Efficient Simulations of Option Pricing and Greeks Under Three-Factor Model by Conditional Monte Carlo Method

This paper proposes a hybrid Monte Carlo simulation method for pricing European options under the stochastic volatility model and three-factor model.First,the European options are expressed as a conditional expectation formula,which can be used not only for reducing variance of simulations,but also for calculating the value of Greeks easily,due to the elimination of the weak singularity for the payoff of the option.Then,in order to reduce variance further,the authors also construct a new explicit regression based control variate under Heston model and three-factor model respectively.Numerical results of experiments show that the proposed method can greatly reduce the variance of simulation for pricing European option,and is easy to complement for the calculation of Greeks.

Variance reduction for generalized likelihood ratio method by conditional Monte Carlo and randomized Quasi-Monte Carlo methods

The generalized likelihood ratio(GLR)method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances.We put the GLR methods from previous work into a single framework,simplify regularity conditions to justify the unbiasedness of GLR,and relax some of those conditions that are difficult to verify in practice.Moreover,we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance.Numerical experiments show that variance reduction could be significant in various applications.

Kernel based statistic: identifying topological differences in brain networks

Background Brain network describing interconnections between brain regions contains abundant topological information.It is a challenge for the existing statistical methods(e.g.,t test)to investigate the topological differences of brain networks.Methods We proposed a kernel based statistic framework for identifying topological differences in brain networks.In our framework,the topological similarities between paired brain networks were measured by graph kernels.Then,graph kernels are embedded into maximum mean discrepancy for calculating kernel based test statistic.Based on this test statistic,we adopted conditional Monte Carlo simulation to compute the statistical significance(i.e.,P value)and statistical power.We recruited 33 patients with Alzheimer’s disease(AD),33 patients with early mild cognitive impairment(EMCI),33 patients with late mild cognitive impairment(LMCI)and 33 normal controls(NC)in our experiment.There are no statistical differences in demographic information between patients and NC.The compared state-of-the-art statistical methods include t test,t squared test,two-sample permutation test and non-normal test.Results We applied the proposed shortest path matched kernel to our framework for investigating the statistical differences of shortest path topological structures in brain networks of AD and NC.We compared our method with the existing state-of-the-art statistical methods in brain network characteristic including clustering coefficient and functional connection among EMCI,LMCI,AD,and NC.The results indicate that our framework can capture the statistically discriminative shortest path topological structures,such as shortest path from right rolandic operculum to right supplementary motor area(P=0.00314,statistical power=0.803).In clustering coefficient and functional connection,our framework outperforms the state-of-the-art statistical methods,such as P=0.0013 and statistical power=0.83 in the analysis of AD and NC.Conclusion Our proposed kernel based statistic framework not only can be used to investigate the topological differences of brain network,but also can be used to investigate the static characteristics(e.g.,clustering coefficient and functional connection)of brain network.