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By exploiting the structure of particular financial instruments it is possible to derive the discount curve. This technique is often used in the construction of a swap curve. The value of a new swap is zero. By equating the fixed and floating sides of the swap it is possible to solve for the relevant discount factors assuming that all cashflows that occur at the same time in the future are discounted at the same rate. Unfortunately, while this technique is easy to apply it does not guarantee that the discount curve will behave, particulary at the long end.T

Bootstrapping basically uses short term rates to find longer term rates. Using the zero-coupon factor Taking an example to illustrate this:take Z(0,0.5) as the zero coupon factor for a payment to be recieved in half a year from, Cash Flow (0.5) as the cash flow from a treasury instrument 6 months from now and P(0) to be the price of instrument at t=0.You can consider the corresponding instrument to be the Price of a 6 month bond .P(0) = Cash flow(0.5) / Z(0,0.5)Assume that the coupon is 3%. This would imply a Cash Flow of 101.5 (as 3% is annual) for an instrument with price at t=0 of 100. Filling in our equation above, we can calculate the zero coupon factor Z(0,0.5) of 101.5/100 = 1.5bootstrapping effectively breaks up the longer periods into shorter periods so if we extend the relationship forward to 1 year:We have a similar relationship, accommodating the half year factor into the the 1 year factorP(0) = [Cash Flow(0.5) / Z(0,0.5)] + [Cash Flow(1.0) / Z(0,1.0)]As we know [Cash Flow(0.5) / Z(0,0.5)] and P(0), we can determine the Zero coupon factor for 1 year assuming we have the annual coupon rate for the 1 year instrument.And so forth.....

However, in practice there may be some missing maturity, say, the 6th and the 6.5th year zero coupon due to liquidity constraints. Then some interpolation is needed to estimate that zero coupon factors.