# 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
Additionally, it is necessary to use a real option pricing model to anticipate the trend of the volatility of the optimal price over a certain range of option expiration dates. Take this project as an example: if the option period is expected to be within 0.5 years, the bidding price can be increased within a reasonable range according to the real option pricing model of group bidding. If the option period is expected to be more than 1.5 years, to improve the winning probability, the bidding price can be reduced to control the degree of group deviation. Figure 5: Sensitivity analysis of the option period. (**a**) Period sensitivity; (**b**) Fluctuation trend of optimal price. (\(C_{t}\) = 50,000,000; \(b\) = 10; \(n\) = 1.1; \(u\) = 0.3; \(r\) = 0.01; \(\sigma\) = 0.2; \(N\) = 50; \(AP_{comps}\) = 52.79 million). 3. The Sensitivity Analysis of The Estimated Costs As an important factor in price decision making, the estimated costs in the bidding preparation stage are different during the same period of different enterprises or different periods of the same enterprise. The one-way sensitivity analysis of the estimated costs, \(C\)t, is carried out, and the results are shown in Figure 6. With the increase in the estimated costs, the maximum weighted option value shows a downward trend, and the optimal price shows an upward trend. This is because considering the pricing strategy in the group bidding environments, with the increase in the estimated costs of the enterprise, the less space to markup and the lower the winning probability, the lower value. To study the relationship between the optimal price and the estimated costs further, the curve is drawn as shown in Figure 6b, in which the ratio of optimal price to corresponding estimated costs, in other words, the optimal mark-up ratio, has been marked. As can be seen from the figure, in the same bidding project, as the estimated costs rise, the mark-up space on this basis shrinks, the optimal price is less sensitive to the estimated costs, and the optimal mark-up ratio decreases. If the estimated costs are too high, the optimal price will tend to respond linearly, that is, no matter what the estimated costs are, the optimal mark-up ratio remains the same, with an average mark-up ratio of 1.078 and an average sensitivity of 35.06%. Therefore, the results of the analysis on estimated cost show that, in the actual bidding process, the enterprises should combine the internal resource environment and external competitive environment, reduce the cost as far as possible, expand the markup space and enhance the sensitivity to the estimated cost. To obtain higher option value and improve the winning probability, at the same time, based on the group bidding pricing model, the optimal markup ratio of the project is estimated according to the decision flexibility. (4) The Sensitivity Analysis of The Number of Competitors The characteristics of the bidding price data under different numbers of competitors are summarized in Table 2, with the same average value and the similar maximum, minimum and median values. Figure 6: Sensitivity analysis of the estimated costs. (**a**) Costs sensitivity; (**b**) Fluctuation trend of optimal price. (\(b=10\); \(n=1.1\); \(u=0.3\); \(r=0.01\); \(\sigma=0.2\); \(T\):\(t=0.5\); \(N=50\); \(AP_{\text{comps}}=52.79\) million). The one-way sensitivity analysis of the number of competitors, \(N\), is carried out, and the results are shown in Figure 7. The bidding price, weighted option value and the winning probability are not sensitive to changes in the number of competitors in the same bidding project. This is because the bidding price is more influenced by the average than the number of competitors. Assuming that the other parameters are constant, an increase or decrease in the number of competitors does not affect the trend in the winning probability and the weighted option value when there is no significant change in the average.