Effect of credit spread can be measured using spread duration and have a same concept with interest rate (yield) movement toward price (corporate bond price decrease when yield increase, vice versa).
When corporate bond spread get narrower, Curriculum concluded that the corporate bond price shall be increase, with notes of interest rates are unchanged.
My question is, what is the effect if the spread duration get narrower because of interest rates are increasing and the bond yield itself doesn’t change? Based on bond price valuation using discounted cash flow, the price of corporate bond is supposed to be same as yield for the bond is still the same. Somehow, using spread duration, the price is supposed to be increased, because of drop in spread.
I find these quite contradicted. Can somebody help me to explain the right concept?