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Floating Rate Floors

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Anthony Calleja

Floating Rate Floors

Hi,

I've read this stackoverflow post (https://stackoverflow.com/questions/42195781/using-quantlib-to-compute-cash-flows-for-floatingratebond-with-floor) with interest. I've quoted the salient bit of the reply below. My question is does QuantLib have a pricer that just takes the expected LIBOR rate from the forecast curve and takes the minimum between that and the floor. I do understand this is not the valid/right way of doing things but I'm just checking whether QuantLib can do as so at this point.

"The theory first: when pricing the coupon with a floor, you can't just take the expected LIBOR rate from your forecast curve and take the minimum between that and the floor. Instead, you need to take the expected value of the minimum between the rate and the floor, and unfortunately E[min(R,F)] is not the same as min(E[R],F). So no, the floor doesn't just provide a minimum; you need a different formula to estimate the expected payoff."

Thanks

Anthony

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Peter Caspers-4

Re: Floating Rate Floors

Hi Anthony,

this is an edge case with zero input volatility (which you can set up using the constant optionlet volatility class). If you look into blackformula.cpp, this is even explicitly handled as you describe

if (stdDev==0.0)

return std::max((forward-strike)*optionType, Real(0.0))*discount;

Best Regards

Peter

On 01 Aug 2017, at 11:39, Anthony Calleja <[hidden email]> wrote:

Hi,

I've read this stackoverflow post (https://stackoverflow.com/questions/42195781/using-quantlib-to-compute-cash-flows-for-floatingratebond-with-floor) with interest. I've quoted the salient bit of the reply below. My question is does QuantLib have a pricer that just takes the expected LIBOR rate from the forecast curve and takes the minimum between that and the floor. I do understand this is not the valid/right way of doing things but I'm just checking whether QuantLib can do as so at this point.

"The theory first: when pricing the coupon with a floor, you can't just take the expected LIBOR rate from your forecast curve and take the minimum between that and the floor. Instead, you need to take the expected value of the minimum between the rate and the floor, and unfortunately E[min(R,F)] is not the same as min(E[R],F). So no, the floor doesn't just provide a minimum; you need a different formula to estimate the expected payoff."
Thanks

Anthony

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