The risk manager should perform a quantitative risk analysis to determine the potential impact of risks on the project's completion date. This will help in providing a more accurate project completion date to the customer, considering the risks and their potential effects on the project schedule.
According to the PMI Risk Management Professional (PMI-RMP)Examination Content Outline1, one of the tasks in the domain of Risk Analysis is to perform quantitative risk analysis using techniques such as Monte Carlo simulation, decision tree analysis, sensitivity analysis, etc., to quantify the possible outcomes for the project and their probabilities, and to evaluate the cost and schedule impacts of risks1. In this scenario, the risk manager should perform a quantitative risk analysis and update the results, because the project costs have increased significantly and the customer has imposed a strict deadline for the project completion. A quantitative risk analysis will help the risk manager to estimate the probability of meeting the project objectives, such as cost and schedule, and to determine the appropriate contingency reserves for the project. A quantitative risk analysis will also provide more accurate and reliable information for the customer and the project team, and will support the risk response planning process2. Reference: 1: PMI Risk Management Professional (PMI-RMP)Examination Content Outline, page 92: A Guide to the Project Management Body of Knowledge (PMBOKGuide) - Sixth Edition, pages 431-432.