Interview Test # 3: Job Interview of a rates structurer
Team Latte April 7, 2007
The following is a partial transcript of a job interview for the position of a fixed income exotics structurer in a bank in Asia . The interviewers  two of them  were the head of rates structuring and the senior trader in the exotics desk. The interviewee had around 2 to 3 years of structuring experience.
Interviewer's Question :
We are working on an inflation swap deal currently. Our client fears that there is a significant inflation risk in his portfolio of bonds and wants to buy inflation protection from us. Do you have any idea as to how these swaps are structured and priced?
Candidate's Answer :
Not available.
Our Comment :
Inflation swap is a good way to hedge inflation risk. Typically, the bank is the inflation seller and the institution (client) is the inflation buyer. The swap is a bet on the breakeven inflation level and is similar to an unfunded interest rate swap except for the fact that the underlying payments depend on the level of an inflation index. If breakeven inflation, which can be defined as the nominal yield less the real yield, is equal to the actual/realized inflation at the end of the investment period then an investor is indifferent between holding inflation linked bonds and nominal bonds. However, if the breakeven inflation is less than the actual/realized inflation  as the investor (client) in the above question fears  then he or she should ideally be holding an inflation linked bond to receive protection from higher than expected inflation. But if he holds nominal bonds then he needs to hedge his inflation risk.
Interviewer's Question :
The market volatility of a 2yr x 1yr swaption is 14%. The volatility of a 24x30 caplet is 15% and that of 30x36 volatility is 16%. Can you find the instantaneous correlation between the 24x30 caplet and 30x36 caplet?
Candidate's Answer :
Not available.
Our Comment :
Yes, the instantaneous correlation can be estimated from the above. Swaptions and caplets have overlapping periods and one can use the following formula: Here, and are two adjacent caplets and if the instantaneous correlation between them is between time t=0 to T (assumed to be constant) then we have:
Interviewer's Question :
A two factor HullWhite model is calibrated to the ATM caplet volatilities. The model is used to calculate the swaption volatilities. It is observed that the model generated swaption volatilities are consistently "higher" than the market swaption volatilities. Would you say that the model is wrong?
Candidate's Answer :
Not available.
Our Comment :
We refer to a discussion panel with Ka Lok Chau. Such phenomenon was indeed observed in the USD and GBP markets in late 1998 to Summer 1999. A mismatch between market dynamics and model can exist for a long period of time, and though there is nothing wrong in the model, perhaps it signals some kind of an arbitrage opportunity around which a trading strategy can be devised.
Interviewer's Question :
Suppose you are pricing a 2/30 CMS spread note. My first question is: Can you use a single factor tree to price this note? And what kind of a model will you use to generate the binomial path.
Candidate's Answer :
Yes, you can use any single factor tree to price this note. The biggest issue in using trees to model rates is to take into account the existing forward (term) structure of the rates. A 2/30 spread is a spread between 2y UST and 30y UST so we can use the forward spread to calibrate the model's diffusion process.
As far as the model is concerned, I am not sure, but I think we can use BDT model. Am I right?
Interviewer's Question :
No, BDT is not suitable to model spreads. Can you tell me why? Anyway, that is a separate question. My second question on this issue is whether you would use a Monte Carlo simulation framework or would you prefer to use a single factor tree to price such spread structures?
Candidate's Answer :
Not available
Our Comment :
Spreads like the 2/30 CMS, can indeed be modeling using trees, as long as we can properly calibrate the tree. Using trees in modeling short rates is a complex exercise on paper, and computationally heavy; there exists a forward term structure in the market that is observable and all trees should be calibrated to that forward term structure. Secondly, it is essential to see that risk neutral probabilities of up and down moves are estimated in a manner that is consistent with a recombining tree (though this is only a problem with the normal trees, like the Vasicek or HoLee trees). A 2/30 CMS spread can be negative depending upon the 2y UST and 30y UST and therefore we need a normal model here. A normal models models the diffusion of the rates as a normal distribution. Such models are Vasicek, CIR, etc. A properly calibrated Vasicek tree can be used to price a 2/30 CMS. BlackDermanToy (BDT) tree is lognormal and is not a good model to price spreads.
Monte Carlo simulations can be used with ease to price a European style CMS spread note, and is in fact much simpler and easier to implement in practice. Only when the note is American or Bermudan in nature that Monte Carlo becomes a very cumbersome process. A polynomial approximation, suggested by Longstaff, should be used and incorporated inside a Monte Carlo schedule. For an American or Bermudan structure a tree may be a faster way out.
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