# Sustainable Construction and Financing—Asset-Backed Securitization of Expressway’s Usufruct with Redeemable Rights

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review of Asset-Backed Securitization Product Pricing

## 3. Issuance Scale and Coupon Rate Pricing of Redeemable ABN

#### 3.1. The Issuance Steps of a Redeemable ABN

#### 3.2. NS Model and SV Model

#### 3.3. Two-Factor Vasicek Model and Kalman Filter Method

## 4. Empirical Simulation Analysis

#### 4.1. Basic Conditions and Assumptions of the Project

#### 4.2. Redeemable ABN Pricing

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Wang, D.; Li, Z.; Zhao, Z.; Zhao, X.B. Urban Infrastructure Financing in Reform-era China. Urban Stud.
**2011**, 48, 2975–2998. [Google Scholar] [CrossRef] - Pan, F.; Zhang, F.; Zhu, S.; Wojcik, D. Developing by borrowing? Inter-jurisdictional competition, land finance and local debt accumulation in China. Urban Stud.
**2017**, 54, 897–916. [Google Scholar] [CrossRef] - Filipović, D.; Willems, S. A term structure model for dividends and interest rates. Math. Financ.
**2020**, 30, 1461–1496. [Google Scholar] [CrossRef] - Sheraz, M.; Preda, V.; Dedu, S. Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling. Aims Math.
**2020**, 5, 300–310. [Google Scholar] [CrossRef] - Rojo-Suárez, J.; Alonso-Conde, A.B. Relative Entropy and Minimum-Variance Pricing Kernel in Asset Pricing Model Evaluation. Entropy.
**2020**, 22, 721. [Google Scholar] [CrossRef] [PubMed] - Liao, Z.; Zhang, H.; Guo, K.; Wu, N. A Network Approach to the Study of the Dynamics of Risk Spillover in China’s Bond Market. Entropy.
**2021**, 23, 920. [Google Scholar] [CrossRef] [PubMed] - Dunsky, R.M.; Ho, T.S. Valuing Fixed Rate Mortgage Loans with Default and Prepayment Options. J. Fixed Income
**2007**, 16, 7–31. [Google Scholar] [CrossRef] - Jacob, D.P.; Hong, T.C.H.; Lee, L.H. An Options Approach to Commercial Mortgages and CMBS Valuation and Risk Analysis. The Handbook of Non-agency Mortgage-backed Securities; Wiley: Grafton, NH, USA, 2000; pp. 465–495. [Google Scholar]
- Sharp, N.J.; Newton, D.P.; Duck, P.W. An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options. J. Real Estate Financ. Econ.
**2008**, 36, 307–342. [Google Scholar] [CrossRef] - Liu, Z.Y.; Fan, G.Z.; Lim, K.G. Extreme Events and the Copula Pricing of Commercial Mortgage-Backed Securities. J. Real Estate Financ. Econ.
**2009**, 38, 327–349. [Google Scholar] [CrossRef] - Hürlimann, W. Valuation of Fixed and Variable Rate Mortgages: Binomial tree versus analytical approximations. Decis. Econ. Financ.
**2012**, 35, 171–202. [Google Scholar] [CrossRef] - Qian, X.S.; Jiang, L.S.; Xu, C.L.; Wu, S. Explicit formulas for pricing of callable mortgage-backed securities in a case of prepayment rate negatively correlated with interest rates. J. Math. Anal. Appl.
**2012**, 393, 421–433. [Google Scholar] [CrossRef] [Green Version] - Fan, G.Z.; Sing, T.F.; Ong, S.E. Default Clustering Risks in Commercial Mortgage-Backed Securities. J. Real Estate Financ. Econ.
**2012**, 45, 110–127. [Google Scholar] [CrossRef] - Fermanian, J.D. A Top-Down Approach for Asset-Backed-Securities: A Consistent Way of Managing Prepayment, Default and Interest Rate Risks. J. Real Estate Financ. Econ.
**2013**, 46, 480–515. [Google Scholar] [CrossRef] - Hayre, L.S. Understanding Option-adjusted Spreads and Their Use. J. Portf. Manag.
**1990**, 16, 68–69. [Google Scholar] [CrossRef] - Green, R.K. Chapter 11-The Yield Curve, Monte Carlo Methods, and the Option-Adjusted Spread. In Introduction to Mortgages & Mortgage Backed Securities; Elsevier Inc.: Amsterdam, The Netherlands, 2014. [Google Scholar]
- Dong, J.C.; Liu, J.X.; Wang, C.H.; Yuan, H.; Wang, W.J. Pricing Mortgage-Backed Security: An Empirical Analysis. Syst. Eng.-Theory Pract. Online
**2009**, 29, 46–52. [Google Scholar] [CrossRef] - Vasicek, O. An Equilibrium Characterization of the Term Structure. J. Financ. Econ.
**1977**, 5, 627. [Google Scholar] [CrossRef] - Vázquez-Vázquez, M.; Alonso-Conde, A.B.; Rojo-Suárez, J. Are the Purchase Prices of Solar Energy Projects under Development Consistent with Cost of Capital Forecasts? Infrastructures
**2021**, 6, 95. [Google Scholar] [CrossRef] - Falbo, P.; Paris, F.M.; Pelizzari, C. Pricing Inflation Linked Bonds. Quant. Financ.
**2010**, 10, 279–293. [Google Scholar] - Longstaff, F.A.; Schwartz, E.S. Valuing American Options by Simulation: A Simple Least Squares Approach. Rev. Financ. Stud.
**2001**, 14, 113–147. [Google Scholar] [CrossRef] [Green Version] - Fabozzi, F.J. Fixed Income Analysis; John Wiley & Sons: Hoboken, NJ, USA, 2007; Volume 6. [Google Scholar]
- Nelson, C.; Siegel, A.F. Parsimonious Modeling of Yield Curves. J. Bus.
**1987**, 60, 473–489. [Google Scholar] [CrossRef] - Svensson, L.E. Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994. Natl. Bur. Econ. Res. 1994. [CrossRef]

Parameter | ${\mathit{\beta}}_{\mathbf{0}}$ | ${\mathit{\beta}}_{\mathbf{1}}$ | ${\mathit{\beta}}_{\mathbf{2}}$ | ${\mathit{\beta}}_{\mathbf{3}}$ | ${\mathit{\tau}}_{\mathbf{1}}$ | ${\mathit{\tau}}_{\mathbf{2}}$ |
---|---|---|---|---|---|---|

Value | 0.0421 | −0.041834 | 0.113045 | −0.129213 | 1.773025 | 1.887328 |

Maturity (Years) | 1 | 2 | 3 | 5 | 10 | 20 | 30 |
---|---|---|---|---|---|---|---|

Spot Rate (%) | 0.011381 | 0.015799 | 0.019473 | 0.025125 | 0.033514 | 0.036471 | 0.038727 |

Parameter | ${\mathit{\delta}}_{\mathbf{0}}$ | ${\mathit{\delta}}_{\mathbf{1}}$ | ${\mathit{\delta}}_{\mathbf{2}}$ | ${\mathit{\lambda}}_{\mathbf{1}}$ | ${\mathit{\lambda}}_{\mathbf{2}}$ | ${\mathit{q}}_{\mathbf{1}}$ | ${\mathit{q}}_{\mathbf{2}}$ |
---|---|---|---|---|---|---|---|

Value | 0.0573 | 0.0262 | 0.0163 | 0.2013 | 0.0837 | 0.0464 | 0.0493 |

Senior A Bonds, Class AAA, Coupon Rate 4.21%, The Issuance Period Is 20 Years | |||||

Yield Change (%) | Duration | Convexity Change (%) | Price Change (%) | Initial Price | New Price |

+100 | 13.4450 | −5.4113 | 12.2433 | 100 | 87.7567 |

+50 | 13.6753 | −2.9661 | −6.3872 | 100 | 93.6128 |

+10 | 13.8575 | −0.5393 | −1.3224 | 100 | 98.6775 |

0 | 13.9027 | 0.0000 | 0.0000 | 100 | 100.0000 |

−10 | 13.9478 | 0.5394 | 1.3459 | 100 | 101.3459 |

−50 | 14.1269 | 2.6972 | 6.9730 | 100 | 106.9730 |

−100 | 14.3474 | 5.3929 | 14.5927 | 100 | 114.5927 |

Senior B bonds, Class AA+, Coupon Rate 6.38%, The Issuance Period Is 25 Years | |||||

Yield Change (%) | Duration | Convexity Change (%) | Price Change (%) | Initial Price | New Price |

+100 | 13.1436 | −10.6206 | −11.9497 | 100 | 88.0503 |

+50 | 13.5989 | −5.4212 | −6.2801 | 100 | 93.7199 |

+10 | 13.9720 | −1.1017 | −1.3086 | 100 | 98.6914 |

0 | 14.0664 | 0.0000 | 0.0000 | 100 | 100.0000 |

−10 | 14.1613 | 1.1103 | 1.3362 | 100 | 101.3362 |

−50 | 14.5451 | 5.6363 | 6.9717 | 100 | 106.9717 |

−100 | 15.0338 | 11.4788 | 14.7284 | 100 | 114.7284 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, Q.; Tjia, L.Y.-n.; Wang, B.; Ersoy, A.
Sustainable Construction and Financing—Asset-Backed Securitization of Expressway’s Usufruct with Redeemable Rights. *Sustainability* **2021**, *13*, 9113.
https://doi.org/10.3390/su13169113

**AMA Style**

Zhang Q, Tjia LY-n, Wang B, Ersoy A.
Sustainable Construction and Financing—Asset-Backed Securitization of Expressway’s Usufruct with Redeemable Rights. *Sustainability*. 2021; 13(16):9113.
https://doi.org/10.3390/su13169113

**Chicago/Turabian Style**

Zhang, Qiming, Linda Yin-nor Tjia, Biyue Wang, and Aksel Ersoy.
2021. "Sustainable Construction and Financing—Asset-Backed Securitization of Expressway’s Usufruct with Redeemable Rights" *Sustainability* 13, no. 16: 9113.
https://doi.org/10.3390/su13169113