scholarly journals Arbitrage opportunities in sub-fractional Black-Scholes model

2021 ◽  
Author(s):  
Xiao Weilin ◽  
Zhou Qing ◽  
Wu Weixing
Keyword(s):  
Black Scholes Model ◽  
Arbitrage Opportunities ◽  
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.

Financial Pricing in Property and Liability Insurances, Evidence From the Egyptian Insurance Market

2018 ◽  
Vol 9 (4) ◽  
pp. 55-69
Author(s):  
Hamed Abd Elkaway El Kawaga ◽  
Asharf Sayed Abdelzaher
Keyword(s):  
Insurance Market ◽  
Insurance Companies ◽  
Corporate Risk Management ◽  
Insurance Contracts ◽  
Black Scholes Model ◽  
Arbitrage Opportunities ◽  
Black Scholes ◽  
Equilibrium Relationships ◽  
Financial Prices ◽  
Corporate Risk

The use of pricing a model's insurance derivatives in corporate risk management, particularity in insurance has grown rapidly recently. Financial prices for insurance reflects equilibrium relationships between risk and return or, minimally, avoid the creation of arbitrage opportunities. The major objective of this article is to provide evidence that in the Egyptian insurance market during the period 2002-2013, using Black-Scholes model, there was a transfer of wealth from policyholders to insurance companies via overvaluation of insurance premiums. This contribution may have some crucial implications in terms of the “fairness” of pricing insurance contracts.

scholarly journals Bayesian Inference Approach to Inverse Problems in a Financial Mathematical Model

2019 ◽  
Author(s):  
Yasushi Ota ◽  
Yu Jiang ◽  
Gen Nakamura ◽  
Masaaki Uesaka
Keyword(s):  
Bayesian Inference ◽  
Inverse Problems ◽  
Sampling Strategy ◽  
Measured Data ◽  
Unknown Parameters ◽  
Black Scholes Model ◽  
Arbitrage Opportunities ◽  
Black Scholes ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

An analytical approximation formula for the pricing of credit default swaps with regime switching

2021 ◽  
Vol 63 ◽  
pp. 143-162
Author(s):  
Xin-Jiang He ◽  
Sha Lin
Keyword(s):  
Regime Switching ◽  
Credit Default Swap ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Current Time ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Credit Default

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments. doi:10.1017/S1446181121000274

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