Approximate basket options valuation for a jump-diffusion model

Xu, Guoyang; Zheng, Harry

doi:10.1016/j.insmatheco.2009.05.012

Cited by 19 publications

(25 citation statements)

References 15 publications

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“…The lower bound plays a dominant role in the approximation with a weight 2/3, the other two parts with a weight 1/6 each are the second moment adjustment to the lower bound. Xu and Zheng (2009) show that LB ≤ C A (T, K) ≤ U B, which provides the error bounds for the approximate basket option value. The PEA method is fast and accurate in comparison with some other well known numerical schemes for basket options, see Xu and Zheng (2009) for details.…”

Section: Modelmentioning

confidence: 85%

“…The lower bound can be calculated exactly in the Black-Scholes framework. Xu and Zheng (2009) show that the lower bound can also be calculated exactly in a special jump-diffusion model with constant volatility and two types of Poisson jumps (systematic and idiosyncratic jumps). The usefulness of Rogers and Shi's lower bound depends crucially on one's ability of finding some highly correlated random variables to the basket value and computing the conditional expectation exactly.…”

Section: Introductionmentioning

confidence: 93%

“…If the local volatility function is time independent then there is a closed-form expression for the approximation. Numerical tests show that the lower bound approximation is fast and accurate in most cases in comparison with the Monte Carlo method, the partial-exact approximation (Xu and Zheng (2009)) and the asymptotic expansion approximation (Xu and Zheng (2010)). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Models

Xu¹,

Zheng

2014

Int. J. Theor. Appl. Finan.

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Abstract. In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there is a closed-form expression for the approximation. Numerical tests show that the suggested approximation is fast and accurate in comparison with the Monte Carlo and other approximation methods in the literature.

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Section: Modelmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Models

Xu¹,

Zheng

2014

Int. J. Theor. Appl. Finan.

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“…Flamouris and Giamouridis (2007) propose the use of a simplified jump process, namely, a Bernoulli jump process, and obtain approximate basket option valuation formulas. Xu and Zheng (2009) show that a lower bound similar to that of Rogers and Shi (1995) can also be calculated exactly in a special jump diffusion model with constant volatility and two types of Poisson jumps. An asymptotic expansion with a variance approximation and a lower bound to basket option values for local volatility jump diffusion models are studied by Zheng (2010, 2014), respectively.…”

mentioning

confidence: 82%

General closed-form basket option pricing bounds

Caldana

Fusai

Gnoatto

et al. 2015

Quantitative Finance

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This is the accepted version of the paper.This version of the publication may differ from the final published version. This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms, hence they do not suffer from the curse of dimensionality and can be applied also to high dimensional problems where most existing methods fail. In particular we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate. Permanent repository link

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“…The first test problem we consider is a basket option on six assets. We use a jump-diffusion model similar to that of [38]. The corresponding Hilbert space is H = (R 6 , ·, · 2 ), where ·, · 2 denotes the Euclidean scalar product.…”

Section: Test Problemsmentioning

confidence: 99%

Option Pricing in Hilbert Space-Valued Jump-Diffusion Models Using Partial Integro-Differential Equations

Hepperger¹

2010

SIAM J. Finan. Math.

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Abstract. Hilbert space-valued jump-diffusion models are employed for various markets and derivatives. Examples include swaptions, which depend on continuous forward curves, and basket options on stocks. Usually, no analytical pricing formulas are available for such products. Numerical methods, on the other hand, suffer from exponentially increasing computational effort with increasing dimension of the problem, the "curse of dimension." In this paper, we present an efficient approach using partial integro-differential equations. The key to this method is a dimension reduction technique based on a Karhunen-Loève expansion, which is also known as proper orthogonal decomposition. Using the eigenvectors of a covariance operator, the differential equation is projected to a low-dimensional problem. Convergence results for the projection are given, and the numerical aspects of the implementation are discussed. An approximate solution is computed using a sparse grid combination technique and discontinuous Galerkin discretization. The main goal of this article is to combine the different analytical and numerical techniques needed, presenting a computationally feasible method for pricing European options. Numerical experiments show the effectiveness of the algorithm.

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Approximate basket options valuation for a jump-diffusion model

Cited by 19 publications

References 15 publications

Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Models

Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Models

General closed-form basket option pricing bounds

Option Pricing in Hilbert Space-Valued Jump-Diffusion Models Using Partial Integro-Differential Equations

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