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This paper investigates volatility spillover in the Nigerian sovereign bond market arising from oil price shocks, using Vector Autoregressive Moving Average ‐ Asymmetric Generalized Autoregressive Conditional Heteroscedasticity (VARMA‐AGARCH) model. The paper covers the period March 22, 2011 to April 14, 2016 and makes use of the daily data of the Nigerian Sovereign Bond, Brent oil and West Texas Intermediate (WTI), respectively. We endogenously and sequentially detect structural break points using the test of Bai and Perron (2003) framework. In order to accurately estimate the model, we modify it by incorporating the break points into the VARMA‐AGARCH model, a process which if ignored would lead to model misspecification. The results obtained demonstrate a significant cross‐market volatility transmission between oil and sovereign bond market with ample sensitivity to structural breaks. The study also computes optimum weight portfolio and hedge ratio both with and without structural breaks and results equally indicate sensitivity to structural breaks.