TR-BDF2 for Stable American Option Pricing

Floc'h, Fabien Le

doi:10.2139/ssrn.1648878

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…We combine a finite element approximation in space with a Backward Differentiation Formula (BDF) scheme in time, since Crank-Nicholson time-stepping or ADI schemes can give rise to instabilities for Dirac initial data (see [35,50]; we refer to [6] for a stability analysis and to [20] for some financial applications of BDF schemes). Equation (4.4) can be written as…”

Section: Transformation and Weak Formulationmentioning

confidence: 99%

Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method

Cozma¹,

Mariapragassam²,

Reisinger³

2019

SIAM J. Finan. Math.

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We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models (LSV) with stochastic short rates. We build upon the particle method introduced by Guyon and Henry-Labordère [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from: a calibrated pure local volatility model; a two-factor Heston-type LSV model (both with deterministic rates); the stochastic (CIR) short rates. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. However, we address in the paper some specific difficulties arising from the Heston model, notably by a new PDE formulation and finite element solution to bypass the singularities of the density when zero is attainable by the variance. The calibration procedure is performed on market data for the EUR-USD currency pair and has a comparable run-time to the PDE calibration of a two-factor LSV model alone.

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Section: Transformation and Weak Formulationmentioning

confidence: 99%

Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method

Cozma¹,

Mariapragassam²,

Reisinger³

2019

SIAM J. Finan. Math.

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“…However, to do this, we have to hold the data v (n+1) . Since the entire computational domain is a grid of size N × N, N 2 amount of storage is needed in memory to hold v (n+1) throughout the time period, ∆t, to obtain v (n) in Equation (7). Therefore, the amortized cost is on the order of N 2 .…”

Section: Computational Costmentioning

confidence: 99%

“…However, in practice, the time to obtain one more significant digit on the option price grows exponentially with the first order convergence speed in time. Therefore, it would be natural to try second order schemes such as Crank-Nicolson, BDF-2 [6,7], etc. Each of the second order schemes has its own advantages and disadvantages.…”

Section: Introductionmentioning

confidence: 99%

Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets

Pak

Han²,

Hong

2017

Symmetry

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Abstract:The Crank-Nicolson method can be used to solve the Black-Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank-Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of equations resulting from the Crank-Nicolson discretization help us to use the standard pre-conditioner for the iterative matrix solver and reduces the number of iterations to get an accurate option values. In addition, the number of iterations that is required to solve the preconditioned system, resulting from the proposed iterative Crank-Nicolson scheme, does not grow with the size of the system. Thus, we can effectively reduce the order of complexity in multidimensional option pricing. The numerical results are compared to the one with implicit Operator Splitting Method (OSM) to show the effectiveness.

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Local Volatility and Milstein Discretization in Practice

Floc'h¹

2012

SSRN Journal

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TR-BDF2 for Stable American Option Pricing

Cited by 3 publications

References 13 publications

Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method

Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method

Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets

Local Volatility and Milstein Discretization in Practice

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