Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/315064 
Erscheinungsjahr: 
2024
Quellenangabe: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 28 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2024 [Pages:] 285-328
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
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.
Schlagwörter: 
Transient price impact
Multiplicative impact
Hedging
Option settlement
Resilience
Viscosity solution
Geometric dynamical programming
Effective coordinates
JEL: 
C61
G12
G13
Persistent Identifier der Erstveröffentlichung: 
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Dokumentart: 
Article
Dokumentversion: 
Published Version

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