Thursday, April 12, 2012

Short Note on Corp (or Risky) Credit Term Structure

Bootstrapping the risk-free yield curve is (relatively) straightforward. One might be tempted to repeat the same trick for Corp bonds, i.e. bootstrapping a risky yield curve and use it for pricing by adding it to the risk free rate.

However, this approach would produce very poor results especially for lower rating bonds. If one starts from short maturity and move to longer maturities according to the naive scheme, the yield usually
  • fluctuates a lot
  • drops sharply (thus almost surely producing an inverted curve)
  • or even unfolds in a way such that the PV of the earlier coupons of a long dated bond exceeds its observed price!
The problems arise because by adopting the naive bootstrapping approach that is borrowed from the risk free case, we completely ignored the effects of 1) recovery; and 2) CF timing shortening (due to default), which are dominant in the case of low rating bonds. Remember, the naive procedure is based on discounted (known) CF with no uncertainties either in timing or amount. When default is not only possible (since we are considering corp) but probable (since we are considering low ratings), this method breaks down.

One way to get by is to back out not the risky yield but the hazard rate (or equivalently the risk neutral default probability). To do that we have to express market bond price as a function of recovery and hazard rate, much like what is done for CDS pricing.

Reference:
Berd et al. 2004, "Defining, Estimating and Using Credit Term Structures" Part 1-3

Monday, April 9, 2012

Quant Interview: High Frequency

1. What is CAPM?

2. If I have a portfolio of long option that are Delta hedged, what daily P&L can be expected?

3. If on average the probability of seeing one car passing by per hour is $\kappa$, what is the probability of seeing one car passing by within 15 minutes?
Ans: $1-(1- \kappa)^{1/4}$

4. How many integers fulfill all 3 criteria below:
  • 3-digited
  • Odd
  • Does not contain any '5' in any place

See here for more interview questions/brainteasers