New Method of Sensitivity Computation Based on Markov Models with Its Application for Risk Management

Abstract

Sensitivity analysis is at the core of risk management for financial engineering; to calculate the sensitivity with respect to parameters in models with probability expectation, the most traditional approach applies the finite difference method, whereafter integration by parts formula was developed based on the Brownian environment and applied in sensitivity analysis for better computational efficiency than that of finite difference. Establishing a similar version of integration by parts formula for the Markovian environment is the main focus and contribution of this paper. It is also shown by numerical simulation that our proposed methodology and approach outperform the traditional finite difference method for sensitivity computation. For empirical studies of sensitivity analysis on an NPV (net present value) model, we show the approaches of modeling, especially for parameter estimation of Markov chains given data of company loan states. Applying our newly established integration by parts formula, numerical simulation estimates the variations caused by the capital return rate and multiplier of overdue loan. Furthermore, managemental implications of these results are discussed for the effectiveness of modeling and the investment risk control.