In the context of yield curve construction, bootstrapping refers to a technique used to determine the zero-coupon yield curve that is consistent with a given set of bond prices. The basic idea behind the technique is to start with the closest bond maturity available and use its price to estimate the zero-coupon yield at that maturity. Then, this yield is used to calculate the present value of the bond cash flows, and the resulting present value is subtracted from the bond price to obtain the value of the residual cash flow. This process is repeated for all the other available bonds, and the resulting set of residual cash flows provides the information needed to estimate the zero-coupon yields at the remaining maturities.
To illustrate the process more formally, suppose we have a set of n coupon-bearing bonds with maturities T1, T2, ..., Tn and coupon rates C1, C2, ..., Cn, and suppose that the market prices of these bonds are P1, P2, ..., Pn, respectively. The goal is to estimate the zero-coupon yield curve at maturities T1, T2, ..., Tn. The first step is to estimate the zero-coupon yield at the shortest maturity, T1. This can be done by solving the following equation for y1:
$$P_1 = \frac{C_1}{1+y_1} + \frac{C_1}{(1+y_1)^2} + ... + \frac{C_1}{(1+y_1)^{T_1-1}} + \frac{1}{(1+y_1)^{T_1}}$$
Once y1 is determined, it can be used to estimate the value of the residual cash flow for the second bond, which is given by:
$$R_2 = P_2 - \frac{C_2}{(1+y_1)} - \frac{C_2}{(1+y_1)^2} - ... - \frac{C_2}{(1+y_1)^{T_2-1}} - \frac{1}{(1+y_1)^{T_2}}$$
The zero-coupon yield at maturity T2 can then be estimated by solving the following equation for y2:
$$R_2 = \frac{1}{(1+y_2)^{T_2}}$$
This process is repeated for all the remaining bonds, resulting in a set of n zero-coupon yields that are consistent with the observed bond prices. These yields can then be used to construct the zero-coupon yield curve, which is a function that maps bond maturities to zero-coupon yields.
Overall, the bootstrapping technique is a powerful tool for yield curve construction, as it provides a way to estimate the zero-coupon yield curve using only a set of observable bond prices. However, the technique relies on a number of assumptions about the underlying bond market, such as the absence of arbitrage opportunities and the existence of a unique zero-coupon yield curve, and it requires careful consideration of a number of practical issues, such as the choice of interpolation method and the treatment of missing data.