Static-arbitrage upper bounds for the prices of basket options

Hobson, David; Laurence, Peter; Wang, Tai‐Ho

doi:10.1080/14697680500151392

Cited by 112 publications

(114 citation statements)

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“…It might be expected that very little can be said with this approach, but the model-free literature ( [18,6,20,8,13,19,22,21,23,3,15,1]) shows that if we take the prices of vanilla options as given, and only consider martingale models which are consistent with these prices, then we can find non-trivial bounds on the prices of exotic derivatives. In this literature the idea is to not specify a model, or even a probability space or filtration.…”

Section: Consistent Pricing Modelsmentioning

confidence: 99%

“…Originating with work of Hobson [18] for lookback options, model-free or robust bounds have been identified for barrier options (Brown, Hobson, and Rogers [6]), double no touch options (Cox and Obloj [13]), basket options (Hobson, Laurence and Wang [20]), variance swaps (Hobson and Klimmek [21]), options on variance (Carr and Lee [8]) and forward start options (Hobson and Neuberger [22]). Kahalé [23] describes a general approach via convex programming for pricing and hedging European path-dependent claims in the presence of European options, using a set-up which is similar to that in the main part of this paper.…”

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confidence: 99%

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Model uncertainty and the pricing of American options

Hobson

Neuberger

2016

Finance Stoch

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when we do not impose a model, but rather consider the class of all models which are consistent with a family of European call prices. The bound is enforced by a hedging strategy involving these call options which is robust to model error. Permanent

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Section: Consistent Pricing Modelsmentioning

confidence: 99%

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confidence: 99%

Model uncertainty and the pricing of American options

Hobson

Neuberger

2016

Finance Stoch

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“…It is clear from the proof that Theorem 1 holds for any random variable ε as long as it is symmetric and satisfies (7) and (9). A normal distribution seems a natural choice, but then one has to deal with a numerical integration.…”

Section: Theorem 1 Letmentioning

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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“…In the latter article, subreplicating strategies are developed for European-style basket options consisting of two assets. The so-called sheeptrack portfolio has a price that can only be realized by a countermonotonic pair as defined in (3).Whereas Hobson et al (2005a) only concentrate on basket options, Chen et al (2008) investigate static super-replicating strategies for European-type call options written on a weighted sum of asset prices. This class of exotic options includes Asian options and basket options among others.…”

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confidence: 99%

“…dividend paying stocks with no explicit dividend process known. As opposed to Hobson et al (2005a) who use Lagrange optimization techniques, the proofs in Chen et al (2008) are based on the theory of integral stochastic orders, comonotonicity and convex bounds, see Sections 1 and 2.…”

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confidence: 99%

Advanced Mathematical Methods for Finance

Nunno¹,

Øksendal²

2011

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Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool for solving several research and practical problems in the domain of finance and insurance. In this paper, we give an extensive bibliographic overview -without claiming to be complete -of the developments of the theory of comonotonicity and its applications, with an emphasis on the achievements over the last five years. These applications range from pricing and hedging of derivatives over risk management to life insurance. ComonotonicityOver the last two decades, researchers in economics, financial mathematics and actuarial science have introduced results related to the concept of comonotonicity in their respective fields of interest. In this paper, we give an overview of the relevant literature in these research fields, with the main emphasis on the development of the theory and its applications in finance and insurance over the last five years. Although it is our intention to give an extensive bibliographic overview, due to the high number of papers on applications of comonotonicity, it is impossible to present here an exhaustive overview of the recent literature. Further, we restrict this paper to a description of how and where comonotonicity comes in and refer to the relevant papers for a detailed mathematical description. In order to make this paper self-contained, we also provide a short overview of the basic definitions and initial main results of comonotonicity theory, hereby referring to part of the older literature on this topic.The concept of comonotonicity is closely related to the following well-known result, which is usually attributed to both Hoeffding (1940) and Fréchet (1951): For any n-dimensional random vector X ≡ (X 1 , X 2 , . . . , X n ) with multivariate cumulative distribution function (cdf) F X and marginal univariate cdf's F X 1 , F X 2 , . . . , F Xn and for any x ≡ (x 1 , x 2 , . . . , x n ) ∈ R n it holds that F X (x) ≤ min (F X 1 (x 1 ) , F X 2 (x 2 ) , . . . , F Xn (x n )) .(1)In the sequel, the notation R n (F X 1 , F X 2 , . . . , F Xn ) will be used to denote the class of all random vectors Y ≡ (Y 1 , Y 2 , . . . , Y n ) with marginals F Y i equal to the respective marginals F X i . The set R n (F X 1 , F X 2 , . . . , F Xn ) is called the Fréchet class related to the random vector X.The upper bound in (1) is reachable in the Fréchet class R n (F X 1 , F X 2 , . . . , F Xn ) in the sense that it is the cdf of an n-dimensional random vector with marginals given by F X i , i = 1, 2, . . . , n. * Department of Mathematics, ECARES, Université Libre de Bruxelles, CP 210, 1050 Brussels, Belgium † Faculty of Business and Economics, Katholieke Universiteit, 3000 Leuven, Belgium. ‡ Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000 Gent, Belgium 1 In order to prove the reachability property, consider a random variable U , uniformly distributed on the unit interval (0, 1). Then one has that F −1 X 1 (U ), F −1 X 2 (U ), . . . , F −1 Xn (U ) ∈ ...

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Static-arbitrage upper bounds for the prices of basket options

Cited by 112 publications

References 10 publications

Model uncertainty and the pricing of American options

Model uncertainty and the pricing of American options

Approximate basket options valuation for a jump-diffusion model

Advanced Mathematical Methods for Finance

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