Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation

References

• Acciaio B, Beiglböck M, Penkner F, Schachermayer W (2016) A model-free version of the fundamental theorem of asset pricing and the super-replication theorem. Math. Finance 26(2):233–251.Crossref, Google Scholar
• Auslender A, Goberna MA, López MA (2009) Penalty and smoothing methods for convex semi-infinite programming. Math. Oper. Res. 34(2):303–319.Link, Google Scholar
• Auslender A, Ferrer A, Goberna MA, López MA (2015) Comparative study of RPSALG algorithm for convex semi-infinite programming. Comput. Optim. Appl. 60(1):59–87.Crossref, Google Scholar
• Bartl D, Kupper M, Neufeld A (2020) Pathwise superhedging on prediction sets. Finance Stochastics 24(1):215–248.Crossref, Google Scholar
• Bartl D, Kupper M, Prömel DJ, Tangpi L (2019) Duality for pathwise superhedging in continuous time. Finance Stochastics 23(3):697–728.Crossref, Google Scholar
• Bartl D, Kupper M, Lux T, Papapantoleon A, Eckstein S (2022) Marginal and dependence uncertainty: Bounds, optimal transport, and sharpness. SIAM J. Control Optim. 60(1):410–434.Google Scholar
• Bayraktar E, Zhang Y (2016) Fundamental theorem of asset pricing under transaction costs and model uncertainty. Math. Oper. Res. 41:1039–1054.Link, Google Scholar
• Bayraktar E, Huang YJ, Zhou Z (2015) On hedging American options under model uncertainty. SIAM J. Financial Math. 6(1):425–447.Crossref, Google Scholar
• Bayraktar E, Zhang Y, Zhou Z (2014) A note on the fundamental theorem of asset pricing under model uncertainty. Risks 2:425–433.Crossref, Google Scholar
• Beiglböck M, Henry-Labordère P, Penkner F (2013) Model-independent bounds for option prices—A mass transport approach. Finance Stochastics 17:477–501.Crossref, Google Scholar
• Beissner P (2017) Equilibrium prices and trade under ambiguous volatility. Econom. Theory 64(2):213–238.Crossref, Google Scholar
• Beissner P, Riedel F (2019) Equilibria under Knightian price uncertainty. Econometrica 87(1):37–64.Crossref, Google Scholar
• Bertsimas D, Bushueva N (2006) Option pricing without price dynamics: a probabilistic approach. Preprint, submitted December 3, https://arxiv.org/abs/0612075.Google Scholar
• Bertsimas D, Popescu I (2002) On the relation between option and stock prices: A convex optimization approach. Oper. Res. 50(2):358–374.Link, Google Scholar
• Betrò B (2004) An accelerated central cutting plane algorithm for linear semi-infinite programming. Math. Programming 101(3):479–495.Crossref, Google Scholar
• Biagini S, Bouchard B, Kardaras C, Nutz M (2017) Robust fundamental theorem for continuous processes. Math. Finance 27:963–987.Crossref, Google Scholar
• Borwein JM, Lewis AS (1991a) Convergence of best entropy estimates. SIAM J. Optim. 1(2):191–205.Crossref, Google Scholar
• Borwein JM, Lewis AS (1991b) Duality relationships for entropy-like minimization problems. SIAM J. Control Optim. 29(2):325–338.Crossref, Google Scholar
• Bouchard B, Nutz M (2015) Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probabilities 25(2):823–859.Crossref, Google Scholar
• Bouchard B, Deng S, Tan X (2019) Superreplication with proportional transaction cost under model uncertainty. Math. Finance 29(3):837–860.Crossref, Google Scholar
• Burzoni M, Frittelli M, Maggis M (2016) Universal arbitrage aggregator in discrete-time markets under uncertainty. Finance Stochastics 20(1):1–50.Crossref, Google Scholar
• Burzoni M, Riedel F, Soner HM (2021) Viability and arbitrage under Knightian uncertainty. Econometrica 89(3):1207–1234.Crossref, Google Scholar
• Burzoni M, Frittelli M, Hou Z, Maggis M, Obłój J (2019) Pointwise arbitrage pricing theory in discrete time. Math. Oper. Res. 44(3):1034–1057.Link, Google Scholar
• Chen X, Deelstra G, Dhaene J, Vanmaele M (2008) Static super-replicating strategies for a class of exotic options. Insurance Math. Econom. 42:1067–1085.Crossref, Google Scholar
• Cheridito P, Kupper M, Tangpi L (2017) Duality formulas for robust pricing and hedging in discrete time. SIAM J. Financial Math. 8(1):738–765.Crossref, Google Scholar
• Cho H, Kim KK, Lee K (2016) Computing lower bounds on basket option prices by discretizing semi-infinite linear programming. Optim. Lett. 10:1629–1644.Crossref, Google Scholar
• Cohen SN, Reisinger C, Wang S (2020) Detecting and repairing arbitrage in traded option prices. Appl. Math. Finance 27(5):345–373.Google Scholar
• Coope ID, Price CJ (1998) Exact penalty function methods for nonlinear semi-infinite programming. Semi-Infinite Programming (Kluwer Academic Publishers, Boston, MA), 137–157.Crossref, Google Scholar
• Dana RA, Riedel F (2013) Intertemporal equilibria with Knightian uncertainty. J. Econom. Theory. 148(4):1582–1605.Crossref, Google Scholar
• d’Aspremont A, El Ghaoui L (2006) Static arbitrage bounds on basket option prices. Math. Programming 106(3, ser. A):467–489.Crossref, Google Scholar
• Daum S, Werner R (2011) A novel feasible discretization method for linear semi-infinite programming applied to basket option pricing. Optimization. 60(10–11):1379–1398.Crossref, Google Scholar
• Davis M, Obłój J, Raval V (2014) Arbitrage bounds for prices of weighted variance swaps. Math. Finance 24(4):821–854.Crossref, Google Scholar
• De Gennaro Aquino L, Bernard C (2020) Bounds on multi-asset derivatives via neural networks. Internat. J. Theoretical Appl. Finance 23(8):2050050.Crossref, Google Scholar
• Dhaene J, Denuit M, Goovaerts MJ, Kaas R, Vyncke D (2002a) The concept of comonotonicity in actuarial science and finance: Applications. Insurance Math. Econom. 31:133–161.Crossref, Google Scholar
• Dhaene J, Denuit M, Goovaerts MJ, Kaas R, Vyncke D (2002b) The concept of comonotonicity in actuarial science and finance: Theory. Insurance Math. Econom. 31:3–33.Crossref, Google Scholar
• Dolinsky Y, Neufeld A (2018) Super-replication in fully incomplete markets. Math. Finance 28(2):483–515.Crossref, Google Scholar
• Dolinsky Y, Soner HM (2014a) Martingale optimal transport and robust hedging in continuous time. Probability Theory Related Fields 160(1–2):391–427.Crossref, Google Scholar
• Dolinsky Y, Soner HM (2014b) Robust hedging with proportional transaction costs. Finance Stochastics 18:327–347.Crossref, Google Scholar
• Eckstein S, Kupper M (2021) Computation of optimal transport and related hedging problems via penalization and neural networks. Appl. Math. Optim. 83(2):639–667.Crossref, Google Scholar
• Eckstein S, Kupper M, Pohl M (2020) Robust risk aggregation with neural networks. Math. Finance 30:1229–1272.Crossref, Google Scholar
• Eckstein S, Guo G, Lim T, Obłój J (2021) Robust pricing and hedging of options on multiple assets and its numerics. SIAM J. Financial Math. 12(1):158–188.Crossref, Google Scholar
• Epstein LG, Ji S (2013) Ambiguous volatility and asset pricing in continuous time. Rev. Financial Stud. 26(7):1740–1786.Crossref, Google Scholar
• Galichon A, Henry-Labordère P, Touzi N (2014) A stochastic control approach to no-arbitrage bounds given marginals, with an application to lookback options. Ann. Appl. Probabilities 24(1):312–336.Crossref, Google Scholar
• Goberna MA, López MA (1998) Linear Semi-Infinite Optimization (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Goberna MA, López MA (2018) Recent contributions to linear semi-infinite optimization: An update. Ann. Oper. Res. 271(1):237–278.Crossref, Google Scholar
• Gurobi Optimization (2020) Gurobi optimizer reference manual. http://www.gurobi.com.Google Scholar
• Henry-Labordère P (2013) Automated option pricing: Numerical methods. Internat. J. Theoretical Appl. Finance 16(08):1350042.Crossref, Google Scholar
• Hettich R, Kortanek KO (1993) Semi-infinite programming: Theory, methods, and applications. SIAM Rev. 35:380–429.Crossref, Google Scholar
• Hobson DG (1998) Robust hedging of the lookback option. Finance Stochastics 2(4):329–347.Crossref, Google Scholar
• Hobson D, Laurence P, Wang TH (2005a) Static-arbitrage optimal subreplicating strategies for basket options. Insurance Math. Econom. 37:553–572.Crossref, Google Scholar
• Hobson D, Laurence P, Wang TH (2005b) Static-arbitrage upper bounds for the prices of basket options. Quant. Finance 5:329–342.Crossref, Google Scholar
• Hu J, Li J, Mehrotra S (2019) A data-driven functionally robust approach for simultaneous pricing and order quantity decisions with unknown demand function. Oper. Res. 67(6):1564–1585.Link, Google Scholar
• Kahalé N (2017) Superreplication of financial derivatives via convex programming. Management Sci. 63(7):2323–2339.Link, Google Scholar
• Karlin S, Studden WJ (1966) Tchebycheff Systems: With Applications in Analysis and Statistics (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Lin CJ, Fang SC, Wu SY (1998) An unconstrained convex programming approach to linear semi-infinite programming. SIAM J. Optim. 8(2):443–456.Crossref, Google Scholar
• López M, Still G (2007) Semi-infinite programming. Eur. J. Oper. Res. 180(2):491–518.Crossref, Google Scholar
• Lütkebohmert E, Sester J (2019) Tightening robust price bounds for exotic derivatives. Quant. Finance 19(11):1797–1815.Crossref, Google Scholar
• Lux T, Papapantoleon A (2017) Improved Fréchet–Hoeffding bounds on d-copulas and applications in model-free finance. Ann. Appl. Probabilities 27:3633–3671.Google Scholar
• Maruhn JH (2009) Robust Static Super-Replication of Barrier Options (Walter de Gruyter GmbH & Co. KG, Berlin).Crossref, Google Scholar
• Neufeld A, Nutz M (2013) Superreplication under volatility uncertainty for measurable claims. Electron. J. Probab. 18(48):1–14.Crossref, Google Scholar
• Nishihara M, Yagiura M, Ibaraki T (2007) Duality in option pricing based on prices of other derivatives. Oper. Res. Lett. 35(2):165–171.Crossref, Google Scholar
• Papapantoleon A, Yanez Sarmiento P (2021) Detection of arbitrage opportunities in multi-asset derivatives markets. Dependence Model. 9(1):439–459.Google Scholar
• Peña J, Vera JC, Zuluaga LF (2010b) Static-arbitrage lower bounds on the prices of basket options via linear programming. Quant. Finance 10:819–827.Crossref, Google Scholar
• Peña J, Vera JC, Zuluaga LF (2012) Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads. Eur. J. Oper. Res. 222(2):369–376.Crossref, Google Scholar
• Peña J, Saynac X, Vera JC, Zuluaga LF (2010a) Computing general static-arbitrage bounds for European basket options via Dantzig–Wolfe decomposition. Algorithmic Oper. Res. 5(2):65–74.Google Scholar
• Possamaï D, Royer G, Touzi N (2013) On the robust superhedging of measurable claims. Electron. Commun. Probab. 18(95):1–13.Crossref, Google Scholar
• Puccetti G, Rüschendorf L, Manko D (2016) VaR bounds for joint portfolios with dependence constraints. Dependence Model. 4:368–381.Google Scholar
• Reemtsen R, Rückmann JJ (1998) Semi-Infinite Programming, vol. 25 (Springer Science & Business Media, New York).Crossref, Google Scholar
• Riedel F (2015) Financial economics without probabilistic prior assumptions. Decision Econom. Finance 38(1):75–91.Crossref, Google Scholar
• Rigotti L, Shannon C (2005) Uncertainty and risk in financial markets. Econometrica 73(1):203–243.Crossref, Google Scholar
• Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Stein O (2012) How to solve a semi-infinite optimization problem. Eur. J. Oper. Res. 223(2):312–320.Crossref, Google Scholar
• Tankov P (2011) Improved Fréchet bounds and model-free pricing of multi-asset options. J. Appl. Probabilities 48:389–403.Crossref, Google Scholar
• Tavin B (2015) Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals. J. Bank. Finance 53:158–178.Crossref, Google Scholar
• Yan Z, Natarajan K, Teo CP, Cheng, C (2022) A representative consumer model in data-driven multiproduct pricing optimization. Management Sci., ePub ahead of print January 20, https://doi.org/10.1287/mnsc.2021.4182.Google Scholar