Stochastic Evolution Equations for Large Portfolios of Stochastic Volatility Models

@article{Hambly2017StochasticEE,
  title={Stochastic Evolution Equations for Large Portfolios of Stochastic Volatility Models},
  author={Ben M. Hambly and Nikolaos Kolliopoulos},
  journal={SIAM J. Financial Math.},
  year={2017},
  volume={8},
  pages={962-1014}
}
We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their volatilities are correlated through systemic Brownian motions. We are interested in the loss process that arises in this setting and we prove the existence of a large portfolio limit for the empirical measure process of this system. This limit evolves as a… CONTINUE READING

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