Negative Convexity in Pass-Through MBS: Mechanisms and Conditions
Kaname Imagawa
Abstract
This paper investigates the mechanisms and conditions underlying negative convexity in pass-through mortgage-backed securities (MBSs) backed by fixed-rate mortgages. We first derive an exact decomposition of MBS prices into three components: the present value of interest-rate-independent cash flows, the present value of principal repaid early through interest-rate-dependent prepayments, and an interest rate option component capturing the reduction in future cash flows due to prepayments. Under a first-order approximation, the latter two components resemble portfolios of floorlets and Asian-style interest rate options, respectively. We then apply a cumulant expansion to derive closed-form valuation approximations under the one-factor Hull--White model. Numerical results show that including the second cumulant improves accuracy relative to a first-cumulant approximation. Building on the price decomposition, we decompose duration and convexity into component-level contributions and express the condition for negative convexity in terms of their second-order interest rate sensitivities. Finally, phase diagrams across interest rate levels and refinancing sensitivities identify the regions where negative convexity occurs and the corresponding sign boundaries. The negative-convexity region expands as the long-run mean of refinancing sensitivity increases. Negative convexity can arise even when no refinancing incentive exists initially, while its magnitude may vary nonmonotonically with the interest rate level. These findings explain negative MBS convexity through the sensitivities of its price components and quantitatively characterize the conditions governing its occurrence.
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