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Capital Management: Do You Have the Right Strategy?

Capital Management: Do You Have the Right Strategy?. Casualty Actuarial Society 1999 Special Interest Seminar Dynamic Financial Analysis Chicago, IL, July 19-20, 1999. Using the Bootstrap in DFA: An Experiment. William C. Scheel Swiss Re Investors Falcon Group.

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Capital Management: Do You Have the Right Strategy?

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  1. Capital Management:Do You Have the Right Strategy? Casualty Actuarial Society 1999 Special Interest Seminar Dynamic Financial Analysis Chicago, IL, July 19-20, 1999

  2. Using the Bootstrap in DFA:An Experiment William C. Scheel Swiss Re Investors Falcon Group

  3. Where Do You WantTo Go Today? • Bootstrap • What Can It Do for You? • Uses in DFA…an Illustration • Pricing Experiment • It’s Fast. It’s Cool.

  4. The Statistician’s Fractal The bootstrap is a computer-based method of statistical inference. No formulas are needed to answer many statistical questions. (I like it already)

  5. Same Method…All Statistics The BCa confidence interval method has transformation-respecting properties. This means that the procedures are invariant whether we seek to band the sample mean, median or some other statistic of interest.

  6. Bootstrap Method • Make Bootstrap Samples (sample with replacement) • Calculate statistic using bootstrap samples • Bias factor is standard normal value evaluated for the proportion of sample statistics below average statistic • Acceleration coefficient from jackknife samples

  7. Getting a Bootstrap Sample • Make a vector* of uniformly distributed numbers • Shuffle the vector • Use each element as an offset into the original data • Evaluate the statistic for each shuffled vector • Repeat steps (1)-(4) about 2,000-5,000 times *vector has N elements each with a value of u

  8. Obtaining BCa Confidence Interval Evaluate standard normal at adjusted z value z0 is bias correction factor Adjusted z value: zα is standard normal at α probability a is acceleration coefficient

  9. Acceleration Coefficient = the sample statistic calculated using the ith jackknife sample

  10. What Can It Do for You? • Confidence bands for DFA probability distributions • Tighter standard errors of the estimate • Chance-constrained banding of really wacko statistics • Put option pricing • Getting more out of less

  11. Computer Stuff (fortran) • The technique is a sampling activity and requires Monte Carlo sampling with replacement • Extensive calculations, sorting and scanning • Ancillary calculations for the statistic for each bootstrap sample • Jackknife for the bootstrap samples’ statistics (You really burn calories running a bootstrap!)

  12. Excel-fortran Interface • No bootstrap tools generally available • Microsoft Excel • Fortran DLL does bootstrap sampling (Excel is a tad weak for bootstrap confidence interval work…you’ll need fortran or C)

  13. Graphics Palette with Bootstrap Applying Bootstrap to DFA (Let the show begin!)

  14. Experiment with Individual Claims The experiment seeks to use bootstrap results as a convenient and powerful way to put a confidence band around the expected incremental payment emanating from a policy within a relatively cluttered collection of risk classes. (This kinda flopped. But, I’ll be back again!)

  15. Central Limit Theorem Using Bootstrap Use bootstrap mean and standard error for μ and σ. The number of independent claims is n. (At last! A use for the Central Limit Theorem. Well, I’ll admit I’m stretching it a bit here!)

  16. Bootstrap References • Efron & Tibshirani, Introduction to the Bootstrap • Davison & Hinkley, Bootstrap Methods and Their Application

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