Journal of Computational Finance

Risk.net

A general firm value model under partial information

Cheikh Mbaye, Abass Sagna and Frédéric Vrins

  • We study a structural model where information is made of the default event and a noisy version of the firm-value process.
  • This model offers a realistic description of the actual information being available to the investors, but his computationally challenging.
  • The computational complexity of the model is mitigated by adopting a fast recursive quantization.
  • The method is applied to CDS options. This example emphasizes the importance of the uncertainty impacting the firm-value on the option prices.

We introduce a new structural default model intended to combine enhanced economic relevance and affordable computational complexity. Our approach exploits the information conveyed by a noisy observation of the firm’s value combined with the firm’s actual default state. Moreover, the model is reasonably general, since any diffusion can be used to depict the firm’s dynamics. However, this realistic setup comes at the cost of significant computational challenges. To mitigate these, we propose an implementation based on recursive quantization. A thorough analysis of the approximation error resulting from our numerical procedure is provided.We find that the observation noise has a significant impact on the credit spreads’ implied volatilities. The power of our method is illustrated through the pricing of credit default swap options.

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