Numerical Valuation of Cross-Currency Swaps and Swaptions

Dempster, M. A. H.; Hutton, J.P.

doi:10.2139/ssrn.40872

Cited by 20 publications

(16 citation statements)

References 8 publications

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“…Accuracy of finite difference schemes is well established (see Carr andFaguet 1994 in general or Dempster andHutton, 1997b, for the LP method investigated here), so here we only investigate timings and plot solution surfaces.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Thought should be invested into exploiting such a structure. (See Hutton (1995) or Dempster and Hutton (1997b) for an application of finite difference methods to complex European-style cross-currency derivatives, driven by three stochastic variables.) However, the conclusions about the superiority of explicit schemes to standard implicit ones for a three-state variable complex European option case in Hutton (1995) will apply equally to simplex solution of implicit schemes for American options in higher dimensions.…”

Section: Discussionmentioning

confidence: 99%

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Pricing American Stock Options by Linear Programming

Dempster

Hutton

1999

Mathematical Finance

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We investigate numerical solution of finite difference approximations to American option pricing problems, using a new direct numerical method: simplex solution of a linear programming formulation. This approach is based on an extension to the parabolic case of the equivalence between linear order complementarity problems and abstract linear programs known for certain elliptic operators. We test this method empirically, comparing simplex and interior point algorithms with the projected successive overrelaxation (PSOR) algorithm applied to the American vanilla and lookback puts. We conclude that simplex is roughly comparable with projected SOR on average (faster for fine discretizations, slower for coarse), but is more desirable for robustness of solution time under changes in parameters. Furthermore, significant speedups over the results given here have been achieved and will be published elsewhere. Copyright Blackwell Publishers Inc 1999.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Pricing American Stock Options by Linear Programming

Dempster

Hutton

1999

Mathematical Finance

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“…We choose Dirichlet-type "stopped process" boundary conditions where we stop the processes s(t), r f (t), r d (t) when any of the three hits the boundary. Thus, the value on the boundary is simply the discounted payoff for the current values of the state variables [4].…”

Section: The Model and The Associated Pdementioning

confidence: 99%

“…The term r d u in (3) is distributed evenly over A m 1 , A m 2 and A m 3 . The FD discretization for the spatial variable described in (4) implies that if the grid points are ordered appropriately, then A m 1 , A m 2 and A m 3 are tridiagonal. (There is a different ordering for each of A m 1 , A m 2 and A m 3 .)…”

Section: The Adi Schemementioning

confidence: 99%

A PDE pricing framework for cross-currency interest rate derivatives

Dang¹,

Christara²,

Jackson³

et al. 2010

Procedia Computer Science

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We propose a general framework for efficient pricing via a Partial Differential Equation (PDE) approach of crosscurrency interest rate derivatives under the Hull-White model. In particular, we focus on pricing long-dated foreign exchange (FX) interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. We formulate the problem in terms of three correlated processes that incorporate FX skew via a local volatility function. This formulation results in a time-dependent parabolic PDE in three spatial dimensions. Finite difference methods on uniform grids are used for the spatial discretization of the PDE. The Crank-Nicolson (CN) method and the Alternating Direction Implicit (ADI) method are considered for the time discretization. In the former case, the preconditioned Generalized Minimal Residual (GMRES) method is employed for the solution of the resulting block banded linear system at each time step, with the preconditioner solved by Fast Fourier Transform (FFT) techniques. Numerical results indicate that the numerical methods considered are second-order convergent, and, asymptotically, as the discretization granularity increases, almost optimal, with the ADI method being modestly more efficient than CN-GMRES-FFT. An analysis of the impact of the FX volatility skew on the PRDC swaps' prices is presented, showing that the FX volatility skew results in lower prices (i.e. profits) for the payer of PRDC coupons.

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“…Amin and Bodurtha (1995) and Takahashi and Tokioka (1999) gave numerical solutions to price currency American options with stochastic interest rates by lattice methods; Bodurtha (1995) used HJM (1992) models and Takahashi and Tokioka (1999) applied White (1990, 1994) term structure models. Dempster and Hutton (1997) considered terminable (Bermudan) differential swaps with Gaussian interest rates models by using the partial differential equations (PDE) approach. Schlögl (2002) extended market models to a cross-currency framework.…”

Section: Introductionmentioning

confidence: 99%