# A Real Option Pricing Decision of Construction Project under Group Bidding Environment
## 3 The Model Application and Analysis
### Simulation Results Analysis in the Independent Bidding Environment
#### 3.2.2 The Sensitivity Analysis of Parameters  
(1) Sensitivity analysis of the volatility level  
The estimated costs in the bidding preparation stage have volatility, due to the changes in market environments. The one-way sensitivity analysis of the cost volatility level, \(\sigma\), is carried out, and the results are shown in Figure 4. With the increase in the volatility level, the maximum weighted option value increases, while the price corresponding to it, the optimal price, decreases. In other words, with the increase in the uncertainty of the market environments, the competitors will put forward a lower bidding price to obtain a higher option value, thus the average value of group bidding prices will be reduced. Then, the enterprise will put forward a bidding price closer to the average, to obtain a greater option value. To study the relationship between the optimal price and the volatility level further, the curve is shown in Figure 4b. As the volatility decreases, the sensitivity of the optimal price increases, and when the volatility is less than 25%, the optimal price changes nearly linearly, then it decreases gently until the volatility exceeds 40%, and the curve tends to be stable. This is because the enterprise will only lower the bidding price for a higher probability under the condition of ensuring profits. The optimal bidding price has an average sensitivity of 9.77% to the volatility. Figure 4: Sensitivity analysis of volatility. **(a)** Volatility sensitivity; **(b)** Fluctuation trend of optimal price. (\(C_{t}\) = 50,000,000; \(b=10\); \(n=1.1\); \(u=0.3\); \(r=0.01\); \(T\)-\(t=0.5\); \(N=50\); \(AP_{\text{comps}}=52.79\) million). Figure 3: Concentration of the optimal bidding price. Therefore, the results of the one-way sensitivity analysis of the cost volatility level indicate that in the actual bidding process, the market environment should be estimated in the bid preparation stage to sort out the factors that may have an impact on the costs and the scope of it after the price decision, especially in the construction stage of the project. If the market environment is more volatile, a higher option value can be obtained by lowering the bidding price to reduce the degree of group deviation. At the same time, the timing of the estimated costs decision can be postponed to reduce the impact of uncertainty in the market environment on the bidding price decision. The one-way sensitivity analysis of the option period, \(T-t\), is carried out, and the results are shown in Figure 5. With the extension of the option period, the maximum weighted option value increases, while the optimal price decreases. In other words, with the extension of the period from the determination of the bidding price to the final winning, the uncertainties of the internal and external environments faced by the enterpriser will increase, and the competitors will propose lower prices to increase the winning probability, thus the average value of group bidding prices will be reduced. Then, the enterprise will put forward a price closer to the average, to obtain a greater option value. To study the relationship between the optimal price and the option period further, the curve is drawn as shown in Figure 5b. As the extension of the period, the sensitivity of the optimal price decreases, and when the period is less than 0.5 years, the optimal price makes a linear response to the option period. That is because if the period is short, the enterprise will pay more attention to the influence of internal strength which tends to be stable in a short time. Then, it decreases gently until the period exceeds 1.5 years, and the curve tends to be stable. The optimal bidding price has an average sensitivity of 7.70% to the period. Thus, the results of the one-way sensitivity analysis of the option period indicate that in the actual bidding process, it is necessary for companies to anticipate the length of the option period in the bidding preparation stage.