CrossRef] - Steinberger, J.; Niel, J.; Bourg, D. Profiting from megawatts: Reducing absolute consumption and emissions through a performance-based energy economy. Energy Policy
**2009**, 37, 361–370. [Google Scholar] [CrossRef] - Vine, E. An International Survey of the Energy Service Company (ESCO) Industry. Energy Policy
**2005**, 33, 691–704. [Google Scholar] [CrossRef] - Gan, D. Energy Service Companies to Improve Energy Efficiency in China: Barriers and Removal Measures. Procedia Earth Planet. Sci.
**2009**, 1, 1695–1704. [Google Scholar] - Jensen, J.O.; Nielsen, S.B.; Harsen, J.R. Greening Public Buildings: ESCO-Contracting in Danish Municipalities. Energies
**2013**, 6, 2407–2427. [Google Scholar] [CrossRef] - Li, J.; Colombier, M. Managing carbon emissions in China through building energy efficiency. J. Environ. Manag.
**2009**, 90, 2436–2447. [Google Scholar] [CrossRef] [PubMed] - Myers, S. Finance theory and financial strategy. Interfaces
**1984**, 14, 126–137. [Google Scholar] [CrossRef] - Trigeorgis, L.; Mason, S. Valuing managerial flexibility. Midl. Corp. Financ. J.
**1987**, 5, 14–21. [Google Scholar] - Copeland, T.; Antikarov, V. Real Options: A Practitioner’s Guide; Texere: New York, NY, USA, 2003. [Google Scholar]
- Martins, J.; Marques, R.C.; Cruz, C.O. Real Options in Infrastructure: Revisiting the Literature. J. Infrastruct. Syst.
**2015**. [Google Scholar] [CrossRef] - Cui, Q.; Johnson, P.; Quick, A.; Hastak, M. Valuing the Warranty Ceiling Clause on New Mexico Highway 44 Using a Binomial Lattice Model. J. Constr. Eng. Manag.
**2008**, 134, 10–17. [Google Scholar] [CrossRef] - Kim, B.; Lim, H.; Kim, H.; Hong, T. Determining the Value of Governmental Subsidies for the Installation of Clean Energy Systems Using Real Options. J. Constr. Eng. Manag.
**2012**, 138, 422–430. [Google Scholar] [CrossRef] - Park, T.; Kim, B.; Kim, H. Real Option Approach to Sharing Privatization Risk in Underground Infrastructures. J. Constr. Eng. Manag.
**2013**, 139, 685–693. [Google Scholar] [CrossRef] - Lee, H.W.; Choi, K.; Gambatese, J.A. Real Options Valuation of Phased Investments in Commercial Energy Retrofits under Building Performance Risks. J. Constr. Eng. Manag.
**2014**. [Google Scholar] [CrossRef] - Kashani, H.; Ashuri, B.; Shahandashti, S.M.; Lu, J. Investment Valuation Model for Renewable Energy Systems in Buildings. J. Constr. Eng. Manag.
**2015**. [Google Scholar] [CrossRef] - Mirzadeh, I.; Birgisson, B. Evaluation of Highway Projects under Government Support Mechanisms Based on an Option-Pricing Framework. J. Constr. Eng. Manag.
**2015**. [Google Scholar] [CrossRef] - Black, F.; Scholes, M. The Pricing of Options and Corporate Liabilities. J. Polit. Econ.
**1973**, 81, 637–659. [Google Scholar] [CrossRef] - Hull, J.C. Options, Futures, and Other Derivatives; Prentice-Hall: Upper Saddle River, NJ, USA, 1997. [Google Scholar]
- Shan, L.; Garvin, M.J.; Kumar, R. Collar Options to Manage Revenue Risks in Real Toll Public-Private Partnership Transportation Projects. Constr. Manag. Econ.
**2010**, 28, 1057–1069. [Google Scholar] [CrossRef] - Bettis, J.C.; Bizjak, J.M.; Lemmon, M.L. Managerial Ownership, Incentive Contracting, and the Use of Zero-Cost Collars and Equity Swaps by Corporate Insiders. J. Financ. Quant. Anal.
**2001**, 36, 345–370. [Google Scholar] [CrossRef] - Cox, J.; Ross, S.; Rubinstein, M. Option pricing: A simplified approach. J. Financ. Econ.
**1979**, 7, 229–263. [Google Scholar] [CrossRef] - Ho, P.S.; Liu, L.Y. How to Evaluate and Invest in Emerging A/E/C Technologies under Uncertainty. J. Constr. Eng. Manag.
**2003**, 129, 16–24. [Google Scholar] [CrossRef]

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## Share and Cite

**MDPI and ACS Style**

Lee, S.; Tae, S.; Shin, S.
Profit Distribution in Guaranteed Savings Contracts: Determination Based on the Collar Option Model. *Sustainability* **2015**, *7*, 16273-16289.
https://doi.org/10.3390/su71215816

**AMA Style**

Lee S, Tae S, Shin S.
Profit Distribution in Guaranteed Savings Contracts: Determination Based on the Collar Option Model. *Sustainability*. 2015; 7(12):16273-16289.
https://doi.org/10.3390/su71215816

**Chicago/Turabian Style**

Lee, Sanghyo, Sungho Tae, and Sungwoo Shin.
2015. "Profit Distribution in Guaranteed Savings Contracts: Determination Based on the Collar Option Model" *Sustainability* 7, no. 12: 16273-16289.
https://doi.org/10.3390/su71215816