Inferring Real - World Distribution Parameters from Risk - Neutral Distribution via Ross Theorem

The current research work is devoted to the Inferring real-world distribution parameters from risk-neutral distribution via Ross theorem and implementing them to estimate the Value at Risk. After obtaining the natural probability distribution using the Recovery Theorem by S. Ross, we implemented this natural distribution in VaR measure and compared it with VaR measure, based on the historical simulated distribution. After implementation of the described algorithm we got exciting results. Investigated recovery procedure and constructing VaR measure, based on the recovered distribution, showed great result with instruments from developed countries with developed and stable markets and gave us the same result for VaR measure as the historical simulated distribution. At the same time we can see that investigated algorithm of constructing VaR measure, based on the recovered distribution is not applicable for the instruments from developing countries and high volatile assets. Overall, current research provides us with a significant and powerful result as we can use recovered distribution, which is based on the future, forward looking information, for such risk metric as VaR in cases when historical data are not applicable. And we proved it for several instruments from developed markets in the current research work. It is crucial due to the fact that often historical simulated distribution is violated and it becomes hard to implement it in constructing the VaR measure. In that cases investigated algorithm can provide us with a powerful instrument, which we can use in constructed applicable measures of risk. Moreover, when there is a need to prepare predictive analysis for some new asset, which doesn’t have any historical data, we can use the investigated recovery algorithm, because it is based on the future, forward looking information. Therefore, the current research work carries significant knowledge and ideas for the theory of risk management and predictive analysis.