Pricing exotic options with L-stable Padé schemes

Khaliq, Abdul; Voss, D.A.; Yousuf, M.

doi:10.1016/j.jbankfin.2007.04.012

Cited by 38 publications

(9 citation statements)

References 15 publications

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“…This has been widely adopted in financial engineering practice. Khaliq, Voss & Yousuf (2007), Khaliq extend this to more general Padé schemes and demonstrate numerically the stability and accuracy in practice for options with exotic payoffs. Further adaptations are possible, for instance, where Wade, Khaliq, Yousuf, Vigo-Aguiar & Deininger (2007) give an application to discretely sampled barrier options, where discontinuities are introduced at certain points in time and a new 'start-up' is needed (see already Rannacher (1974) for the provision of such restarts in an abstract context).…”

Section: Introductionmentioning

confidence: 89%

The impact of a natural time change on the convergence of the Crank-Nicolson scheme

Reisinger

Whitley

2013

IMA Journal of Numerical Analysis

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We first analyse the effect of a square root transformation to the time variable on the convergence of the Crank-Nicolson scheme when applied to the solution of the heat equation with Dirac delta function initial conditions. In the original variables, the scheme is known to diverge as the time step is reduced with the ratio, λ, of the time step to space step held constant and the value of λ controls how fast the divergence occurs. After introducing the square root of time variable we prove that the numerical scheme for the transformed partial differential equation now always converges and that λ controls the order of convergence, quadratic convergence being achieved for λ below a critical value. Numerical results indicate that the time change used with an appropriate value of λ also results in quadratic convergence for the calculation of the price, delta and gamma for standard European and American options without the need for Rannacher start-up steps.

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Section: Introductionmentioning

confidence: 89%

The impact of a natural time change on the convergence of the Crank-Nicolson scheme

Reisinger

Whitley

2013

IMA Journal of Numerical Analysis

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“…When the pricing equation is linear, vertical MOL reduces to a system of ordinary differential equations (ODE's), which can quickly be solved by computing a matrix exponential. Khaliq et al (2007) proposed vertical MOL for option pricing and explained its stability and accuracy. This paper uses vertical MOL as unreported simulations show that vertical MOL is quicker and more accurate than the implicit finite difference method, with no stability problems because the ''time" dimension is not discretised.…”

Section: Vertical Methods Of Lines (Mol)mentioning

confidence: 99%

Tests of non linear Gaussian term structure models

Realdon

2016

Journal of International Financial Markets, Institutions and Mo

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Available online xxxx JEL classification: G12 G13 Keywords: Quadratic model Black model Vasicek model Black-Karasinski model Method of lines Extended Kalman filter a b s t r a c tSince the 2008 financial crisis Government bond yields in US, Europe and elsewhere have been historically low and challenged term structure models that cannot rule out negative yields. This paper uses US and German Government yields to test three factor Gaussian models that do and that do not rule out negative yields, namely affine models, quadratic models, extensions of the Black and Black-Karasinski models. Quadratic models and a Vasicek-type model best fit observed yields when the stochastic factors driving the short rate are correlated. However the Black-Karasinski model for the US and the Black model for both US and Germany can best fit yields when interest rates are lowest, i.e. after 2008, despite the restriction of independent factors driving the short rate. A new linearquadratic model whereby the central tendency of the short rate is a non-negative quadratic function of Gaussian factors performs particularly well for German yields. All models fit German yields better than US yields. All models fit the one year yield worse than longer term yields.

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“…MOL is based on exponential time integration, according to which partial di¤erential equations are only discretised in space, but not in time. Vertical MOL was proposed in …nance by Khaliq, Voss and Yousuf (2007) to value exotic options with L-stable Pade'schemes. Vertical MOL proves particularly suitable for pricing problems involving default intensities.…”

Section: Literaturementioning

confidence: 99%

Non-linear Gaussian sovereign CDS pricing models

Realdon

2018

Quantitative Finance

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Prior literature indicates that quadratic models and the Black-Karasinki model are very promising for CDS pricing. This paper extends these models and the Black (1995) model for pricing sovereign CDS' s. For all ten sovereigns in the sample quadratic models best …t CDS spreads insample, and a four factor quadratic model can account for the joint e¤ects on CDS spreads of default risk, default loss risk and liquidity risk with no restriction to factors correlation. Liquidity risk appears to a¤ect sovereign CDS spreads. However quadratic models tend to over-…t some CDS maturities at the expense of other maturities, while the BK model is particularly immune from this tendency. The Black model seems preferable because its out-of-sample performance in the time series dimension is the best.

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Pricing exotic options with L-stable Padé schemes

Cited by 38 publications

References 15 publications

The impact of a natural time change on the convergence of the Crank-Nicolson scheme

The impact of a natural time change on the convergence of the Crank-Nicolson scheme

Tests of non linear Gaussian term structure models

Non-linear Gaussian sovereign CDS pricing models

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