A PDE based Implementation of the Hull&White Model for Cashflow Derivatives
SummaryA new implementation for the one-dimensional Hull&White model is developed. It is motivated by a geometrical approach to construct an invariant manifold for the future dynamics of forward zero coupon bond prices under a forward martingale measure. This reduces the option-pricing problem f...
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| Veröffentlicht in: | Computational statistics 2003-09, Vol.18 (3-4), p.417-434 |
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| creator | Meyer, Sascha Schwarz, Willi |
| description | SummaryA new implementation for the one-dimensional Hull&White model is developed. It is motivated by a geometrical approach to construct an invariant manifold for the future dynamics of forward zero coupon bond prices under a forward martingale measure. This reduces the option-pricing problem for cashflow derivatives to the solution of a series of heat equations. The heat equation is solved by a standard Crank-Nicolson scheme. The new method avoids the calibration used in traditional solution approaches. The computation of prices for European and Bermudan swaptions shows the convergence behavior of our new implementation. We also demonstrate the efficiency of our new approach resulting in a speed improvement by one order of magnitude compared to traditional trinomial tree implementations. |
| doi_str_mv | 10.1007/BF03354607 |
| format | Article |
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It is motivated by a geometrical approach to construct an invariant manifold for the future dynamics of forward zero coupon bond prices under a forward martingale measure. This reduces the option-pricing problem for cashflow derivatives to the solution of a series of heat equations. The heat equation is solved by a standard Crank-Nicolson scheme. The new method avoids the calibration used in traditional solution approaches. The computation of prices for European and Bermudan swaptions shows the convergence behavior of our new implementation. We also demonstrate the efficiency of our new approach resulting in a speed improvement by one order of magnitude compared to traditional trinomial tree implementations.</description><identifier>ISSN: 0943-4062</identifier><identifier>EISSN: 1613-9658</identifier><identifier>DOI: 10.1007/BF03354607</identifier><language>eng</language><publisher>Heidelberg: Springer Nature B.V</publisher><subject>Bonding ; Calibration ; Cash flow ; Computation ; Convergence ; Derivatives ; Heat equations ; Invariants ; Martingales ; Mathematical models ; Partial differential equations ; Statistics ; Thermodynamics ; Zero coupon bonds</subject><ispartof>Computational statistics, 2003-09, Vol.18 (3-4), p.417-434</ispartof><rights>Computational Statistics is a copyright of Springer, (2003). 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| ispartof | Computational statistics, 2003-09, Vol.18 (3-4), p.417-434 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Bonding Calibration Cash flow Computation Convergence Derivatives Heat equations Invariants Martingales Mathematical models Partial differential equations Statistics Thermodynamics Zero coupon bonds |
| title | A PDE based Implementation of the Hull&White Model for Cashflow Derivatives |
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