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.

scholarly journals Parameters Identification for Inverse Option Problems Using Markov Chain Monte Carlo Methods

2019 ◽  
Author(s):  
Yasushi Ota ◽  
Yu Jiang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Financial Markets ◽  
Sampling Strategy ◽  
Measured Data ◽  
Mcmc Algorithm ◽  
Unknown Parameters ◽  
Posterior Probability Density

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm 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 trend and volatility coefficients from the measured data.

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.

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Mikhaylov ◽  
Victor Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problems ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Unknown Parameters ◽  
Stieltjes String ◽  
Propagation Of Waves ◽  
Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

scholarly journals Sensitivity-informed Bayesian Inference for Home PLC Network Models with Unknown Parameters

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2402
Author(s):  
David S. Ching ◽  
Cosmin Safta ◽  
Thomas A. Reichardt
Keyword(s):  
Bayesian Inference ◽  
Transfer Function ◽  
Network Topology ◽  
Random Search ◽  
Network Models ◽  
Training Data ◽  
Unknown Parameters ◽  
Network Parameter ◽  
Dimensional Parameter ◽  
Discrete Random Variables

Bayesian inference is used to calibrate a bottom-up home PLC network model with unknown loads and wires at frequencies up to 30 MHz. A network topology with over 50 parameters is calibrated using global sensitivity analysis and transitional Markov Chain Monte Carlo (TMCMC). The sensitivity-informed Bayesian inference computes Sobol indices for each network parameter and applies TMCMC to calibrate the most sensitive parameters for a given network topology. A greedy random search with TMCMC is used to refine the discrete random variables of the network. This results in a model that can accurately compute the transfer function despite noisy training data and a high dimensional parameter space. The model is able to infer some parameters of the network used to produce the training data, and accurately computes the transfer function under extrapolative scenarios.

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