what is the zero volatility spread z spread 
the zero volatility spread z spread is the constant spread that makes the price of a security equal to the present value of its cash flows when added to the yield at each point on the spot rate treasury curve where cash flow is received in other words each cash flow is discounted at the appropriate treasury spot rate plus the z spread the z spread is also known as a static spread formula and calculation for the zero volatility spreadto calculate a z spread an investor must take the treasury spot rate at each relevant maturity add the z spread to this rate and then use this combined rate as the discount rate to calculate the price of the bond the formula to calculate a z spread is p c 1 1 r 1 z 2 2 n c 2 1 r 2 z 2 2 n c n 1 r n z 2 2 n where p current price of the bond plus any accrued interest c x bond coupon payment r x spot rate at each maturity z z spread n relevant time period begin aligned text p frac c 1 left 1 frac r 1 z 2 right 2n frac c 2 left 1 frac r 2 z 2 right 2n frac c n left 1 frac r n z 2 right 2n textbf where text p text current price of the bond plus any accrued interest c x text bond coupon payment r x text spot rate at each maturity z text z spread n text relevant time period end aligned p 1 2r1 z 2nc1 1 2r2 z 2nc2 1 2rn z 2ncn where p current price of the bond plus any accrued interestcx bond coupon paymentrx spot rate at each maturityz z spreadn relevant time period for example assume a bond is currently priced at 104 90 it has three future cash flows a 5 payment next year a 5 payment two years from now and a final total payment of 105 in three years the treasury spot rate at the one two and three year marks are 2 5 2 7 and 3 the formula would be set up as follows 104 90 5 1 2 5 z 2 2 1 5 1 2 7 z 2 2 2 105 1 3 z 2 2 3 begin aligned 104 90 frac 5 left 1 frac 2 5 z 2 right 2 times 1 frac 5 left 1 frac 2 7 z 2 right 2 times 2 frac 105 left 1 frac 3 z 2 right 2 times 3 end aligned 104 90 1 22 5 z 2 1 5 1 22 7 z 2 2 5 1 23 z 2 3 105 with the correct z spread this simplifies to 104 90 4 87 4 72 95 32 begin aligned 104 90 4 87 4 72 95 32 end aligned 104 90 4 87 4 72 95 32 this implies that the z spread equals 0 25 in this example 