Rates Quant Interview Questions

Real rates interview questions worked in full, covering a forward rate derivation and receiver swaption convexity.

Rates quant interviews test a specific combination of skills: fast, accurate arithmetic on curve and duration calculations, a solid grip on no-arbitrage reasoning, and the ability to explain why a given instrument's value moves the way it does as rates change. The questions below are the kind that recur across rates desks at banks and at multi-strategy and macro funds, worked through in full rather than summarized.

Given a one year zero rate of 4 percent and a two year zero rate of 4.51 percent, the question asks for the one year forward rate starting in one year, the rate at which the market is implicitly willing to lend money for the second year given today's curve. The no-arbitrage condition requires that investing for two years at the two year zero rate produces the same result as investing for one year at the one year zero rate and then reinvesting for the second year at the forward rate.

Setting one plus the two year zero rate, squared, equal to one plus the one year zero rate, multiplied by one plus the forward rate, and solving for the forward rate gives 1.0451 squared, divided by 1.04, minus 1, which comes to approximately 5.02 percent. The forward rate sits above both zero rates here because the curve is upward sloping between year one and year two, and a steepening curve always implies a forward rate above the longer of the two zero rates that produced it.

The same zero rates used here come directly from the worked bootstrapping example in yield curve construction and bootstrapping, and an interviewer will often ask this forward rate question as a direct follow-up to a bootstrapping question, testing whether a candidate can move fluently from building a curve to reading information out of it.

A receiver swaption gives its holder the right, but not the obligation, to enter a swap receiving fixed and paying floating at a predetermined rate. Its value rises as rates fall, since the fixed rate locked into the option becomes more attractive relative to the lower prevailing floating rate, and it behaves like a call option on a bond, since a receiver position gains in exactly the same direction as a bondholder benefits when yields decline.