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Arbitrage-free market models for option prices: the multi-strike case

Martin Schweizer, Johannes Wissel
2008 Finance and Stochastics  
We give explicit examples of volatility coefficients satisfying the required assumptions, and hence of arbitrage-free multi-strike market models of option prices.  ...  This paper studies modeling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity  ...  We are grateful for valuable comments and suggestions by several anonymous referees. We thank Damir Filipović and Jerzy Zabczyk for useful references from the SPDE literature.  ... 
doi:10.1007/s00780-008-0068-6 fatcat:7a6k57xzdjeyzmvyxejepaft3y

DG method for numerical pricing of multi-asset Asian options---the case of options\newline with floating strike
english

Jiří Hozman, Tomáš Tichý
2017 APPLICATIONS OF MATHEMATICS  
PDE models for multi-asset Asian options We follow the standard approach to the derivation of a general model for the valuation of path-dependent basket options with a few modifications for the case of  ...  While most of the assets at the market get the right price when the supply matches the demand, in case of financial derivatives the traders mostly follow the no-arbitrage conditions.  ... 
doi:10.21136/am.2017.0273-16 fatcat:bszsfhm5ibaazmgc3idhtg4g74

Duality in option pricing based on prices of other derivatives

Michi Nishihara, Mutsunori Yagiura, Toshihide Ibaraki
2007 Operations Research Letters  
We clarify a financial meaning of duality in the semi-infinite programming problem which emerges in the context of determining a derivative price range based only on the no-arbitrage assumption and the  ...  The interpretation links studies in the above context to studies in stochastic models.  ...  Acknowledgments The authors would like to thank Professor Masao Fukushima of Kyoto University and Professor Hiroshi Nagamochi of Kyoto University for helpful suggestions.  ... 
doi:10.1016/j.orl.2006.03.007 fatcat:mc3b32v3zvdfdnzghpla4xv7pq

Robust option pricing

Chaithanya Bandi, Dimitris Bertsimas
2014 European Journal of Operational Research  
We then formulate the option pricing problem as a robust optimization problem that identifies the portfolio which minimizes the worst case replication error for a given uncertainty set defined on the underlying  ...  Our explanation of the implied volatility smile is that it is caused by different levels of risk aversion of an option writer for different strikes.  ...  Acknowledgements We would like to thank the three reviewers of the paper for insightful comments.  ... 
doi:10.1016/j.ejor.2014.06.002 fatcat:ukh2z6gkdzc4rfaoiii5wfrlq4

Neural Options Pricing [article]

Timothy DeLise
2021 arXiv   pre-print
This research investigates pricing financial options based on the traditional martingale theory of arbitrage pricing applied to neural SDEs.  ...  Furthermore, it is conjectured that the error of the option price implied by the learnt model can be bounded by the very Wasserstein distance metric that was used to fit the empirical data.  ...  The remaining core assumption of the theory is that arbitrage (risk-free profits) cannot exist in the market.  ... 
arXiv:2105.13320v1 fatcat:2pbv37aryncpzguftzgyqs5on4

Pricing FX Options under Intermediate Currency [article]

S. Maurer, T.E. Sharp, M.V. Tretyakov
2021 arXiv   pre-print
, and also to the model-free approach of option pricing  ...  for the inverse pair (the foreign market).  ...  To conclude, we derived consistent pricing formulas (4.18) and (4.23) for FX options in the multi-currency case.  ... 
arXiv:1912.01387v2 fatcat:e5grxan4yrfirp4gnf4pv6g4fq

Model-Free Option Prices

Kuo-Ping Chang
2014 Social Science Research Network  
In this paper, I have used simple arbitrage argument to derive a dozen of model-free option price properties.  ...  I have also used the Arbitrage Theorem under the binomial option pricing model to examine these properties.  ...  Model-Free Option Prices A call option gives its owner the right to purchase an asset (the underlying asset) for a given price (the exercise or strike price: K ) on or before a given date (the expiration  ... 
doi:10.2139/ssrn.2459464 fatcat:w455ivpb4vd6howaurayepik6e

Pricing average price advertising options when underlying spot market prices are discontinuous

Bowei Chen, Mohan Kankanhalli
2018 IEEE Transactions on Knowledge and Data Engineering  
A general option pricing algorithm is obtained based on Monte Carlo simulation. In addition, an explicit pricing formula is derived for the case when the option payoff is based on the geometric mean.  ...  Many studies on advertising options so far have been restricted to the situations where the option payoff is determined by the underlying spot market price at a specific time point and the price evolution  ...  This design is a generalisation of the dual-strike call option [4] and the multi-exercise option [36] .  ... 
doi:10.1109/tkde.2018.2867027 fatcat:jni7fzfigfbb5nt7adfmbaucka

Gated Neural Networks for Option Pricing: Rationality by Design [article]

Yongxin Yang, Yu Zheng, Timothy M. Hospedales
2020 arXiv   pre-print
We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable.  ...  To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing.  ...  Acknowledgements This project received support from the European Union's Horizon 2020 research and innovation programme under grant agreement #640891.  ... 
arXiv:1609.07472v3 fatcat:xahjmsbbzzba5emvrpsyaxwhn4

Static versus Dynamic Arbitrage Bounds on Multivariate Option Prices [article]

Alexandre d'Aspremont
2004 arXiv   pre-print
While there is no gap between these two sets of prices in the univariate case, we observe here that contrary to our intuition about model risk for at-the-money calls, there is a somewhat large gap between  ...  We compare static arbitrage price bounds on basket calls, i.e. bounds that only involve buy-and-hold trading strategies, with the price range obtained within a multi-variate generalization of the Black-Scholes  ...  Discrete model Here, we simulate a set of arbitrage free basket call prices using a simple discrete model.  ... 
arXiv:cs/0407029v1 fatcat:g7enp2hynje3hlajr6cz42kv6i

Actuarial versus Financial Pricing of Insurance

PAUL EMBRECHTS
2000 The Journal of Risk Finance  
The Working Paper Series is made possible by a generous grant from the Alfred P. Sloan Foundation  ...  to premium calculation principles in an arbitrage-free market!  ...  Besides the Cox-Ross-Rubinstein (binomial) and Black-Scholes (geometric Brownian motion) models, further nice cases (complete models) for instance include multi-dimensional Brownian motion and some special  ... 
doi:10.1108/eb043451 fatcat:6juv3k4qnnhsvl374oh4woemm4

Consistency of option prices under bid-ask spreads [article]

Stefan Gerhold, I. Cetin Gülüm
2019 arXiv   pre-print
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices.  ...  We fully solve this problem in the case of a single maturity, and give several partial results for multiple maturities.  ...  for the existence of arbitrage free models.  ... 
arXiv:1608.05585v2 fatcat:5c65ivpejzajfp6q7dcv6rc3ky

A New Approach to Model Free Option Pricing [article]

Raphael Hauser, Sergey Shahverdyan
2015 arXiv   pre-print
In this paper we introduce a new approach to model-free path-dependent option pricing.  ...  Though the experiments are carried out for simple path-dependent options on a single stock, the model is easy to generalise for multi-asset framework.  ...  prices for the barriers as strikes and then construct our model.  ... 
arXiv:1501.03701v1 fatcat:5wuyl3ncs5auzndpmg46uxl5vy

Multivariate Option Pricing With Copulas

Umberto Cherubini, Elisa Luciano
2001 Social Science Research Network  
As applications, we provide prices for binary digital options, options on the minimum and options to exchange one asset for another.  ...  Copulas enable us to imbed the marginal distributions extracted from vertical spreads in the options markets in a multivariate pricing kernel.  ...  case in which the market for options written on any single underlying asset is incomplete.  ... 
doi:10.2139/ssrn.269868 fatcat:ysrxntraxrar3ozu4mxfs42ppe

Gated Neural Networks for Option Pricing: Rationality by Design

Yongxin Yang, Yu Zheng, Timothy Hospedales
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable.  ...  To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing.  ...  Acknowledgements This project received support from the European Union's Horizon 2020 research and innovation programme under grant agreement #640891.  ... 
doi:10.1609/aaai.v31i1.10505 fatcat:ocuyuf2qo5a5xhhxudwnuor67y
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