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Bond sensitivities when the interest rates are near the zero lower bound

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Zero Lower Bound (ZLB) and even negative values for the interest rates have been present in markets since the 2008 financial crisis.
This situation has caused troubles on available well-established financial theory and tools (as common pricers)
leading various authors to explore suitable term structures
suitable for the ZLB setting.

Though having a bond price is highly desirable, from the perspective of position and risk managements, it is also of paramount importance to have the corresponding parameter sensitivities. As this aspect does not seem to be covered by the recent literature, then we aim here to contribute in this direction.

Therefore we first derive analytic approximations
of the yield-rate level sensitivities,
with respect to the shock affecting the underlying shadow rate.
This finding is then used to provide
high order sensitivities of any Zero-Coupon-Bond
(ZCB) price.
Our results may be applied to perform the hedging of
bond portfolio by a portfolio linked to interest rates,
as is very often required in practice.

Author(s):

CĂ©lia Bayet    
ECE Paris
France

Jean-Marc Le Caillec    
Telecom Brest
France

Yves Rakotondratsimba    
ECE Paris
France

 

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