Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/315064 
Year of Publication: 
2024
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 28 [Issue:] 2 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2024 [Pages:] 285-328
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract We solve the superhedging problem for European options in an illiquid extension of the Black–Scholes model, in which transactions have transient price impact and the costs and strategies for hedging are affected by physical or cash settlement requirements at maturity. Our analysis is based on a convenient choice of reduced effective coordinates of magnitudes at liquidation for geometric dynamic programming. The price impact is transient over time and multiplicative, ensuring nonnegativity of underlying asset prices while maintaining an arbitrage-free model. The basic (log-)linear example is a Black–Scholes model with a relative price impact proportional to the volume of shares traded, where the transience for impact on log-prices is modelled like in Obizhaeva and Wang (J. Financ. Mark. 16:1–32, 2013 ) for nominal prices. More generally, we allow nonlinear price impact and resilience functions. The viscosity solutions describing the minimal superhedging price are governed by the transient character of the price impact and by the physical or cash settlement specifications. The pricing equations under illiquidity extend no-arbitrage pricing à la Black–Scholes for complete markets in a non-paradoxical way (cf. Çetin et al. (Finance Stoch. 14:317–341, 2010 )) even without additional frictions, and can recover it in base cases.
Subjects: 
Transient price impact
Multiplicative impact
Hedging
Option settlement
Resilience
Viscosity solution
Geometric dynamical programming
Effective coordinates
Persistent Identifier of the first edition: 
Additional Information: 
C61;G12;G13
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version
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