{"title":"Fast and Efficient Nested Simulation for Large Variable Annuity Portfolios: A Surrogate Modeling Approach","authors":"X. Lin, Shuai Yang","doi":"10.2139/ssrn.3342701","DOIUrl":"https://doi.org/10.2139/ssrn.3342701","url":null,"abstract":"Abstract The nested-simulation is commonly used for calculating the predictive distribution of the total variable annuity (VA) liabilities of large VA portfolios. Due to the large numbers of policies, inner-loops and outer-loops, running the nested-simulation for a large VA portfolio is extremely time consuming and often prohibitive. In this paper, the use of surrogate models is incorporated into the nested-simulation algorithm so that the relationship between the inputs and the outputs of a simulation model is approximated by various statistical models. As a result, the nested-simulation algorithm can be run with much smaller numbers of different inputs. Specifically, a spline regression model is used to reduce the number of outer-loops and a model-assisted finite population estimation framework is adapted to reduce the number of policies in use for the nested-simulation. From simulation studies, our proposed algorithm is able to accurately approximate the predictive distribution of the total VA liability at a significantly reduced running time.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128843214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Backward Simulation Method for Stochastic Optimal Control Problems","authors":"Zhiyi Shen, Chengguo Weng","doi":"10.2139/ssrn.3319160","DOIUrl":"https://doi.org/10.2139/ssrn.3319160","url":null,"abstract":"A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic control problems as analytical solutions are not tractable in general. This paper generalizes the LSMC algorithm proposed in Shen and Weng (2017) to solve a wide class of stochastic optimal control models. Our algorithm has three pillars: a construction of auxiliary stochastic control model, an artificial simulation of the post-action value of state process, and a shape-preserving sieve estimation method which equip the algorithm with a number of merits including bypassing forward simulation and control randomization, evading extrapolating the value function, and alleviating computational burden of the tuning parameter selection. The efficacy of the algorithm is corroborated by an application to pricing equity-linked insurance products.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126238115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Monte Carlo Calibration Method of Stochastic Volatility Model with Stochastic Interest Rate","authors":"Mingyang Xu","doi":"10.2139/ssrn.3406240","DOIUrl":"https://doi.org/10.2139/ssrn.3406240","url":null,"abstract":"Implied volatility skew and smile are ubiquitous phenomena in the financial derivative market especially after the Black Monday 1987 crash. Various stochastic volatility models have been proposed to capture volatility skew and smile in derivative pricing and hedging. Almost 30 years after the advent of the first type of stochastic volatility model calibrating them to the market volatility surface still remains challenging, especially when stochastic interest rate has to be also taken into account for long-dated options. Many techniques have been applied to tackle this problem, including Fast Fourier Transform, singular perturbation expansion, heat kernel expansion, Markovian projection, to name a few. Although they have achieved some success in deriving either a close-form solution for a specific type of model or asymptotic solution in more general, none of them can really solve the calibration problem satisfying our need in term of both efficiency and accuracy. Monte Carlo method is a flexible numerical pricing method but has not been considering for calibration because of its slow convergence. However, with the great advance in computational power, in particular, parallel computation and the invention of other variance reduction techniques fast and accurate calibration using Monte Carlo becomes possible. This paper presents a Monte Carlo calibration method for stochastic volatility models with stochastic interest rate, which reduces simulation dimension by conditional expectation and further improves speed by vectorization. Numerical experiments show that both the calibration speed and accuracy of this generic method are satisfactory for almost all applications.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122968743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Crude Estimation of XVA Sensitivities","authors":"S. Alavian","doi":"10.2139/ssrn.3314837","DOIUrl":"https://doi.org/10.2139/ssrn.3314837","url":null,"abstract":"This paper proposes a simple and crude way of approximating the XVA sensitivities. In short, the idea is simply to recycle the existing base simulated portfolio values for the bumped ones. This is done by re-simulating the risk factors for the bumped market and finding out which other base state is closest to each given bumped state. Once that base state is found, its portfolio value can be used for the bumped one. The approach, therefore, removes the need to revaluate the trades during the secondary round of bump calculations while leaving other steps of the process intact.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122371743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Investment-Cash Flow Sensitivities Are Very Probably Not Valid Measures of Financing Constraints: on the Accounting Partial Identities Problem","authors":"Javier Sánchez Vidal","doi":"10.2139/ssrn.3341335","DOIUrl":"https://doi.org/10.2139/ssrn.3341335","url":null,"abstract":"This experiment uses a Monte Carlo simulation designed to test whether the problems about the use of accounting identities are present in the model of Fazzari, Hubbard, and Petersen (1988). The Monte Carlo simulation creates 10,000 sets of randomly generated cash flows, Tobin’s Q, and an error term variables, which in turn shape an investments variable that depends on them. These two variables are also related through an accounting semi identity or accounting partial identity (API). OLS estimations verify that estimated coefficients do not represent reality. The closer the data are to the accounting identity, the less the regression will tell about the causal relation.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123772414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Eignung von Varianz-Kovarianz-Ansätzen und Copula-Modellen zur Risikoaggregation in bankaufsichtlichen Risikotragfähigkeitskonzepten (How Adequate Are Covariance and Copula Based Approaches of Risk Aggregation?)","authors":"M. Graalmann, F. Lehrbass","doi":"10.2139/ssrn.3454418","DOIUrl":"https://doi.org/10.2139/ssrn.3454418","url":null,"abstract":"<b>German Abstract:</b> Mit einer Simulationsstudie zeigen wir, dass die Skepsis der Aufsicht hinsichtlich der Anerkennung von Diversifikationseffekten berechtigt scheint.<br><br><b>English Abstract:</b> We run a simulation study to check whether the scepticism of regulators to accept diversification benefits is well-founded. Our findings are confirmatory.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"299 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123659079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Innovation or Shock Size for Stata’s PVAR","authors":"George S. Ford","doi":"10.2139/ssrn.3288004","DOIUrl":"https://doi.org/10.2139/ssrn.3288004","url":null,"abstract":"In this note I show how to obtain the exact size of the innovation (or shock) for Stata's pvar and pvarinf commands.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122047663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Second Order Weak Approximation of SDEs Using Markov Chain Without Levy Area Simulation","authors":"T. Yamada, Kenta Yamamoto","doi":"10.2139/ssrn.3257365","DOIUrl":"https://doi.org/10.2139/ssrn.3257365","url":null,"abstract":"This paper proposes a new Markov chain approach to second order weak approximation of stochastic differential equations driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order and any discrete moment matched random variables or Levy area simulation method are not used. The number of required random variables is still d in one-step simulation on the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment matched random variables.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115253104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimating Average Treatment Effects With Propensity Scores Estimated With Four Machine Learning Procedures: Simulation Results in High Dimensional Settings and With Time to Event Outcomes","authors":"Kip Brown, P. Merrigan, Jimmy Royer","doi":"10.2139/ssrn.3272396","DOIUrl":"https://doi.org/10.2139/ssrn.3272396","url":null,"abstract":"Background: The increased availability of claims data allows one to build high dimensional datasets, rich in covariates, for accurately estimating treatment effects in medical and epidemiological cohort studies. This paper shows the full potential of machine learning for the estimation of average treatment effects with propensity score methods in a context rich and high dimensional datasets. \u0000Methods: Four different methods are used to estimate average treatment effects in the context of time to event outcomes. The four methods explored in this study are LASSO, Random Forest, Gradient Descent Boosting and Artificial Neural networks. Simulations based on an actual medical claims data set are used to assess the efficiency of these methods. The simulations are performed with over 100, 000 observations and 1,100 explanatory variables. Each method is tested on 500 datasets that are created from the original dataset, allowing us to report the mean and standard deviation of estimated average treatment effects. \u0000Results: The results are very promising for all four methods; however, LASSO, Random Forest and Gradient Boosting seem to be performing better than Random Forest. \u0000Conclusion: Machine Learning methods can be helpful for observational studies that use the propensity score when a very large number of covariates are available, the total number of observations is large, and the dependent event rare. This is an important result given the availability of big data related to Health Economics and Outcomes Research (HEOR) around the world.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126109681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal Unbiased Estimation for Expected Cumulative Cost","authors":"Zhenyu Cui, M. Fu, Yijie Peng, Lingjiong Zhu","doi":"10.2139/ssrn.3161030","DOIUrl":"https://doi.org/10.2139/ssrn.3161030","url":null,"abstract":"We consider estimating an expected infinite-horizon cumulative cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the random horizon are given. Moreover, we characterize when the optimal randomized estimator is preferred over a fixed truncation estimator by considering the tradeoff between bias and variance. Numerical experiments substantiate the theoretical results.","PeriodicalId":364869,"journal":{"name":"ERN: Simulation Methods (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116319024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}