Models mostly quantify these two types of risks separately due to the complexity in determination of the correlation between market and credit risk. Reduced form models (Jarrow and Turnbull (1995), Jarrow et al. (1997)) consider market and credit risk jointly with the assumption of independency!
Let's assume that we have a bond portfolio, Which model includes Interest Rate risk, Spread risk and Credit Risk with the assumption of dependency?
is that not the definition of a reduced form model in the first place? a parsimonious model that considers all the factors of default collectively
the independency assumption greatly simplifies the models and modelling.
i am not sure whether it is necessary to separate the factors in the model. the only reason i can think of one would want to do this, is if one measures them individually and want to follow their impact individually. for what reason do you wish to separate them?
one would also need a proper theory of the relationship between default risk and market risk - how the default risk of individual issues affect market risk - risk in the market.
the moment you relax the independency assumption, it may become a case of considering the probability that an issue will default, given that other issues in the market defaults.
market risk should be related to the default risk of a portfolio of bonds
look at my papers on default probability term structures.
A landmark, using copula functions to assure risk correlation:
ROSENBERG, J. V. & SCHUERMANN, T. 2006. A general approach to integrated risk management with skewed, fat-tailed risks. Journal of Financial Economics, 79, 569-614.
Abstract:
Integrated risk management for financial institutions requires an approach for aggregating risk types (market, credit, and operational) whose distributional shapes vary considerably. We construct the joint risk distribution for a typical large, internationally active bank using the method of copulas. This technique allows us to incorporate realistic marginal distributions that capture essential empirical features of these risks such as skewness and fat-tails while allowing for a rich dependence structure. We explore the impact of business mix and inter-risk correlations on total risk. We then compare the copula-based method with several conventional approaches to computing risk.
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