Thomas F. Coleman

Robustly Hedging Variable Annuities with Guarantees Under Jump and Volatility Risks

Recent variable annuities offer participation in the equity market and attractive protection against downside movements. Accurately quantifying this additional equity market risk and robustly hedging options embedded in the guarantees of variable annuities are new challenges for insurance companies. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black-Scholes model is inadequate in preventing excessive liabilities. A model which realistically describes the real world price dynamics over a long time horizon is essential for the risk management of the variable annuities. In this article, both jump risk and volatility risk are considered for risk management of lookback options embedded in guarantees with a ratchet feature. We evaluate relative performances of delta hedging and dynamic discrete risk minimization hedging strategies. Using the underlying as the hedging instrument, we show that, under a Black-Scholes model, local risk minimization hedging can be significantly better than delta hedging. In addition, we compare risk minimization hedging using the underlying with that of using standard options. We demonstrate that, under a Mertons jump diffusion model, hedging using standard options is superior to hedging using the underlying in terms of the risk reduction. Finally, we consider a market model for volatility risks in which the at-the-money implied volatility is a state variable. We compute risk minimization hedging by modeling at-the-money Black-Scholes implied volatility explicitly; the hedging effectiveness is evaluated, however, under a joint model for the underlying price and implied volatility. Our computational results suggest that, when implied volatility risk is suitably modeled, risk minimization hedging using standard options, compared to hedging using the underlying, can potentially be more effective in risk reduction under both jump and volatility risks. Copyright The Journal of Risk and Insurance, 2007.

Min-max robust and CVaR robust mean-variance portfolios

Lei Zhu David R Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1; email: l7zhu@cs.uwaterloo.ca Thomas F. Coleman Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1; email: tfcoleman@uwaterloo.ca Yuying Li David R Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1; email: yuying@uwaterloo.ca

Optimal Portfolio Execution Strategies and Sensitivity to Price Impact Parameters

When liquidating a portfolio of large blocks of risky assets, an institutional investor wants to minimize the cost as well as the risk of execution. An optimal execution strategy minimizes a weighted combination of the expected value and the variance of the execution cost, where the weight is given by a nonnegative risk aversion parameter. The execution cost is determined from price impact functions. In particular, a linear price impact model is defined by the temporary impact matrix

Optimal Execution Under Jump Models For Uncertain Price Impact

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Smoothing and parametric rules for stochastic mean-CVaR optimal execution strategy

and the permanent impact matrix

A note on ‘new algorithms for constrained minimax optimization’

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Fast (Structured) Newton Computations

, which represent the expected price depression caused by trading assets at a unit rate. In this paper, we analyze the sensitivity of the optimal execution strategy to estimation errors in the impact matrices under a linear price impact model. We show that, instead of depending on

Primal explicit max margin feature selection for nonlinear support vector machines

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Stable local volatility function calibration using spline kernel

and

A secant method for nonlinear least-squares minimization

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