Ordinary static cash flow is a method of discounting future cash flows generated by an asset at a fixed discount rate using a simple model without considering the effects of changes in interest rates and fluctuations in the early repayment rate.In asset securitization pricing studies, for the issue of cash flows, Dunsky and Ho. (2007) proposed to analyze the expected future cash flows that can be generated by the project and determine the discount rate at which the cash flows are discounted in order to obtain the net present value of the underlying project.

The static discounted cash flow method (SCF) method has the simplest expression, and the basic formula for this model is P = ∑ i = 1 n C F i 1 + r i

In this model, the price of the securitized product is denoted by P, the number of periods of the product is denoted by n, CF is the expected cash flow in period i, and r is the discount rate.

The biggest advantage of the static discounted cash flow method is that it is simple to use and easy to calculate to obtain the desired result quickly. However, this method also has the disadvantage that it does not consider any changes in interest rates in the best-case scenario, so the results obtained by this method may deviate significantly from the actual situation. In the actual pricing of PPP projects ABS product, changes in interest rates and early repayment rates are often considered. Thus, the pricing of PPP asset products obtained from this model can only be used as a basic reference and cannot be applied to the actual pricing of PPP projects ABS product.

The biggest optimization between the static spread (SS) method and the original static discounted cash flow method is that it considers the yield to maturity of treasury bonds. This method sets the discount rate as the yield of each maturity on the yield-to-maturity curve of Treasury bonds, plus a set fixed spread. The price of the bond is determined using this method as a measure of the entire yield-to-maturity curve.

The most concise formula for the Static Spread Method (SS) is: P = ∑ i = 1 n C F i 1 + r i + s i

In this model, the product price is denoted by P, CF is the expected cash flow in period i, r is the yield of treasury bonds with different maturities, and S is the static spread.

The static and static cash flow methods do not differ significantly when cash flows are concentrated but can differ significantly when cash flows are more dispersed.

The static spread method considers the changes in yields to maturity of different treasury bonds and adds changes in interest rates to the application of the model, yielding more accurate results than the cash flow model. However, the spread model does not consider fluctuations in early repayment rates caused by different interest rate paths, which are not well addressed by the spread model because of the uncertainty of future cash flows in PPP projects ABS product and the refinancing interest rates may change, which will affect the pricing of the overall PPP projects ABS product. However, the static spread method does not consider these factors in the model and therefore does not accurately measure the price of the PPP projects ABS product.

The option-adjusted spread (OAS) method is better than the static spread method, which considers early repayment of future cash flows from the underlying asset. This method combines the static cash flow method and static spread method and integrates interest rate risk by considering as many interest rate paths as possible, with the main paths utilized being the binomial tree pricing model interest rate path, Monte Carlo model interest rate path, and finite difference interest rate path.

Dunn and McConnell. (1981) predicted the likelihood of early repayment based on the movement of interest rates and proposed an option-adjusted spread method applied to mortgage-backed securities. Subsequently, they proposed an early repayment model based on the assumption of rationality in 2001. Researchers such as Kalotay et al. (2004), adapted and modified the method to broaden its pricing scope.

The option attribute in the OAS method applied in the pricing of PPP projects ABS product, in the concept of an option, for the purchaser of a call option, the purchaser has the right to buy a certain underlying amount at a price specified by the seller during the agreed period. For the buyer of a call option, the gain is derived from the increase in the price of the option due to an increase in the price of the underlying option and the gain from the exercise of the option. Still, if there is a fall in the price, the buyer’s loss will only be the cost of buying the call option. By analogy with a debtor who raises money in capital markets, the risk of early repayment is treated as a call option.

The basic form of the option-adjusted spread (OAS) method model is P = 1 T ∑ T = 1 T ∑ S = 1 S C F S , T 1 + R S T + O A S

In this model, P refers to the price of the securitized product, R is the interest rate for period S under the Tth path, T is the total number of bars in the simulated interest rate, and CF is the cash flow for period i under the Sth path.

The key to this method is how to use the binomial tree model to determine the path of the interest rate, set to build a binomial tree where the value of the change is ∂ , and the change at each time is the same as t. The interest rate is initially set to R, so if the interest rate rises, it is recorded as Ra; if the interest rate falls, it is recorded as Rb. If the interest rate decreases, then it is Rb, again, at the next moment, there are three possible scenarios R a 2 , R, R b 2 , and by analogy, there should be n+1 possible outcomes for the interest rate in the nth cycle of the subsequent binomial tree loop. Figure 2 shows the correspondence between interest rates of the binomial tree paths.

In its application, the OAS method can simulate early repayment and default behavior under different interest rate change paths and can obtain more reasonable forecasts of future cash flows in the pricing of PPP securitization products. The OAS model considers changes in early repayment rates and interest rates and is closer to reality than the static cash flow and static spread methods. The scenarios considered using this model are more complex, and thus, the requirements for the overall model are high, requiring the design of an option-adjusted spread model suitable for the operation of the product in the pricing of the product.

The Monte Carlo model is currently widely used in finance as a representation of high value, and high flexibility in the field of finance, and the method was first applied to the pricing of financial securitization products by Paulier in 1977.McConnel and Singh. (1994) used a Monte Carlo simulation pricing method for fixed-rate and variable-rate mortgage bonds. In an exploration of PPP project financing, Yuan et al. (2011) constructed a Monte Carlo-based model for optimising the financing structure and analysed the main influencing factors and their mechanism of action.

Compared with other models, it is clear that the Monte Carlo model is more comprehensive in its consideration of factors, especially the choice of interest rates under multiple paths, and is more in line with changes in financial markets, making it highly applicable. The Monte Carlo model ensures independence of the predicted standard errors, and the results are more realistic.

In its current application, the Monte Carlo model relies heavily on computers to simulate several possible paths to obtain the value of the asset under the current path, and the risk-free rate can be applied to discount the current value of the entire asset.

In the pricing of ABS products, it is the value at the moment T = 0 that is required, that is, the unconditional expectation of the discounted payment. The probability distributions of the parameter estimates calculated by Monte Carlo model simulations are complex; therefore, the workload of calculating the simulation parameter estimates using probability distribution methods is high, and in practice, the first-order moments of the discounted payments are generally used.

Paulier systematically described the methodology regarding the use of Monte Carlo models in the pricing of financial securitization products. The basic formula for the model is: d P t = r P t d t + σ P t d B t Where P t denotes the price of the underlying asset at time t, t denotes the time to maturity, r denotes the market risk-free rate, σ is the volatility of the underlying asset’s return, and B(t) is Brownian motion under a risk-neutral measure.

In the pricing of ABS products, it can be assumed that the ABS product’s underlying asset is C, the risk-free interest rate is assumed to be a constant N, and this product pays out at the end of the period. We analyze the application of the Monte Carlo model to the pricing of PPP ABS products and calculate the present value of the product by following these steps.

1. Simulation of the stochastic process obeyed by all underlying assets of the PPP ABS product.

However, the Monte Carlo model also has great limitations, the main one of which is that the experimental difficulty is relatively large because Monte Carlo needs to perform a large number of simulation experiments; if it encounters complex securitization products, it will certainly increase the experimental difficulty substantially, and the processing of obtaining more data is also more troublesome. Therefore, in response to this problem, scholars at home and abroad have made some improvements, most of which lie in the basic variance in the experiment, which commonly includes importance sampling, pairwise variables, and control variables.

As the first PPP ABS project in China, this project has good reference value for developing PPP projects in China and the ABS of PPP projects. Table 2 shows the basic information about this particular scheme.

Figure 3 shows the transaction structure of the special scheme.In the whole plan issue, the whole plan is proposed by China Merchants Capital Management as the initiator of the whole plan, the project is set up, Huaxia Happiness Party as the guarantor is providing external credit enhancement, and Jutong Public Utilities as the original equity owner and the service provider of the assets, which entrusts China Postal Savings Bank as the supervising bank to manage the funds for it, and Postal Savings Bank as the custodian, and China Merchants Securities Company.

As the first PPP ABS project issued in China, the overall transaction structure and issuance method of the asset securities of the Huaxia Happiness Gu’an PPP project, from the initial construction to the start of the issuance and finally identified as the first exemplary PPP ABS project in China, has high reference value for subsequent PPP ABS projects.

The total target size of the Huaxia Happiness PPP ABS Special Programme is RMB 706 million. Table 3 provides basic information on this securities issue.The target size of senior asset-backed securities is RMB 672 million, representing 95% of the total size. The target size of Tier 1 asset-backed securities was RMB58 million, representing 8% of the total size; the target size of Tier 2 asset-backed securities was RMB 80 million, representing 11% of the total size; the target size of Tier 3 asset-backed securities was RMB 102 million, representing 14% of the total size; the target size of Tier 3 asset-backed securities was RMB 128 million, representing 18% of the total size; the Tier 5 asset-backed securities project size was RMB 143 million, accounting for 20% of the total size; and the target size of the Level 6 asset-backed securities project was RMB 159 million, accounting for 23% of the total size. The size of subordinated asset-backed securities raised was RMB 36 million, accounting for 5% of the total size.

Throughout the special plan, the underlying assets are the rights of the original equity holders to collect heating charges from heating customers for a specific period as a result of the provision of heating services in the Gouan Industrial Park, which are allocated to the special plan by the original equity holders on the delivery date and are still recorded in the underlying asset documents.

In the Huaxia PPP project, according to the standard terms and conditions entered into, the underlying assets are the heat supply service provided by the original equity holders to the industrial park on the delivery date following the relevant documents and the heat supply fee income charged to the special plan, set for the period from 2017 to March 2023.

The PPP project heating tariff rights refer to the heating tariff revenue enjoyed by Jutong utilities for the provision of heating services under the PPP project.

After the project is put into operation, a fee agreement is signed with the residents in September-November each year, with cash or credit cards as the method of payment, and with the companies in September-December to collect the heating fee by transfer. According to the agreements signed and the negotiations with the authorities, the price per square meter of heat was 22 RMB for residents and 38 RMB per square meter for non-residents, looking for statistics Table 4 shows the from 2013 to 2016 before the project was signed.

Based on statistical information, as well as the project’s publicly available accounting reports, the forecast assumptions are divided into two segments for residents and businesses and are assumed separately when making the forecast.

The main factors underlying projections regarding future cash flows for residents are the total area of residential heating bids, heating rates, and tariffs. The main assumptions regarding cash flow projections are as follows.

1. No legal risks are associated with the right to receive proceeds and the entire valuation base date.

The final overall resident projection assumption assumes that 80% of the completed homes are occupied and under contract in the current year, with the remaining 20% expected to contract the next year. The total forecast resulted in a combined cash flow of RMB551,443,500 from 2017 to 2022.

For enterprise heating, the main elements considered are the total area of the tender section and the tariff, where the main factors that will have an impact on the tariff are local GDP, local fiscal revenue, the number of enterprises in the park, and the amount of fixed asset investment completed in the park. The following assumptions are made for enterprise cash flow.

1. No legal risks are associated with the right to receive proceeds and the entire valuation base date.

Using the above assumptions on the total surface of the impact factors of the heating section of the enterprise, the weights are assigned to 20% of the regional GDP, 15% of the amount of fixed asset investment, 35% of the fiscal revenue, and 30% of the number of enterprises in the park. The data are adjusted and collated for events that are highly likely to have an impact. Table5 shows the income forecasts for residents and companies.

It is possible to see the totals for 2017–2022 for the overall income of residents and businesses for 2017–2019, which can then be used as a reference for pricing products when pricing assets.

Based on the overall project analysis, the cash flow projections for the PPP projects under normal circumstances are made into a chart from 2017-2022, as shown in Table 6 below.

Conduct a first test cash flow analysis of a simulated scenario stress situation.

In this scenario, cash flow is projected to be under pressure if there is an increase in yield, and the cash flow is projected to continue from year four to year 6, with the expected yield increasing by 10 BP based on each additional year of the measured yield according to the issue term, on which the measured yield increases by 50 BP per tranche, as shown in Table 7 below.

As seen from the Table 7 above, in this scenario, all the underlying assets generate cash flows to cover each tranche of senior asset-backed securities a multiple of one time or more to pass the stress test.

Conducting a simulated scenario stress situation in the second test cash flow analysis.

Changes in heating cash flow income may be affected by changes in the total heating tender area, heating charges, heating tariffs, and payback rates.

For the changes in the total residential heating bid area, the residential heating area for 2017-2022 will be increased according to the average of the annual increase in heating area from 2013-2016, and the bid area will not be increased after 2020.

For businesses, another criterion is used to increase their heating area from 2017-2022 to in increments of 1.1 times the average annual increase in heating area from 2013-2016.

Another important influence is in the adjustment of the heating rate, through the statistics for past historical data, as the heating rate increased in the first 5 years and has remained stable since then, Table 8 shows the cash flow measurement.

The heating fee collection rate refers to historical data, both residential and non-residential heat are 100%, combined with the heating rate change scenario, it is reasonable to assume that the heating fee collection rate is 97%, assuming that the special plan continues to survive from the fourth to the sixth year, the expected yield is increased by 10BP for each additional year of the issue term, and a new cash flow forecast Table 9 is made for comparison.

The calculations based on the above table and various assumptions made in the current stress environment result in the following Table 10 of cash flows.

The Huaxia Happiness Heating Revenue PPP Asset Securitisation Project, based on the cash flow forecast from 2017 to 2022, the project issue is expected to arrive at the interest rate in 2018–2023. This project issue has a senior-1 interest rate of 3.9%, a senior-2 rate of 5.0%, and the senior 3–6 rate of 5.2%; from this information, we can see that senior-1 and senior-2 are the first 2 years of interest payment rate; the project does not open for an interest rate adjustment, repurchase, and sale back until the end of the third year, so with a target interest rate of 5.2% for the project, the overall term of the project is 6 years.

The 6-year Treasury yield in the bond market is the underlying factor for the risk-free rate in the model, with an average rate r of approximately 3.1%, as shown in Figure 4 below.

The volatility of interest rates was used in the research of Lin Hai and Zheng Zhenlong, which set the volatility of interest rates at 0.4%, that is, ∂ = 0.4% in the model, and the upward multiplier of interest rate changes was obtained as u = 1.004008 and d = 0.996008 according to u = e σ Δ t , which resulted in a binomial tree of interest rates. Set the time T for each segment to 1 year, for 6 years. This is depicted in the Figure 5.

From this, it can be seen that, under multiple interest rate paths, the interest rate on each path is obtained by adding the interest rate changes and plotted in Figure 6. There are 64 interest rate paths in total. The asset-backed security price volatility is set to 10.5% of the corporate bond volatility index using the DerivaGem software designed explicitly for option pricing,and plotted in Figure 6.

The value of the option at the zero moment is calculated, and the cash flows are discounted separately for each period to obtain the theoretical price on each path, call option price, and put option price. And the binomial tree of option prices is drawn based on the interest rate binomial tree as shown in Figure 7.

From the binomial tree model of option prices, the price under 64 paths can be obtained, with the second cell on the graph representing the price of the lookalike option. The posting limit for the option was found to be RMB 105.63 using arithmetic averaging. The previous pricing theory on ABS, which is equivalent to a call option for project redeemers, so the final price of the ABS product = the discounted value of the expected future cash flows - the option value of the early repayment by the originator. Therefore, the final price of the ABS product is 105.63–8.8 = 96.83.

Compared to the issue price of RMB 100 for the Huaxia Happiness PPP ABS project, the price of RMB 96.83 obtained using the option-adjusted spread method is less than that of RMB 100.

In the Monte Carlo simulation method, the underlying idea is to build a probabilistic model or stochastic process first, such that its parameters are equal to the solution of the problem. The statistical characteristics of the stochastic parameters were then computed by observation and random sampling of the model or process, and an approximation of the solution was obtained. The newly developed software Oracle-Crystal Ball was used to obtain a better experiment structure.

Based on the data in the previous section on cash flow projections and factors affecting the pricing of ABS products for PPP projects, changes in the total area of heating bids, heating fees, heating tariffs, and payback ratios may affect changes in heating cash flow revenue, according to the plan for the whole park will be 1,435,967 square meters of new heating bids in 2017, 5,67,775 square meters in 2018 square meters in 2017, 5,67,775 square meters in 2018, and 136,310 square meters in 2019, and is expected to remain the same overall for 2020–2022. The heating rates will be used as a baseline for the entirety of the previous 2013-2016 period and are expected to increase by 3% per annum in 2017–2019 at the time of the assumptions and remain consistent with assumption 2 in 2020–2022, assuming no change overall. The rate of return will be set to the ideal state, that is, 100% for the entire set period of 2017–2022, and no consideration will be given to national policy changes, industry policies, and other unavoidable factors. This led to the construction and derivation of the model. The hypothetical parameter estimation was performed as shown in Table 12.

Based on the actual situation of the Huaxia PPP Project heating project, a mathematical model was constructed to determine the required hypothetical parameters and the variables affecting the final expected rate of return. The specific equations are as follows:

Operating income in a year, N = monthly heating income per square meter × heating area × number of heating months per year × payback rate × heating rate.

Heating revenue per square meter in year N: business and residential weights set at 25% and 75% I N = 22 * 0.75 + 38 * 0.25 = 26 = 26.0 * 1.1 = 26.0 * 1.1 * 1.1 = 26.0 * 1.1 * 1.1 * 1.1 = 26.0 * 1.1 * 1.1 * 1.1 * 1.1 = 26.0 * 1.1 * 1.1 * 1.1 * 1.1 * 1.1 (1)

Overall heating area per year.

S N = (residential heating area × heating rate + corporate heating area × heating rate) × (1 + growth rate), S N = 2653148 * 75 % + 992772 * 100 % * 1 + g a n − 1 S ≤ 4551064 , n = 1,2,3 , . . . . 6 (2)

Year N cost = depreciation + heating cost, year N heating cost per square foot. D N = 21.5 * 1 + g b n − 1   n = 1 ,   2 ,   3 …   . 6 (3)

Depreciation expense in year N. F N = D N * 0.082 (4)

Total profit in year N. T N = I N − D N − F N * S N (5)

Discounted net profit in year N. P N = T N 1 + R N (6)

As can be seen from the above equation, for annual discounting, the overall price of the project is influenced by the average annual growth rate of heating using g a , growth rate of costs g b , and discount rate R, which were assumed in the previous parameter settings. The analysis was performed using Crystal Ball software, based on the model listed and parameter settings.

Simulations were conducted using Crystal Ball software, and the entire model was set to run 1,000 times, with the rate of return for the time interval of the PPP securitization project obtained in each simulation. Table 13 shows the set variables, the quantities that may change in each simulation are the average annual growth rate of heating use g a , growth rate of costs g b , and discount rate R. The probability functions for the three impact factors were obtained as random numbers and were introduced into the model.

The model was imported into the software, and each parameter was assigned a value corresponding to the rate of return, and the process was repeated 1,000 times. The assumptions regarding the probability variables are as follows: Monte Carlo simulations are performed using the software, and the entire process is run 1,000 times and plotted using EXCELL. The results are shown in Figure 8

The results of the Crystal Ball data are as shown in Figure 9.

From the arithmetic results report, the fundamental values were collated, found, and collated as shown in Table 14.

As can be seen from the Figure 10 above, the mean value of the return is 5.5754%, and its deviation of 0.0174% is greater than zero, indicating that this result has a heavy tail on the right-hand side and the distribution is right-skewed. The right-hand side is more concentrated, and the result is feasible based on the numerical results, as well as the cumulative probability distribution of the model.

Combining the information in Table 14, with Figures 8, 9, 10 the analysis of the statistical results following the Monte Carlo simulation leads to the following conclusions.

1. Combining Table 14 with Figures 8, 9, it can be seen that the maximum value of the heating tariff yield for this PPP project is 7.89%, the minimum value is 3.33%, and the mean expectation of the yield is approximately 5.5754%, which provides a selected range of yields for the entire PPP ABS project. Compared to the actual rate of 5.2% achieved in the actual issue, the mean yield of 5.5754% obtained from this simulation was greater than the actual issue result.

The pricing results obtained through the option-adjusted spread method and the Monte Carlo simulation method are both lower than the actual issue price; that is, the yield of the empirical results is higher than that of the actual issue product. For this reason, the reasons for this situation are analyzed in the context of the basic situation of the Huaxia Happiness PPP project as follows.

1. Project assets are of superior quality, which reduces the risk of default. The Huaxia Happiness PPP project was repaid by the right of return on heat supply, and Gu’an Jiutong and the government signed a stable exclusive heat supply agreement. According to the agreement, the probability of default risk is low during the offering and repayment of the ABS products of this project, and this project has a relatively stable cash flow; therefore, the actual yield of the final issue is lower.

When securitizing assets, the projection of cash flows is subject to more risk factors; therefore, it is necessary to measure the annual risk factors when forecasting cash flows. The use of Monte Carlo simulation in pricing such projects allows for flexibility in modifying risk factors according to project circumstances and changes, allowing for better adaptation to changes in project cash flows.

The use of Monte Carlo simulation to price the ABS products of the heating yield class can yield a more reasonable price range, as can be seen from the ABS products of the Huaxia Happiness PPP project, which have a senior/subordinate classification and issue several senior products with different yields, fluctuating from 3.9% to 5.2%. The use of Monte Carlo simulation can accurately predict a reasonable range of prices and obtain a yield that is suitable for the current situation of the project within a reasonable range. The overall pricing to obtain a more reasonable yield meets the requirements of the characteristics of the heating revenue rights class of projects. Therefore, the Monte Carlo simulations have a high reference value.