At the same time, since the Monte Carlo model is very adaptable, the conditional constraints are small when solving the problems. According to the law of large numbers and the central limit theorem in probability theory, the large number theorem can ensure that the estimated value obtained by the Monte Carlo method can gradually converge to the actual value according to the increase of the number of simulations, and the central limit theorem can give the error estimation range of the Monte Carlo model. It can measure the number of occurrences of events and thereby the probability of occurrence of events. The Monte Carlo method has a wide range of applications in financial engineering. However, considering the value and risk of these products, there will be more considerations for the holding period of these derivatives. At present, there are more companies and users interested in financial derivatives.

After research, the most important factors causing the crisis is considered to be the globalization of financial derivatives and the global proliferation of financial derivatives caused by lack of regulation. However, the most serious losses were the outbreak of the financial crisis and the United States, the most developed financial derivatives market. The financial markets of many developed countries also suffered heavy losses during the financial crisis. The global financial crisis triggered by the US subprime mortgage crisis in 2008 caused a huge blow to the major economic entities worldwide, making the world economy be into a recession. Financial derivatives cannot exist independently, and their values largely depend on basic financial instruments. The financial derivatives are derived from basic financial instruments, such as currency, interest rate stocks, and commodities. With the continuous development of the world economy, financial derivatives become increasingly various. It can be seen that the Monte Carlo model-based variance reduction technology has high application value in the pricing of financial derivatives, and it is of great significance for the pricing of other products. The proposed method is easy to implement and has higher computational efficiency, which can ensure the financial benefits of users holding financial derivatives during the holding period. In addition, the importance sampling method is used to optimize the selection, thereby making it closer to the theoretical values. The results show that the Monte Carlo model-based variance reduction technology can significantly improve the simulation efficiency of financial derivatives pricing. Based on the variance reduction technology, a Monte Carlo model that can effectively analyze financial prices is added to analyze price fluctuations and find the optimal holding time for users of financial derivatives, thereby reducing the risk of holding the financial derivatives. The article shows that a proper combination of lines and FACTS leads to efficient investments by allowing a progressive adaptation of the transmission grid to the changing scenarios.The purpose of the study is to reduce the error in the pricing process of financial derivatives, as well as to obtain more accurate product values, thereby reducing transaction costs, accelerating transaction speed, establishing a larger investment scale, and enabling investors to obtain excellent returns under market conditions as much as possible. In order to illustrate the practicability of the proposed valuation approach, a traditional expansion strategy (lines) and a flexible investment strategy (lines and FACTS) are compared in a real study case. The flexibility provided by FACTS investments-option to abandon and to relocate-is assessed through a real option valuation approach based on the novel least square Monte Carlo method. This article proposes an investment valuation approach which properly assesses the option value of deferring transmission lines investments whereas gaining flexibility by investing in FACTS devices. In this sense, flexible AC transmission systems (FACTS) devices appear as an effective manner of adding flexibility to the transmission expansion planning. Strategic flexibility for seizing opportunities and cutting losses contingent upon an unfavorable unfolding of the long-term uncertainties is an attribute of enormous value when assessing irreversible investments. Efficient and well-timed investments in electric transmission networks that cope with the large ongoing power market uncertainties are currently an open issue of significant research interest.

Real options valuation monte carlo