A Spectral Approach to Pricing of Arbitrage-Free SABR Discrete Barrier Options

Thakoor, Nawdha; Tangman, Désiré Yannick; Bhuruth, Muddun

doi:10.1007/s10614-018-9868-8

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…For Monte Carlo method, we use 100, 000 numbers of simulations, 200 numbers of time steps. Let N � 2 10 for Fourier-cosine method. e parameter values are listed in Table 2 for all our numerical examples.…”

Section: Comparison Of the Approximate Solutions Against Montementioning

confidence: 99%

“…akoor, Tangman, and Bhuruth [10] proposed a novel spectral method by discretizing the pricing equation of the discrete barrier options whose price process is modelled by the stochastic Alpha Beta Rho (SABR) model. Liu and Zhang [11] proposed a novel jumpdiffusion model in present of liquidity risk and derived an approximate solution for the valuation of the discrete barrier options.…”

Section: Introductionmentioning

confidence: 99%

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A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump

Huang

Guo

2020

Mathematical Problems in Engineering

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In this paper, the valuation of the discrete barrier options on the condition that the underlying asset price process follows the GARCH volatility and double exponential jump is studied. We derived an analytical approximation of the characteristic function for the underlying log-asset price. Then, a quasianalytical approximate formula of the price of the discrete barrier option is obtained based the on Fourier-cosine method. Numerical examples show that the Fourier-cosine method is fast and efficient for pricing discrete barrier options compared with the Monte Carlo simulation method. Finally, the influences of some important parameters on the prices of discrete barrier options are studied to further illustrate the rationality of the model.

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Section: Comparison Of the Approximate Solutions Against Montementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump

Huang

Guo

2020

Mathematical Problems in Engineering

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“…Specifying an absorbing boundary condition at zero and using an expansion around a one-dimensional Bessel process, the closed-form approximation for European options [33] has been shown to be accurate for small maturity problems [31]. This implies that the search for a numerical method capable of accurately pricing options with large maturities needs to incorporate the absorbing boundary condition in order to ensure that computed prices are arbitrage-free.…”

Section: Introductionmentioning

confidence: 99%

Localized Radial Basis Functions for No-Arbitrage Pricing of Options Under Stochastic Alpha–beta–rho Dynamics

Thakoor

2021

ANZIAM J.

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Closed-form explicit formulas for implied Black–Scholes volatilities provide a rapid evaluation method for European options under the popular stochastic alpha–beta–rho (SABR) model. However, it is well known that computed prices using the implied volatilities are only accurate for short-term maturities, but, for longer maturities, a more accurate method is required. This work addresses this accuracy problem for long-term maturities by numerically solving the no-arbitrage partial differential equation with an absorbing boundary condition at zero. Localized radial basis functions in a finite-difference mode are employed for the development of a computational method for solving the resulting two-dimensional pricing equation. The proposed method can use either multiquadrics or inverse multiquadrics, which are shown to have comparable performances. Numerical results illustrate the accuracy of the proposed method and, more importantly, that the computed risk-neutral probability densities are nonnegative. These two key properties indicate that the method of solution using localized meshless methods is a viable and efficient means for price computations under SABR dynamics.

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“…Alternatively, numerical methods have been used extensively to price options under the SABR model especially when those options have high maturities and, hence, the asymptotic solution of (Hagan et al, 2002) (for the European option) becomes inaccurate. For instance, in (Thakoor et al, 2019) a computational method based on a spectral discretization of the pricing equation is developed for pricing options with discrete barriers under the arbitrage-free SABR model. The high accuracy of the method is established by comparison with special cases of the SABR model where analytical solutions are available.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytical pricing of barrier options in the time-dependent $λ$-SABR model

Itkin,

Muravey

2021

Preprint

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e extend the approach of Carr, Itkin and Muravey, 2021 for getting semianalytical prices of barrier options for the time-dependent Heston model with time-dependent barriers by applying it to the so-called λ-SABR stochastic volatility model. In doing so we modify the general integral transform method (see Itkin, Lipton, Muravey, Generalized integral transforms in mathematical finance, World Scientific, 2021) and deliver solution of this problem in the form of Fourier-Bessel series. The weights of this series solve a linear mixed Volterra-Fredholm equation (LMVF) of the second kind also derived in the paper. Numerical examples illustrate speed and accuracy of our method which are comparable with those of the finite-difference approach at small maturities and outperform them at high maturities even by using a simplistic implementation of the RBF method for solving the LMVF.

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A Spectral Approach to Pricing of Arbitrage-Free SABR Discrete Barrier Options

Cited by 5 publications

References 18 publications

A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump

A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump

Localized Radial Basis Functions for No-Arbitrage Pricing of Options Under Stochastic Alpha–beta–rho Dynamics

Semi-analytical pricing of barrier options in the time-dependent $λ$-SABR model

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