Investment Analysis of Low-Carbon Yard Cranes: Integrating Monte Carlo Simulation and Jump Diffusion Processes with a Hybrid American–European Real Options Approach
Abstract
:1. Introduction
2. Literature Review
2.1. Clean Energy Applications and Challenges in the Port Energy Transition
2.2. Analysis of Uncertainties in Hydrogen-Powered Yard Cranes Investments
2.3. Applications, Limitations, and Improvements of Real Options Theory
3. Methodology
3.1. Simulation of Uncertainty Factors
3.1.1. Hydrogen Price
3.1.2. Carbon Price
3.1.3. Technology Maturity
3.2. Cost–Benefit Model
- The annual hydrogen energy consumption cost () refers to the total yearly cost of hydrogen energy consumption, which varies according to the hydrogen price and the total number of hydrogen-powered yard crane units. It consists of the product of the number of hydrogen-powered yard cranes invested in (), the number of TEUs of containers to be handled by each hydrogen-powered yard crane per year (), the amount of hydrogen used by the hydrogen-powered yard cranes for each TEU handled (), and the price of hydrogen (), as shown in Equation (11):
- The annual periodic maintenance cost () refers to the yearly maintenance and servicing expenses for hydrogen-powered yard crane equipment, which vary with the total number of units deployed. It consists of the product of the number of hydrogen-powered yard cranes invested in () and the annual maintenance cost (), as shown in Equation (12):
- The annual hydrogen power yard crane equipment investment cost () refers to the total one-time expenditure for the procurement and installation of the equipment, which varies with the number of units. It consists of the product of the number of hydrogen power yard cranes () invested in construction and the annual investment cost per hydrogen power yard cranes (), as shown in Equation (13):
- The annual savings () is the sum of the annual electrical energy cost savings () and annual maintenance cost savings () that the port can realize after completing the equipment transition relative to conventional yard cranes, given that the port has the same number of hydrogen yard cranes and conventional yard cranes, as shown in Equation (15):
- The annual carbon emission reduction benefit () refers to the economic gains generated from the reduction in carbon emissions during the operation of hydrogen-powered yard crane equipment. This benefit varies with both the carbon price and the total number of deployed units. It consists of the product of the number of hydrogen-powered yard crane equipment invested in (), the number of TEUs of containers to be handled by each yard crane per year (), the carbon emissions reduced by each TEU handled by the hydrogen-powered yard cranes () and the carbon price (), as shown in Equation (18):
- The government-related subsidy () consists of the product of the number of hydrogen-powered yard crane equipment invested in the construction () and the government subsidy for the construction of each hydrogen-powered yard cranes (), as shown in Equation (19):
3.3. Real Options Model Solution Methods
- Set and enter the following parameters: the number of simulation paths, i.e., the number of simulations ; the investment time node contained in each simulation path, i.e., the investment decision time node .
- Use the geometric Brownian motion, Markov chain with jump diffusion term and stochastic volatility, and learning curve methods from Section 3.1 to simulate the price of carbon (Equations (3)–(8)), the price of hydrogen (Equations (1) and (2)), and the price of the investment in equipment (Equation (9)).
- Calculate the return on investment for each phase of the investment using the cost–benefit model in Section 3.2 (Equation (20)).
- Based on the return on investment for each stage of investment in the previous step (3), perform a least squares regression on the moments of investment other than the final stage, and fit a model to estimate the future expected value (Hold Value) for each stage.
- Start backtracking from the last investment stage, if Exercise Valued > 0, invest, if Exercise Valued < 0, start backtracking.
- At stage , compare Exercise Valued with Hold Value , invest if Exercise Valued is higher, and continue backtracking if Hold Value is higher.
- After determining the investment time of this path through backtracking, calculate the present value of these real options to obtain the real options investment value of this path.
- Repeat the least squares Monte Carlo simulation and compute the average of real options across all paths.
- Set and enter the following parameters: the number of simulation paths, i.e., the number of simulations ; the investment time nodes contained in each simulation path, i.e., the investment decision time node ;
- Use the geometric Brownian motion, Markov chain with jump diffusion term and stochastic volatility, and learning curve methods in Section 3.1 to simulate the price of carbon (Equations (3)–(8)), the price of hydrogen (Equations (1) and (2)), and the price of the equipment investment (Equation (9)).
- Calculate the return on investment for each phase of the investment using the cost–benefit model in Section 3.2 (Equation (20)).
- Calculate the value of the real options from the first stage onwards.
- If the current real options value is greater than zero, i.e., investment is made, the calculation of the European real options value for the next period continues. If the current real options value is equal to zero, i.e., no investment is made, the path is terminated.
- Calculate the discounted value of the real options value for all stages and sum to obtain the value of the real options investment for the path.
- Repeat the Monte Carlo simulation and compute the average of real options across all paths.
- refers to the final value of the option, that is the average present value of the option across all simulated paths.
4. Case Study Applications
4.1. Design of Real Options Program for Yard Crane Investment
4.2. Analysis of Investment Decision Results
4.2.1. Uncertainty Factor Simulation Results
- Hydrogen price simulation
- Carbon price simulation
- Simulation of changes in equipment investment costs
4.2.2. Analysis of Investment Decision-Making Results
4.3. Sensitivity Analysis
4.3.1. Hydrogen Price Drift Rate and Volatility Rate
4.3.2. Carbon Price Drift Rate and Volatility Rate
4.3.3. Learning Curve Parameters
5. Discussion
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Description | Value | Unit |
---|---|---|---|
Investment cost for the first hydrogen-powered yard crane | 2.4 | Million RMB | |
Number of standard containers to be handled per yard crane per year | 40,000 | TEU | |
Hydrogen consumption for handling one standard container with a hydrogen-powered yard crane | 0.2 | kg/TEU | |
Annual maintenance cost for each hydrogen-powered yard crane | 10,000 | RMB/unit | |
Electricity cost for handling one standard container with a traditional yard crane | 6 | RMB/TEU | |
Annual maintenance cost for each traditional yard crane | 64,000 | RMB/Unit | |
Carbon emission reduction per standard container handled by hydrogen-powered yard crane | 2.1 | kg/TEU | |
Project duration | 15 | Year | |
Discount rate | 0.06 | —— | |
Service life of hydrogen-powered yard crane equipment | 15 | Year | |
Government subsidy for construction of each hydrogen-powered yard crane | 500,000 | ||
Initial hydrogen price | 30 | RMB/kg | |
Drift rate of hydrogen price | −0.03 | —— | |
Fluctuation rate of hydrogen price | 0.03 | —— | |
Initial carbon price | 48 | RMB/ton | |
Drift rate of carbon price | 0.038 | —— | |
Fluctuation rate of carbon price | 0.035 | —— | |
Volatility mean reversion rate | 1.0 | —— | |
Long-term average of volatility | 0.02 | —— | |
Volatility of volatilities | 0.05 | —— | |
Relevance of the Brownian motion | 0.25 | —— | |
Jumping intensity | 0.05 | —— | |
Mean value of jumps | 0 | —— | |
Standard deviation of jump amplitude | 0.1 | —— | |
Proportion of equipment cost reduction as technology matures | 0.1 | —— |
Construction Process | 2021–2025 | 2026–2030 | 2031–2035 |
---|---|---|---|
6 | 15% | 5% | 1% |
19 | 80% | 40% | 10% |
38 | 4% | 55% | 80% |
76 | 1% | 5% | 9% |
Expected construction process | 18 | 32 | 40 |
2021–2025 | 2026–2030 | 2031–2035 | Maximum Number of Investment Units | Investment Strategy | |
---|---|---|---|---|---|
Project 1 | 2021–2035 12 American Real Options | 12 | Conservative | ||
Project 2 | 2021–2025 12 European Call Real Options | 2026–2035 14 American Call Real Options | 26 | Cautious up front, flexible later | |
Project 3 | 2021–2030 12 American Call Real Options | 2031–2035 14 European Call Real Options | 26 | Moderate flexibility at the front end, stable investment at the back end | |
Project 4 | 2021–2025 12 European Call Real Options | 2026–2030 14 European Call Real Options | 2031–2035 8 European Call Real Options | 34 | Aggressive expansionist |
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Yang, A.; Li, A.; Li, Z.; Sun, Y.; Gao, J. Investment Analysis of Low-Carbon Yard Cranes: Integrating Monte Carlo Simulation and Jump Diffusion Processes with a Hybrid American–European Real Options Approach. Energies 2025, 18, 1928. https://doi.org/10.3390/en18081928
Yang A, Li A, Li Z, Sun Y, Gao J. Investment Analysis of Low-Carbon Yard Cranes: Integrating Monte Carlo Simulation and Jump Diffusion Processes with a Hybrid American–European Real Options Approach. Energies. 2025; 18(8):1928. https://doi.org/10.3390/en18081928
Chicago/Turabian StyleYang, Ang, Ang Li, Zongxing Li, Yuhui Sun, and Jing Gao. 2025. "Investment Analysis of Low-Carbon Yard Cranes: Integrating Monte Carlo Simulation and Jump Diffusion Processes with a Hybrid American–European Real Options Approach" Energies 18, no. 8: 1928. https://doi.org/10.3390/en18081928
APA StyleYang, A., Li, A., Li, Z., Sun, Y., & Gao, J. (2025). Investment Analysis of Low-Carbon Yard Cranes: Integrating Monte Carlo Simulation and Jump Diffusion Processes with a Hybrid American–European Real Options Approach. Energies, 18(8), 1928. https://doi.org/10.3390/en18081928