|
:''Not to be confused with Bootstrapping (corporate finance).'' In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps.() A bootstrapped curve, correspondingly, is one where the prices of the instruments used as an ''input'' to the curve, will be an exact ''output'', when these same instruments are valued using this curve. Here, the term structure of spot returns is recovered from the bond yields by solving for them recursively, by forward substitution: this iterative process is called the Bootstrap Method. The usefulness of bootstrapping is that using only a few carefully selected zero-coupon products, it becomes possible to derive par swap rates (forward and spot) for ''all'' maturities given the solved curve. ==General Methodology== + We solve for which is the 1.5 year spot rate. |} As stated above, the selection of the input securities is important, given that there is a general lack of data points in a yield curve (there are only a fixed number of products in the market). More importantly, because the input securities have varying coupon frequencies, the selection of the input securities is critical. It makes sense to construct a curve of zero-coupon instruments from which one can price any yield, whether forward or spot, without the need of more external information.() Note that certain assumptions (e.g. linear interpolation) will always be required. The General Methodology is as follows: (1) Define the set of yielding products - these will generally be coupon-bearing bonds; (2) Derive discount factors for the corresponding terms - these are the internal rates of return of the bonds; (3) 'Bootstrap' the zero-coupon curve, successively calibrating this curve such that it returns the prices of the inputs. A generically stated algorithm for the third step is as follows; for more detail see Yield curve#Construction of the full yield curve from market data. For each input instrument: *solve analytically for all zero-rates where this possible (see side-bar example) *iteratively solve for other rates (initially using an approximation) such that the price of the instrument in question is exactly outputted when calculated using the curve *once solved, save these rates, and proceed to the next instrument. When solved as described here, the curve will be arbitrage free in the sense that it is exactly consistent with the selected prices; see Rational pricing #Fixed income securities and Bond valuation# Arbitrage-free pricing approach. Note that some analysts will instead construct the curve such that it results in a best-fit "through" the input prices, as opposed to an exact match, using a method such as Nelson-Siegel. Regardless of approach, however, there is a requirement that the curve be arbitrage-free in a second sense: that all forward rates are positive. More sophisticated methods for the curve construction — whether targeting an exact- or a best-fit — will additionally target curve "smoothness" as an output,()() and the choice of interpolation method here, for rates not directly specified, will be important. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bootstrapping (finance)」の詳細全文を読む スポンサード リンク
|