Variance Reduction Techniques Research And Application Of Monte Carlo Simulation Methods In Options Pricing

Since the 1990s, as the financial innovation, the financial liberalization and financial whole world integration develop rather quickly, the financial derivation negotiable securities obtained the rapidly development. Because the financial derivation negotiable securities is a basic tool for important the finance activities like finance risk management and guard, congenial arbitrage, investment financing, expense credit and so on important the finance activities, therefore the financial derivation negotiable fixed price securities question becomes an extremely important research area in the modern finance theory. However in today’s financial markets, on the one hand, the market are increasing many uncertainty degree, stocks and other major property’s changing process also becomes more and more complex, so in order to respond these complex characteristics accurately, it must make these process more complex supposition which will make target variable quantity increase massively; On the other hand various types of customer were getting more and more personalized demand as for financial instruments, which will promote new securities generate and develop rapidly, which has complex profit and loss characteristics. These two aspect reasons make high-dimensional derivative securities whose have a complex nature structure take an important position in financial derivatives markets.According to the existing monetary assets fixed price theory, major part option price must be adopted by numerical analysis method. The common financial derivation negotiable securities fixed price’s numerical analysis technology may divide into three fundamental types:Grid analysis technology, finite difference technology and Monte Carlo simulation technique. However the grid analysis technology and the finite difference technology get a better application in the lower derivation negotiable securities fixed price application, multi-subject variables and path-dependent characteristics of high-dimensional derivative securities are very difficult and sometimes impossible because of the rapidly increasing workload, which is namely called "dimension disaster". Monte Carlo technique has two obvious advantages, the first is very flexible and easy to implement and the second is estimated error and convergence rate and independence of dimension of solving problem, which can be able to solve multiple high-dimensional derivative securities pricing. Therefore, with the high-dimensional derivative securities developing faster and faster and transaction scale increasing rapidly, its application is widespread day by day, the grid analysis and finite difference technology applications will be subject to receive increasing restrictions, so Monte Carlo simulation is bound to play a more important role in financial derivation securities pricing. Monte Carlo simulation’s variance reduction technology as an important way to improve the efficiency has been widely applied and developed in the financial derivative securities pricing analysis specially in the controlled variable, the dual variable, the stratified sampling and the importance sampling technique as well as important and stratified sampling aspects. According to variance reducing efficiency, all of the Monte Carlo simulation variance reduction techniques can obviously raise simulation efficiency fixing price, especially the stratified and important sampling are one of kind effective variance reduction technique. This article has analyzed the stratified and important sampling technique in option pricing in the specific application and give the specific algorithms of the simulation. Moreover it proved and examined that the stratified and important sampling can reduce the estimated variance with contrastive analysis’s method. At the same time, the financial derivative securities pricing theory and methods also obtain the widespread application in the socio-economic development, the scope of application field expand rapidly day by day, especially reflect a more important application value in the high technology and new technology investment in enterprise decision-making aspect. In the early-1980s, it is doubt that weather the DCF method is suitable in the enterprise decision-making and innovation management activities, "Harvard Business Review" published a series of articles and carried on the comprehensive reconsideration to this question, the general view is that DCF project evaluation methodology is based on the basic supposition and the realistic enterprise environment, but there are a certain amount of deviation, especially when high-tech enterprises faced with tremendous uncertainty environment, the extent of this deviation is more obvious.In the growing uncertainty world, the real options has the widespread use because it has unique way of thinking and values, it will not only change the way that people create value from the two aspects of passive and active but also will change the way of thinking of practical problems. The real options approach which is based on option pricing theory, becomes the extremely important means to solve high-tech enterprise investment decision-making problems.In recent years, Monte Carlo simulation methods are more widely used in the financial derivative securities pricing of the applications, so they have aroused many experts and scholars’widespread interest. The real options analysis method taking this theory as foundation investment in enterprise decision-making becomes focus which academics and business people cared together. Therefore, regardless of theoretical research or practical application research, it made many very useful progresses.However, there are the obvious limitations on the present research methods and research results, some limitations may even mean there exists nature problems. Specially in domestic, regardless of studies from the theory or the application, it basically was at the first stage. Therefore, they are of great value and significance when we put this research project in theoretical and application study.As to research and development investment, it is hard to achieve the science accurately by take the traditional discount cash flow method, moreover, real options estimate model can’t effectively solve volatility problem of parameter. This article, based on the DCF method, using real option theory, taking Matlab software, applying Monte Carlo simulation method to have R & D decision-making, by these examples, it proved that Monte Carlo simulation method can be more scientific to solve the R & D decision-making which high degree isn’t definite.