Abstract:

Value of constant mix strategy (CM strategy) multi-period return guarantee is theoretical basis of charging by the issuers who use CM strategy set stop-loss to manage a principal guaranteed fund. The underlying asset is driven by compound Poisson process and Wiener process. This pricing problem embeds exotic options. Monte Carlo simulation is good at dealing with such a high dimensional quantitative financial problems. We derive the expression of the present value of CM strategy multi-period return guarantee that based on risk-neutral measurement. Then we use conditional Monte Carlo simulation to derive the simulation formula of this present value. Numerical solutions of value of CM strategy multi-period return guarantee were calculated under given parameters by ordinary Monte Carlo and conditional Monte Carlo. Results show two Monte Carlo methods can calculate the numerical solution effectively. Then we appraise the accuracy of the two methods through the length of the confidence interval under a given level of significance. Results show conditional Monte Carlo is better than ordinary Monte Carlo. Then we use conditional Monte Carlo simulation to analyze value of CM strategy multi-period return guarantee on the different parameters range.

Key words: CM strategy, variance reduction techniques, conditional Monte Carlo, path-dependent, jump processes