Can the Black-Scholes Model Survive under Transaction Costs? An Affirmative Answer

2008 ◽  
Author(s):  
Michal Czerwonko ◽  
Stylianos Perrakis
Keyword(s):  
Transaction Costs ◽  
Affirmative Answer ◽  
Black Scholes Model ◽  
Black Scholes

scholarly journals CRITICAL TRANSACTION COSTS AND 1-STEP ASYMPTOTIC ARBITRAGE IN FRACTIONAL BINARY MARKETS

2015 ◽  
Vol 18 (05) ◽  
pp. 1550029 ◽  
Author(s):  
FERNANDO CORDERO ◽  
LAVINIA PEREZ-OSTAFE
Keyword(s):  
Transaction Costs ◽  
Trading Strategies ◽  
Apparent Contradiction ◽  
New Family ◽  
Black Scholes Model ◽  
Asymptotic Arbitrage ◽  
Arbitrage Opportunities ◽  
Large Financial Market ◽  
Approximating Sequence ◽  
Black Scholes

We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black–Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary markets. Since, in the frictionless case, these markets admit arbitrage, we aim to determine the size of the transaction costs needed to eliminate the arbitrage from these models. To gain more insight, we first consider only 1-step trading strategies and we prove that arbitrage opportunities appear when the transaction costs are of order [Formula: see text]. Next, we characterize the asymptotic behavior of the smallest transaction costs [Formula: see text], called "critical" transaction costs, starting from which the arbitrage disappears. Since the fractional Black–Scholes model is arbitrage-free under arbitrarily small transaction costs, one could expect that [Formula: see text] converges to zero. However, the true behavior of [Formula: see text] is opposed to this intuition. More precisely, we show, with the help of a new family of trading strategies, that [Formula: see text] converges to one. We explain this apparent contradiction and conclude that it is appropriate to see the fractional binary markets as a large financial market and to study its asymptotic arbitrage opportunities. Finally, we construct a 1-step asymptotic arbitrage in this large market when the transaction costs are of order o(1/NH), whereas for constant transaction costs, we prove that no such opportunity exists.

Volatility cones and volatility arbitrage strategies – empirical study based on SSE ETF option

2017 ◽  
Vol 7 (2) ◽  
pp. 203-227 ◽  
Author(s):  
Hong Yu Xin Pan ◽  
Jun Song
Keyword(s):  
Transaction Costs ◽  
Stochastic Volatility Model ◽  
Chinese Market ◽  
Content Type ◽  
Black Scholes Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Arbitrage Strategy ◽  
Real Market ◽  
First Time

Purpose Using volatility cones as the estimate of actual volatility instead of GARCH models, the purpose of this paper is to explore whether volatility arbitrage strategy can provide positive profits and how the transaction costs existed in the real market affect the effectiveness of volatility arbitrage strategy. Design/methodology/approach A number of hedging approaches proposed to improve the hedging results and final returns of Black-Scholes model are analyzed and compared. Findings The general finding is that volatility arbitrage strategy can provide satisfactory returns based on the samples in Chinese market. Regarding transaction costs, the variable bandwidth delta and delta tolerance approach showed better results. Besides, choosing futures together with ETFs as hedging underlying can increase the VaR for better risk management. Practical implications This paper offers a new method for volatility arbitrage in Chinese financial market. Originality/value This paper researches the profitability of the volatility arbitrage strategy on ETF 50 options using volatility cones method for the first time. This method has advantage over the point-wise estimation such as GARCH model and stochastic volatility model.

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