Pricing of arithmetic basket options by conditioning

Deelstra, Griselda; Liinev, Jan; Vanmaele, Michèle

doi:10.1016/j.insmatheco.2003.11.002

Cited by 87 publications

(106 citation statements)

References 8 publications

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“…We use as parameter values the ones also used in Sect. 7 of Deelstra et al [18], hence r = 5 %, X 1 (0) = X 2 (0) = 100, and w 1 = w 2 = 0.5. Table 3 gives numerical values for these basket options.…”

Section: Variance Gammamentioning

confidence: 88%

“…Even in this simple setting, the price of a basket option is not given in a closed form and has to be approximated; see e.g. Hull and White [23], Brooks et al [8], Milevsky and Posner [39], Rubinstein [42], Deelstra et al [18], Carmona and Durrleman [12] and Linders [29], among others. However, the normality assumption for the marginals used in this pricing framework is too restrictive.…”

Section: Introductionmentioning

confidence: 99%

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Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Linders

Schoutens

2016

Innovations in Derivatives Markets

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In this paper we employ a one-factor Lévy model to determine basket option prices. More precisely, basket option prices are determined by replacing the distribution of the real basket with an appropriate approximation. For the approximate basket we determine the underlying characteristic function and hence we can derive the related basket option prices by using the Carr-Madan formula. We consider a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several Lévy models are calibrated to market data and basket option prices are determined. In the last part we show how our newly designed basket option pricing formula can be used to define implied Lévy correlation by matching model and market prices for basket options. Our main finding is that the implied Lévy correlation smile is flatter than its Gaussian counterpart. Furthermore, if (near) atthe-money option prices are used, the corresponding implied Gaussian correlation estimate is a good proxy for the implied Lévy correlation.

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Section: Variance Gammamentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Linders

Schoutens

2016

Innovations in Derivatives Markets

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“…Deelstra et al (2004) extend the conditional moment matching approach further by finding a lognormal variableÃ such that…”

Section: Model Formulationmentioning

confidence: 99%

“…Lord (2006) shows the conditional moment matching approximation of Deelstra et al (2004) lies in between the lower and upper bounds and introduces the class of partially exact and bounded approximations.…”

Section: Model Formulationmentioning

confidence: 99%

Approximate basket options valuation for a jump-diffusion model

Zheng

2009

Insurance: Mathematics and Economics

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In this paper we discuss the approximate basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated diffusion processes with idiosyncratic and systematic jumps. We suggest a new approximate pricing formula which is the weighted sum of Roger and Shi's lower bound and the conditional second moment adjustments. We show the approximate value is always within the lower and upper bounds of the option and is very sharp in our numerical tests.

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“…Vyncke et al (2004) propose a two-moment matching approximation with a convex combination of the comonotonic lower and upper bounds for Asian options while Vanmaele et al (2004) suggest a similar approximation for basket options. Deelstra et al (2004) develop a general framework for pricing basket and Asian options via conditioning and derive lower and upper bounds based on comonotonic risks. The case of Asian basket option is discussed in Deelstra et al (2008).…”

mentioning

confidence: 99%

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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Pricing of arithmetic basket options by conditioning

Cited by 87 publications

References 8 publications

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Approximate basket options valuation for a jump-diffusion model

General closed-form basket option pricing bounds

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