Subject area of monte carlo methods

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Research paper on the subject area of monte carlo methods in financial mathematics. Needs to be 19 pages. In financial mathematics, numerical methods have been of great importance in the current years. There are numerous reasons why these methods are useful. First, the principal model that defines the progression of prices of the significant state variables and basic securities has become more refined and sophisticated. Second, the securities types and their associated offspring of security derivatives are complex. For one to compute the risks sensitivities and the prices of these instruments one needs to assess a high dimensional integral. Third, advancements in management technology of risks and practice nowadays mandate a wide range and complex evaluation at the portfolio level. For instance, because of regulatory requirements, numerous financial institutions nowadays allocate enough resources which will be used in determining or in the computation of value at risk (VaR).The Value at Risk computations comprises numerous different variables. Credit risk computations also encompass extensive numerical work. Of course, there is much advancement that has been made in the calculation of power thus making calculations more feasible. There is a comprehensive numerical approach used in the computation. These methods are discussed as follows. first there those problems which have an analytical solution or are said to have closed-form though we still need numerical work. Even if, the analytical expression is existing one should raise the numerical algorithm to perfect the computation.In addition, to get numerical values one will evaluate two functions that are normally distributed but cumulatively. Though there are many derivative conventions where there is no existence of analytical solutions. Many issues of interest are governed by the price of the derivative in order of partial differential equation (PDE). In the modern world, modern methods are the ones that are employed to derive the efficient pricing of different types of exotic options.

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