Interview #14: Job Interview of a Market Risk Manager
June 8, 2011
Hereís a partial transcript of a real life job interview of a Market Risk management professional.
An asset is trading at 10% volatility. You look at the traderís P&L and see that he is mark to marking a one year ATM (fixed strike) Lookback caplet (call) option at 6% based on a pricing model. You want to get a quick back of the envelope price of this product without getting into an argument about the pricing model. What should the approximate, back of the envelope value of this product?
Lookback argument (the hedging argument) is one of the very powerful, empirical (and quasi-mathematical) arguments in derivatives trading, one that every trader carries in his back pocket. The above question, posed even to a junior trader, would seem utterly trivial. However, many risk managers and model validation experts in banks get totally bogged down with models and all that to understand the valuation of Lookback options.
An asset is trading at 20% volatility. A trader is short a one year 100 strike (ATM), 98 out-strike (knock out barrier 98) and the barrier is being monitored at the close of every day. You notice that he is using the same 98 level as the knock out barrier in his valuation and suspect, quite correctly, that he wants the barrier to be hit as soon as possible. Whatís apparently out of place in this situation?
A trader who is short a barrier would definitely want a barrier to be extinguished as soon as possible so that he can get rid of the liability and pocket the premium. The level of the barrier can make a lot of difference in the price of a barrier (knock out or a knock in) option. In real life barriers are monitored at discrete monitoring points (daily, weekly, etc.) but the closed form pricing models assume continuous monitoring of the barrier. There is barrier shift when we move from continuous to discrete and there is a formula to estimate that (the formula becomes quite simple if you strip the Riemann zeta function and all that). Some traders try to manipulate the level of the barrier to their advantage and donít incorporate barrier shift if it adversely affects their position.
Here, the barrier level of 98 needs to be adjusted due to discrete monitoring. And, the formula by which that can be done is extremely simply and one can remember it in his head.
The random number generator on your Excel spreadsheet has broken down and you have no clue how to write a mathematical algorithm to generate random numbers. However, your Excel spreadsheet is otherwise working fine. Please generate a random walk for your favourite asset.
This is a great question, one that requires key understanding, or rather intuition, about random numbers and their place in probability theory. Itís one of the best interview questions that we have ever come across.
I am sure you must have hear of (or used) "local volatility" models in valuation of derivatives. Every trader swears by it. But I am not too convinced that this is an accurate picture of reality. What is fundamental problem with a "local" volatility model, one that doesnít quite make sense? Can you explain in a sentence or two, in intuitive terms?
The short and apt answer to this question would have probably landed him the job. However, one needs to have ground realities of vol modeling checked before answering this question. And we have to admit, answering this question in a sentence or two may be quite challenging for the uninitiated.
[The interviewer shows a print out of the term structure of implied volatilities of USD caplets.]
As you can see from the term structure of volatility of USD caplets, the implied volatility of the caplets decrease for longer maturities and the decline becomes quite pronounced beyond one year. Can you think of a reason why this is so?
The simple answer lies with the fact of "mean reversion" in the interest rate markets.
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