Frédéric Godin

Optimal hedging when the underlying asset follows a regime-switching Markov process

We develop a flexible discrete-time hedging methodology that minimizes the expected value of any desired penalty function of the hedging error within a general regime-switching framework. A numerical algorithm based on backward recursion allows for the sequential construction of an optimal hedging strategy. Numerical experiments comparing this and other methodologies show a relative expected penalty reduction ranging between 0.9% and 12.6% with respect to the best benchmark.

Minimizing CVaR in global dynamic hedging with transaction costs

This study develops a global derivatives hedging methodology which takes into account the presence of transaction costs. It extends the Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239] framework in two ways. First, to reduce the occurrence of extreme losses, the expected utility is replaced by the conditional Value-at-Risk (CVaR) coherent risk measure as the objective function. Second, the normality assumption for the underlying asset returns is relaxed: general distributions are considered to improve the realism of the model and to be consistent with fat tails observed empirically. Dynamic programming is used to solve the hedging problem. The CVaR minimization objective is shown to be part of a time-consistent framework. Simulations with parameters estimated from the S&P 500 financial time series show the superiority of the proposed hedging method over multiple benchmarks from the literature in terms of tail risk reduction.

Assessing the effectiveness of local and global quadratic hedging under GARCH models

Local and global quadratic hedging are alternatives to delta hedging that more appropriately address the hedging problem in incomplete markets. The objective of this article is to investigate and contrast the effectiveness of these strategies under GARCH models, both experimentally and empirically. Our analysis centers on three important practical issues: (i) the value added of global over local quadratic hedging, (ii) the importance of the choice of measure (real-world or risk-neutral) when implementing quadratic hedging, and (iii) the robustness of quadratic hedging to model mis-specification. We find that a global approach to quadratic hedging significantly reduces the risk of hedging derivatives with long-term maturities (one year or more), provided that it is implemented under the real-world probability measure. Global quadratic hedging should therefore be advocated when hedging LEAPS and other long-term derivatives such as market-linked certificates of deposit.

Optimal Hedging when the Underlying Asset Follows a Regime-Switching Markov Process

We develop a flexible discrete-time hedging methodology that minimizes the expected value of any desired penalty function of the hedging error within a general regime-switching framework. A numerical algorithm based on backward recursion allows for the sequential construction of an optimal hedging strategy. Numerical experiments comparing this and other methodologies show a relative expected penalty reduction ranging between 0.9% and 12.6% with respect to the best benchmark.

A Profitable Modification to Global Quadratic Hedging

Abstract Recent research has shown that global quadratic hedging, also known as variance-optimal hedging and mean-variance hedging, can significantly reduce the risk of hedging call and put options with long-term maturities (one year or more), such as Long-Term Equity AnticiPation Securities (LEAPS). We propose a modification to global quadratic hedging that is more profitable on average to the hedger without substantially increasing his downside hedging risk, if at all. We prove mathematically that the expected terminal hedging gain of our modified strategy is greater than that of the global quadratic hedging strategy. The performance of our strategy is evaluated under simulated return paths from GARCH, regime-switching and jump-diffusion models, and under empirical S&P 500 return paths.

LOCAL HEDGING OF VARIABLE ANNUITIES IN THE PRESENCE OF BASIS RISK

A method to hedge variable annuities in the presence of basis risk is developed. A regime-switching model is considered for the dynamics of market assets. The approach is based on a local optimization of risk and is therefore very tractable and flexible. The local optimization criterion is itself optimized to minimize capital requirements associated with the variable annuity policy, the latter being quantified by the Conditional Value-at-Risk (CVaR) risk metric. In comparison to benchmarks, our method is successful in simultaneously reducing capital requirements and increasing profitability. Indeed the proposed local hedging scheme benefits from a higher exposure to equity risk and from time diversification of risk to earn excess return and facilitate the accumulation of capital. A robust version of the hedging strategies addressing model risk and parameter uncertainty is also provided.

Efficient Semi-Parametric Estimation of Non-Gaussian GARCH Processes

Semi-parametric estimators for non-Gaussian GARCH processes based on Feasible Weighted Least Squares (FWLS) are proposed. The estimators are consistent and do not require the specification of the innovations distribution family. The FWLS estimators incorporate information related to the skewness and kurtosis of residuals. This improves their efficiency in comparison to Normal Quasi-Maximum Likelihood (NQML) estimators which only rely on the first two conditional moments. The improved efficiency of FWLS estimators is illustrated in a simulation experiment; the estimation RMSE decreases observed by using the FWLS estimator instead of the NQML range between 0.07% and 10.3% for all parameters of the considered NGARCH with Variance-Gamma innovations. The methodology is also shown to be applicable for the estimation of multivariate GARCH processes.