Capital Requirements, the Option Surface, Market, Credit and Liquidity Risk

Abstract

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 for bid and ask prices are derived. Liquidity considerations are captured by movements in these prices reflecting possible changes in the set of zero cost cash flows acceptable to the market. Capital requirements supporting a trade are taken to be given by the difference between the ask and bid prices. From this perspective of variations in required capital it is observed that the Lehman bankruptcy was primarily a liquidity event for the remaining banks. Further, we observe that variations in 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.

Keywords: Conic Finance, Bid and Ask Prices, Sato Process, Weibull Distribution

JEL Classification: G10, G12, G13