Capital requirements, the option surface, market, credit and liquidity risk

نویسندگان

  • Ernst Eberlein
  • Dilip Madan
  • Robert H. Smith
  • Wim Schoutens
چکیده

The Sato process model for option prices is expanded to accomodate credit considerations by incorporating a single jump to default occuring at an independent random time with a Weibull distribution. Explicit formulas, in this context, for the bid and ask prices of two price economies that price residual risks to levels of risk acceptability are then derived. Liquidity considerations are thereby captured by the movements in the two prices that indirectly re‡ect changes occuring in the underlying set of zero cost risky cash ‡ows acceptable to the market. In such two price economies it has been proposed that capital requirements supporting a trade are to be set at the di¤erence between the ask and bid prices of the two price economy. We proceed to evaluate the variations in the level of such required capital over time. In particular we observe that the Lehman bankruptcy was primarily a liquidity event for the remaining banks from the perspective of changes in the levels of such a required capital. Additionally, we observe that variations in such capital requirements over time are primarily explained by movements in the option surface and the levels of liquidity, with credit variations playing a part occasionally. The estimations Dilip Madan acknowledges support from the Humboldt foundation as a Research Award Winner.

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تاریخ انتشار 2011