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The zero-volatility spread is a measure of the spread that the investor would realize over the entire Treasury spot rate curve if a mortgage-backed or asset-backed security is held to maturity. Unlike normal spread, zero-volatility spread, is not a spread of one point on the Treasury yield curve. Zero-volatility spread also known as Z-spread and the static spread, is the spread that will make the price of a security equal to the present value of the cash flows from the mortgage-backed and asset-backed security when discounted at the Treasury spot rate plus the spread. In other words, each cash flow is discounted at the appropriate Treasury spot rate plus the Z-spread. A trial and error method is used in determining the
zero-volatility spread. The difference between the zero-volatility spread and the normal spread depends on the maturity or average life of a structured product, i.e., larger the maturity of the security greater is the difference, and shorter the maturity lesser the difference between both the measures. The shape of the curve also determines the magnitude of the difference between both the spreads. The steeper the curve the greater is the difference.
The value of node is determined using a methodology called backward induction. The value at any node depends on the future cash flows; therefore, we need to start from
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