Optimal portfolio allocation with volatility and co-jump risk that Markowitz would like

Abstract

We study a continuous time optimal portfolio allocation problem with volatility and co-jump risk, allowing prices, variances and covariances to jump simultaneously. Differently from the traditional approach, we deviate from affine models by specifying a flexible Wishart jump-diffusion for the co-precision (the inverse of the covariance matrix). The optimal portfolio weights which solve the dynamic programming problem are genuinely dynamic and proportional to the instantaneous co-precision, reconciling optimal dynamic allocation with the static Markowitz-type economic intuition. An application to the optimal allocation problem across hedge fund investment styles illustrates the importance of having jumps in volatility associated with jumps in price.

The Effect of Jumps in the Crude Oil Market on the Sovereign Risks of Major Oil Exporters

“…The overall results indicate evidence of infrequent rapid changes in the CDS spreads, which might suggest the need to account for such changes in any volatility modelling and risk measures. Not accounting for such infrequent rapid changes in the CDS spreads (i.e., jumps) can make the tails fatter, which in turn might magnify risk measures and affect options pricing (Clements and Liao 2017;Oliva and Renò 2018;Ma et al 2019).…”

“…Furthermore, the main findings imply not only the need to account for price discontinuities in modelling the spreads of sovereign risks but also the need to account for the effect of price discontinuity of crude oil volatility on that of sovereign risks of oil exporters. Such implications affect asset and option pricing (Driessen and Maenhout 2013; Clements and Liao 2017) and refine the predictability of models (Oliva and Renò 2018) involving crude oil volatility and sovereign CDS spreads of large oil exporters.…”

“…Risks 2019, 7, 118 3 of 15 tails in their return distributions (e.g., Wilmot and Mason 2013), and the academic literature highlights the role of jumps in capturing the empirical properties of an asset and in modelling volatility dynamics (Eraker et al 2003;Driessen and Maenhout 2013). Recently, the empirical literature on the jump behaviour of assets has flourished, providing important implications for risk management, asset allocation and derivatives pricing (Oliva and Renò 2018;Ma et al 2019).…”

Jumps in energy and non‐energy commodities

“…Given that risk‐averse investors are likely to select low volatile assets, it is crucial to understand the jump behaviour that represents a kind of tail risk (Oliva and Renò, 2018), especially the jump behaviour in asset volatility (Eraker, 2004). In this paper, we consider the commodity markets that represent a major investment destination for portfolio and risk managers and a market outlet for commodity producers.…”

“…A natural extension of our work would be the use of a different approach allowing for the decomposition of realised volatility, as in Masrorkhah and Lehnert (2017). Future research could also consider dynamic asset allocation models while accounting for the occurrence of jumps and cojumps in the realised volatility (Oliva and Renò, 2018). Other extensions can be made to our analyses by constructing more complex networks of jump risk as in Hu et al (2019), while accounting for the role of macroeconomic news.…”