Method: This paper will apply Geometric Brownian Motion (GBM) models to simulate future market prices. The Cox-Ingersoll-Ross approach is used to derive the integral interest rate generator.
Results: Through stochastic simulations, with the key location and shape parameters derived from options market forward curves, the approach yields the full array of price outcomes along with their respective probabilities.
Conclusions: The method generates the requisite distributions and their parameters to efficiently measure capital risk levels as well as fair value premiums and best estimate loss reserves. The modeled results provide credible estimators for risk based and/or economic capital valuation purposes. Armed with these distributions of price outcomes, analysts can readily measure inherent portfolio leverage and more effectively manage these types of financial risk exposures.
Availability: An Excel version of this stochastic GBM method is available from the CAS website, E-Forum section under filename MPiR.xlsm.
Keywords: Dynamic risk models; capital allocation; geometric Brownian motion; options market volatility; stochastic process; Markov Process, It?’s lemma, economic scenario generator.
