Pricing Credit Spread Options: A 2-factor HW-BK Algorithm
When you are one step ahead of the crowd, you’re a genius. When you are two steps ahead, you are a crackpot.
Rabbi Shlomo Riskin
In this chapter we describe what a credit spread option (CSO) is and show a tree algorithm to price it. The tree algorithm we have opted for is a two factor model composed by a Hull and White (HW) (Hull and White, 1994a) one factor for the interest rate process and a Black-Karazinsky (BK) (Black and Karazinsky, 1991) one factor for the default intensity. As opposed to the tree model of Schönbucher (1999a), the intensity process cannot become negative. Having as input the risk-free yield curve and market implied default probability curve, the model by construction will price correctly the associated defaultable bond. We then use market data to calibrate the model to price an at the money (ATM) CSO call and then test it to price an out of the money (OTM) Bermudan CSO call on a CDS. Furthermore, the discussions in this chapter show in practice the difficulties and challenges faced by financial institutions in marking to market those instruments. This chapter is based on Garcia et al. (2003). Although the paper is from 2003 the price exercise shown was made in 2001. We have kept the same numerical example to show that many of the same issues persisted until the end of 2008 - that is, the fact that the credit derivatives markets is still OTC and there is no liquid option market ...