On Sensitivity for Portfolio Optimisation Based on a High-dimensional Jump-diffusion Merton Model - Bahareh Afhami; Mohsen Rezapour; Mohsen Madadi; Vahed Maroufy (Statistics, Optimization & Information Computing, 2022)
The problem of singularity of the variance-covariance matrix and its impact on the sensitivity of Markowitz portfolio optimization has been extensively studied in the literature when the underlying model does not include jump terms. In this paper, we first use a jump-diffusion multivariate Merton model to evaluate sensitivity of portfolio optimization and apply principal component analysis (PCA) for dimensionality reduction as a solution to singularity of the variance-covariance matrix. Finally, we provide a numerical study based on the adjusted daily closing price of $S&P\, 500$ stocks to explore the impact of the dimension of the reduced space and jump terms on the sensitivity of the portfolio optimization. Empirical experiments confirm that for models without jump terms, the sensitivity analysis may not reflect the correct assessment of the impact of dimensionality reduction on the portfolio optimization.