Arbitrage in fractional Brownian motion models

By Patrick Cheridito. Finance and Stochastics, 2003

364 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/aeebd9ab0ddb7f6890d53d70f9b5510413997c50

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Citations in the corpus

The fundamental theorem of asset pricing for continuous processes under small transaction costs (2010, background): “2] implies the existence of arbitrage opportunities in the absence of transaction costs (more precisely: a free lunch with vanishing risk with respect to simple integrands; compare also to [21], [2]).”
Gaussian moving averages, semimartingales and option pricing (2004, background): “In Cheridito (2003) arbitrage for linear and exponential fBm models is constructed for all H ∈ (0; 12 ) ∪ ( 12 ; 1).”
Mixed fractional Brownian motion (2001, methodology): “Moreover, it is shown in Cheridito (2000) that the model (6.1) has no arbitrage in h lF S . Hence, if we conne the strategies to the class h lF S ,w e”
Fractional Processes as Models in Stochastic Finance (2010, methodology): “The claim is Cheridito’s [14, Theorem 4.3].”
Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence (2006, neutral): “Expression (4) implies the European call value equals E[CT ] = e −rT E(max[sT − K, 0]) (7) = s0N(h0) − Ke−rT N(h0 − σ √ T ) , where N(·) denotes the standard cumulative normal distribution function whose argument is ht ≡ log(st) − log K + r(T − t) σ √ T − t + σ 2 √ T − t .”
Estimation and pricing under long-memory stochastic volatility (2012, methodology): “In this way we introduce long-memory in our model, but not directly in the returns, as was suggested by Cheridito (2003, [5]), Rogers (1997, [23]) and Sottinen (2001, [25]).”
No Arbitrage Without Semimartingales (2009, neutral): “23 18 v1 [ m at h. PR ] 1 2 Ju n 20 09 The Annals of Applied Probability 2009, Vol. 19, No. 2, 596–616 DOI: 10.1214/08-AAP554 c© Institute of Mathematical Statistics, 2009”
An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion (2007, background): “These significant properties make fractional Brownian motion a natural candidate as a model for noise in mathematical finance (see Comte and Renault [CR96], Rogers [Rog97], Cheridito, [ Che03 ], and Duncan, [Dun04]); in hydrology (see Hurst, [Hur51]), in communication networks (see, for instance Lel”
Arbitrage with fractional Brownian motion (2007, methodology): “This means that the number of rearranging times is finite on almost every path, but not necessarily bounded as function on Ω. Existence of a self-financing almost simple arbitrage has been shown by Rogers [20], making use of the history of a fractional Brownian motion starting at −∞, and subsequentl”
NO ARBITRAGE UNDER TRANSACTION COSTS, WITH FRACTIONAL BROWNIAN MOTION AND BEYOND (2006, background): “In fact, Rogers (1997), Salopek (1998), Shiryaev (1998), Dasgupta and Kallianpur (2000), and Cheridito (2003) have shown that it allows outright arbitrage in a number of ways.”
Long range dependence in financial markets (2005, neutral): “Cheridito [12] and Rogers [63] give several examples of Gaussian processes with the same long range dependence features as fractional Brownian motion, but which are semimartingales and lead to arbitrage-free models.”