Dynamic optimal investment in equity and credit default swaps in the presence of default
Embargo Date
2027-05-30
OA Version
Citation
Abstract
We consider an equity market subject to risks from both unhedgeable shocks and default. The novelty of our work is that to partially offset the default risk, investors may also dynamically trade in a credit default swap (CDS) market. Assuming investment opportunities are driven by functions of an underlying diffusive factor process, we identify the certainty equivalent with a semi-linear partial differential equation (PDE), which has quadratic growth in both the function and its gradient, for an investor with exponential, or constant absolute risk aversion (CARA), utility. For general model specifications, we prove existence of a solution to the PDE, which is also the certainty equivalent. We show the optimal policies in the CDS market cover not only equity losses upon default (as one would expect), but also losses due to restricted future trading opportunities. We further use our results to price default-dependent claims via the principle of utility indifference. Additionally, we find that provided the underlying equity market is complete absent the possibility of default, the equity-CDS market is complete accounting for default. Finally, through numerical applications, we show that (i) the optimal CDS positions are essentially static (and hence easily implementable), (ii) trading in the CDS market dramatically increases the investor's indirect utility compared to trading in the equity market alone, (iii) and the investor should choose the CDS with the closest maturity that covers her entire horizon.
Description
2025
License
Attribution-NonCommercial-NoDerivatives 4.0 International