A minimal model for ZC is a mathematical representation of the Zero-Coupon (ZC) yield curve, which is the relationship between the yield and maturity of a bond with no coupon payments. It is a simplified model that can be used to estimate the prices of bonds with different maturities.
A minimal model for ZC is different from other yield curve models in that it assumes a constant interest rate for all maturities, whereas other models may include multiple interest rates for different segments of the yield curve. This makes it a simpler and more basic model, but it may be less accurate for longer maturities.
The key assumptions of a minimal model for ZC include a constant interest rate for all maturities, perfect liquidity and no default risk for bonds, and a continuous and liquid market for bonds. It also assumes that the yield curve is upward-sloping, meaning longer maturity bonds have higher yields.
A minimal model for ZC can be used in practice to estimate the prices of bonds with different maturities, which can then be used to determine the yield curve for a particular market or economy. It is also used in financial modeling and forecasting, as well as in bond portfolio management to assess the risk and return of different bond investments.
One of the main limitations of a minimal model for ZC is that it does not account for market fluctuations and economic factors that can affect interest rates and bond prices. It also assumes a linear relationship between yield and maturity, which may not always hold true in real-world scenarios. Additionally, the model may be less accurate for longer maturities and may not capture the full complexity of the yield curve.