REAL OPTION ANALYSIS CASE WITH DYNAMIC RISK NEUTRAL PROBABILITY

This paper constructs a model with dynamic risk neutral probabilities of double stochastic variables and multistage constructions for the cellulosic ethanol project in China. Based on real option analysis, the investors can estimate the unit market value of the cellulosic ethanol project. Because of the great reduction of the gasoline price and the huge increment of the corn cob price, there are some negative decision values. Specially, action “invest” is still the optimal decision if only the stage-1 construction has been completed. Due to the regulation of the Chinese government, the dynamic risk neutral probabilities of the gasoline price and corn cob price are around 0.5, that are obviously different with the fixed risk neutral probabilities.


INTRODUCTION
As one kind of renewable energy, the cellulosic ethanol project was gradually developed in China in recent years. The first large-scale cellulosic ethanol producer with annual capacity of 50,000 tons had been put into operation in Shandong province. However, the Chinese cellulosic ethanol industry developed slowly by the complex technology, high cost and uncertainties. Real option is a typical approach used in renewable energy field. Some researchers (Lee et al., 2010;Sharma et al., 2013;Zhang et al., 2014) had investigated the benefits of investing renewable energy policy using binomial tree model. Sharma et al. (2013) constructed a real option model for a hypothetical, vertically integrated lignocellulosic enterprise that produces cellulosic ethanol and biosuccinic acid. In their model, binomial tree was used to present the uncertainties in bioproduct demands and prices. Different with the previous research, this paper establishes a quadrinomial lattice tree model based on dynamic risk-neutral probability with two construction stages and double stochastic variables.

Parameters Used In Real Option Model
The parameters considered in the real option model conclude the prices of the main raw materials and the products, the subsidy level and the carbon emission cost. We divide them to two types, stochastic variables and non-stochastic parameters. Since the fuel ethanol priceis set at 0.9111 times the price of No.93 gasoline from 1 May, 2011 in China, the gasoline price is one key stochastic variable in cellulosic ethanol investment project. As the main raw material, corn cob price is another stochastic variable. Furthermore, we suppose that these two stochastic variables follow Ornstein-Uhlenbeck processes and they are independent. Let   , g p i t denote the gasoline price with t periods elapsed and i downward moves,   , c p j t denote the corn cob price with t periods elapsed and j downward moves, where 0 t T   , 0 , i j t   . T is the total p . Actually, multistage investment gives investors more time to consider, so we consider the case with two construction stages before the project completed. Let other C denote the total construction costs (such as land, equipment and so on), then the stage-1 construction cost 1 Here, a is the stage-1 construction cost proportion. Meanwhile, Q presents the capacity of the cellulosic ethanol project, S indicates the subsidy for every ton cellulosic ethanol, f r denotes the risk-free interest rate.
Furthermore, the cellulosic ethanol investment right will be lost if the construction program cannot be completed on or before the expiration date T . All these non-stochastic parameters are shown in Exhibit2.

Exhibit2
The non-stochastic parameters used in the real option model

Parameters Estimation
By assumption, the gasoline price and the corn cob price follow OU processes as   1 ln ln can be estimated following the AR(1) process Hence, the estimated values , , can be obtained as According to the daily history data of No.93 gasoline price and corn cob price of Shandong province from 2011 to 2015, the volatilities of the logarithm of gasoline price with the year as unit are 1.2467 g

Exhibit 1
The binomial tree of stochastic variable (without subscript g and c ) Other by-products and raw materials in the cellulosic ethanol producing process are considered as non-stochastic parameters.
According to the report in the conference of Proceeding of the 6 th Stakeholder Plenary Meeting of EBTP by Kang (2014), xylitol, pure lignin are the main by-products, zymin is another important raw material in the cellulosic ethanol project.
Here, a is the stage-1 construction cost proportion. Meanwhile, Q presents the capacity of the cellulosic ethanol project, S indicates the subsidy for every ton cellulosic ethanol, f r denotes the risk-free interest rate.
Furthermore, the cellulosic ethanol investment right will be lost if the construction program cannot be completed on or before the expiration date T . All these non-stochastic parameters are shown in Exhibit2.

Exhibit2
The non-stochastic parameters used in the real option model

Parameters Estimation
By assumption, the gasoline price and the corn cob price follow OU processes as   1 ln ln can be estimated following the AR(1) process Hence, the estimated values , , can be obtained as According to the daily history data The binomial tree of stochastic variable (without subscript g and c ) Other by-products and raw materials in the cellulosic ethanol producing process are considered as non-stochastic parameters.
According to the report in the conference of Proceeding of the 6 th Stakeholder Plenary Meeting of EBTP by Kang (2014) Here, a is the stage-1 construction cost proportion. Meanwhile, Q presents the capacity of the cellulosic ethanol project, S indicates the subsidy for every ton cellulosic ethanol, f r denotes the risk-free interest rate.
Furthermore, the cellulosic ethanol investment right will be lost if the construction program cannot be completed on or before the expiration date T . All these non-stochastic parameters are shown in Exhibit2.

Exhibit2
The non-stochastic parameters used in the real option model

Parameters Estimation
By assumption, the gasoline price and the corn cob price follow OU processes as   1 ln ln can be estimated following the AR(1) process Hence, the estimated values , , can be obtained as According to the daily history data

Exhibit4
The binomial tree of the corn cob price (yuan/ton)

Dynamic Risk-Neutral Probability
The dynamic risk-neutral probabilities of the upward move size of gasoline price   , , g u i n  and corn cob price Here,

Scatter diagram of Shanghai composite index and gasoline price return
Hence, the upward dynamic risk-neutral probability at each node of each stochastic variable can be shown in Exhibit 7.

Real Option Model
According to the report given by Kang (2014) International Journal of Recent Scientific Research Vol. 8, Issue, 5, pp. 16796-16800, May, 2017 16798 | P a g e

Exhibit4
The binomial tree of the corn cob price (yuan/ton)

Dynamic Risk-Neutral Probability
The dynamic risk-neutral probabilities of the upward move size of gasoline price   , , g u i n  and corn cob price Here,

Scatter diagram of Shanghai composite index and gasoline price return
Hence, the upward dynamic risk-neutral probability at each node of each stochastic variable can be shown in Exhibit 7.

Real Option Model
According to the report given by Kang (2014) International Journal of Recent Scientific Research Vol. 8, Issue, 5, pp. 16796-16800, May, 2017 16798 | P a g e

Exhibit3
The binomial tree of the gasoline price (yuan/ton)

Exhibit4
The binomial tree of the corn cob price (yuan/ton)

Dynamic Risk-Neutral Probability
The dynamic risk-neutral probabilities of the upward move size of gasoline price   , , g u i n  and corn cob price Here

Scatter diagram of Shanghai composite index and gasoline price return
Hence, the upward dynamic risk-neutral probability at each node of each stochastic variable can be shown in Exhibit 7.

Real Option Model
According to the report given by Kang (2014)

Exhibit 6 Scatter diagram of Shanghai composite index and corn cob price return
Exhibit 7

The dynamic upward risk-neutral probabilities (only retain four decimal) of gasoline price (G) and corn cob price (C)
It also needs to expense some zymin. Meanwhile, the producers obtain the subsidy from the government and they suffer the carbon emission cost. By BP carbon emission calculator, one ton fuel ethanol can be instead of one ton gasoline and release 3.15 tons carbon. Let

 
, , X i j n is the unit market value of the completed project at node   , , i j n , that is, the gasoline price has i downward movements and the corn cob price has j downward movements at date n .Let   , , m V i j n denote the unit market value of the investment right at node   , , i j n , 1, 2 m  represents the number of construction stage to be invested. Then the unit market value of the investment right at each scenario can be obtained by the back induction method.
with the terminal conditions   2 , , 0 Here, 0 n T   , 0 , i j n   .

RESULTS AND CONCLSIONS
Based on the real option model, all the decision values at each scenario can be shown in Exhibit 8. Since there has 25 cases with the value 0 in 2020, it omits the following same parts as shown. Following this table, investors can make decisions and estimate the unit market value of the cellulosic ethanol project based on the information of the gasoline and corn cob prices. Obviously, the investors will not invest the cellulosic ethanol project intuitively at the expiration date, thus the decision values in the last column of the last tables must be zero.
The gray areas represent that the investors are better to wait for new information about the fuel market and invest the next construction stage latter. In the cellulosic ethanol investment, the fixed risk neutral probabilities of the upward moves of the gasoline price and corn cob price are ,

Exhibit 8 The decision values (million yuan, retain four decimal)
However, the upward dynamic risk neutral probability at each node is around 0.5, which shows obvious difference. This comparison indicates that the dynamic risk neutral probability is more adapt to reflect the possible changes at each nodes, and more convenient for investors to make optimal decisions.