Thursday, November 21, 2019 — 4:00 PM EST

A General Framework for Quantile Estimation with Incomplete Data

Quantile estimation has attracted significant research interests in recent years. However, there has been only a limited literature on quantile estimation in the presence of incomplete data. In this paper, we propose a general framework to address this problem. Our framework combines the two widely adopted approaches for missing data analysis, the imputation approach and the inverse probability weighting approach, via the empirical likelihood method. The proposed method is capable of dealing with many different missingness settings. We mainly study three of them: (i) estimating the marginal quantile of a response that is subject to missingness while there are fully observed covariates; (ii) estimating the conditional quantile of a fully observed response while the covariates are partially available; and (iii) estimating the conditional quantile of a response that is subject to missingness with fully observed covariates and extra auxiliary variables. The proposed method allows multiple models for both the missingness probability and the data distribution. The resulting estimators are multiply robust in the sense that they are consistent if any one of these models is correctly specified. The asymptotic distributions are established using the empirical process theory.


Joint work with Peisong Han, Jiwei Zhao and Xingcai Zhou.

Friday, November 22, 2019 — 10:30 AM EST

Do Jumps Matter in the Long Run? A Tale of Two Horizons

Economic scenario generators (ESGs) for equities are important components of the valuation and risk management process of life insurance and pension plans. As the resulting liabilities are very long-lived, it is a desired feature of an ESG to replicate equity returns over such horizons. However, the short-term performance of the assets backing these liabilities may also trigger significant losses and in turn, affect the financial stability of the insurer or plan. For example, a line of GLWBs with frequent withdrawals may trigger losses when subaccounts suddenly lose after a stock market crash or pension contributions may also need to be revised after a long-lasting economic slump. Therefore, the ESG must replicate both short- and long-term stock price dynamics in a consistent manner, which is a critical problem in actuarial finance. Popular features of financial models include stochastic volatility and jumps, and as such, we would like to investigate how these features matter for typical long-term actuarial applications.

For a model to be useful in actuarial finance, it should at least replicate the dynamics of daily, monthly and annual returns (and any frequency in between). A crucial characteristic of returns at these scales is that the kurtosis tends to be very high on a daily basis (25-30) but close to 4-5 on an annual basis. We show that jump-diffusion models, featuring both stochastic volatility and jumps, cannot replicate such features if estimated with the maximum likelihood. Using the generalized method of moments, we find that simple jump-diffusion models or regime-switching models (with at least three regimes) have an excellent fit for various moments observed at different time scales. Finally, we investigate three typical actuarial applications: $1 accumulated in the long run with no intermediate monitoring, a long-term solvency analysis with frequent monitoring and a portfolio rebalancing problem, also with frequent monitoring and updates. Overall, we find that a stochastic volatility model with independent jumps or a regime-switching lognormal model with three regimes, both fitted with the GMM, yield the best fit to moments at different scales and also provide the most conservative figures in actuarial applications, especially when there is intermediate monitoring.

So yes, jumps or jump-like features are essential in the long run. This also illustrates how typical actuarial models fitted with the maximum likelihood may be inadequate for reserving, economic capital and solvency analyses.

Thursday, November 28, 2019 — 4:00 PM EST

More information about this seminar will be added as soon as possible.

Friday, November 29, 2019 — 10:30 AM EST

Noncausal Affine Processes with Applications to Derivative Pricing

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature much more complicated non affine dynamics in calendar time, while still providing (quasi) closed form term structures and derivative pricing formulas. The framework is illustrated with zero-coupon bond and European call option pricing examples.

Thursday, December 5, 2019 — 4:00 PM EST

More information about this seminar will be added as soon as possible.

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