Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs

2011 ◽  
Vol 390 (9) ◽  
pp. 1623-1634 ◽  
Author(s):  
Xiao-Tian Wang
Keyword(s):  
Option Pricing ◽  
Transaction Costs ◽  
Long Range ◽  
Implied Volatility ◽  
Long Range Dependence ◽  
Black Scholes Model ◽  
Black Scholes

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

scholarly journals A modification term for Black-Scholes model based on discrepancy calibrated with real market data

2021 ◽  
Vol 1 (4) ◽  
pp. 313-326
Author(s):  
Xiaozheng Lin ◽  
◽  
Meiqing Wang ◽  
Choi-Hong Lai ◽  
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Option Prices ◽  
Market Prices ◽  
Market Data ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Real Market ◽  
S Model

<abstract><p>The Black-Scholes option pricing model (B-S model) generally requires the assumption that the volatility of the underlying asset be a piecewise constant. However, empirical analysis shows that there are discrepancies between the option prices obtained from the B-S model and the market prices. Most current modifications to the B-S model rely on modelling the implied volatility or interest rate. In contrast to the existing modifications to the Black-Scholes model, this paper proposes the concept of including a modification term to the B-S model itself. Using the actual discrepancies of the results of the Black-Scholes model and the market prices, the modification term related to the implied volatility is derived. Experimental results show that the modified model produces a better option pricing results when compare to market data.</p></abstract>

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.

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