# Toward Business Integrity Modeling and Analysis Framework for Risk Measurement and Analysis
## 4 Discussion: Benefits and Services Offered by the BIMA Framework
### Risk Calculations by Monte Carlo Simulations (MCS)  
This section describes how MCS simulations (time step = 10) can be used to calculate the precise numeric price and risk options. The least square method (LSM) is a precision method in MCS to calculate results to be as accurate as possible. Risk analysis is carried out using models of both the American and European options due to their popularity. The difference is that while an American option may be exercised at any time, European options can only be exercised at expiry [36]. The majority of exchange-traded options are American. A European option may be used only at the expiry date of the opportunity, which means at a single predefined point in time [36]. Simultaneous calculations in both options are suitable because American options can illustrate the average performance, and the European option can demonstrate the best pricing or risk at the time research work takes place. Both American and European options are used for analysis. Both can be converted to percentages [22]. This means that if a risk price is calculated and is equal to 2.42, it can be interpreted that 2.42% is the percentage that the risk can happen and, as such, the price to accept it is 2.42. Using LSM permits these models to be divided into sections, each of which can be calculated independently, allowing them to be distributed across clouds or grids with consequent improvements in efficiency [29]. LSM can be adapted to run 100,000 simulations in the cloud within a few seconds. The following is the result of running LSM to calculate the expected risk price. MCAmericanPrice = 2.335 (risk price)  
MCEuropeanPrice = 2.287 (risk price)  
This means that the average performance for risk price is 2.335 (2.335% for operational risk to happen). The best risk pricing that the completion of a project or the end of investment (exit/expiry) to happen is 2.287 (2.287% for operational risk to happen). MCS simulations in the BIMA framework can calculate the range of lower, upper, and medium limits. This is a crucial step to calculate precise options and to produce results as accurately as possible. Numerical calculations performed without the precision method may have a broader range in the final result. Thus, the likely range of risk pricing with the highest frequency of occurrence should be computed. The put price is used to calculate risk pricing, as it represents a price to accept this risk [29]. The result shows that the expected European option (for risk price) is 2.22728, with its upper limit as 2.24039 and the lower limit as 2.21430. MCS calculations allow the computation of accurate results of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Company** & **Sector** & **Probability of Bankruptcy** \\ \hline CROWN HOLDINGS INC & Consumer Durables & 0.99612488 \\ TESTRON INC & Technology & 0.00022919 \\ TECH DATA CORP & Technology & 0.16963718 \\ APPLE INC & Technology & 0.00015289 \\ SPARTON CORP POWER SOLUTIONS & Energy & 0.00054959 \\ INGERSOLL-RAND PLC & Capital Goods & 1.29E-06 \\ NF ENERGY SAVING CORP & Energy & 0.23296333 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Seven listed companies undertaking the probability of bankruptcy simulations. up to five decimal places, including its exact price, lower limit, and upper limit. See Table 3. Results are consistent with each other when the number of simulation goes up to 500,000 by 50,000 each time. Gaussian Collateralized Debt Obligation (CDO) is also another model commonly used by financial institutes to compute the interest rates for currencies, mortgages, and bonds. The popularity of relying on CDO due to the lack of regulations is one of the factors that contributed to the financial crisis in 2008 [58]. MCS has a significant performance improvement over Gaussian CDO software under the same circumstances for modeling and simulations. For example, MCS is always under 20 s for up to 500,000 simulations and has up to 10 times better performances than Gaussian CDO, which can fail to simulate beyond 300,000 simulations [59].