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 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 A comparison of approximate versus exact techniques for Bayesian parameter inference in nonlinear ordinary differential equation models

2020 ◽  
Vol 7 (3) ◽  
pp. 191315
Author(s):  
Amani A. Alahmadi ◽  
Jennifer A. Flegg ◽  
Davis G. Cochrane ◽  
Christopher C. Drovandi ◽  
Jonathan M. Keith
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Sequential Monte Carlo ◽  
Simulated Data ◽  
Real Data ◽  
Nonlinear Ordinary Differential Equation ◽  
Unknown Parameters ◽  
Acceptance Probability

The behaviour of many processes in science and engineering can be accurately described by dynamical system models consisting of a set of ordinary differential equations (ODEs). Often these models have several unknown parameters that are difficult to estimate from experimental data, in which case Bayesian inference can be a useful tool. In principle, exact Bayesian inference using Markov chain Monte Carlo (MCMC) techniques is possible; however, in practice, such methods may suffer from slow convergence and poor mixing. To address this problem, several approaches based on approximate Bayesian computation (ABC) have been introduced, including Markov chain Monte Carlo ABC (MCMC ABC) and sequential Monte Carlo ABC (SMC ABC). While the system of ODEs describes the underlying process that generates the data, the observed measurements invariably include errors. In this paper, we argue that several popular ABC approaches fail to adequately model these errors because the acceptance probability depends on the choice of the discrepancy function and the tolerance without any consideration of the error term. We observe that the so-called posterior distributions derived from such methods do not accurately reflect the epistemic uncertainties in parameter values. Moreover, we demonstrate that these methods provide minimal computational advantages over exact Bayesian methods when applied to two ODE epidemiological models with simulated data and one with real data concerning malaria transmission in Afghanistan.

scholarly journals A Monte Carlo approach for determining cluster evaporation rates from concentration measurements

2016 ◽  
Author(s):  
Oona Kupiainen-Määttä
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Markov Chain ◽  
Sulfuric Acid ◽  
Markov Chain Monte Carlo ◽  
Mass Spectrometer ◽  
Large Fraction ◽  
Cluster Formation ◽  
Unknown Parameters ◽  
Ammonia Clusters

Abstract. Evaporation rates of small negatively charged sulfuric acid–ammonia clusters are determined by combining detailed cluster formation simulations with cluster distributions measured at CLOUD. The analysis is performed by varying the evaporation rates with Markov chain Monte Carlo (MCMC), running cluster formation simulations with each new set of evaporation rates and comparing the obtained cluster distributions to the measurements. In a second set of simulations, the fragmentation of clusters in the mass spectrometer due to energetic collisions is studied by treating also the fragmentation probabilities as unknown parameters and varying them with MCMC. This second set of simulations results in a better fit to the experimental data, suggesting that a large fraction of the observed HSO4− and HSO4− ⋅ H2SO4 signals may result from fragmentation of larger clusters, most importantly the HSO4− ⋅ (H2SO4)2 trimer.

Markov Chain Monte Carlo

2015 ◽  
Author(s):  
N. Thompson Hobbs ◽  
Mevin B. Hooten
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Posterior Distribution ◽  
Mcmc Algorithm ◽  
Bayesian Analyses ◽  
Seminal Paper ◽  
Formal Treatment ◽  
High Level

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and Smith (1990). It begins with an explanation of MCMC with a heuristic, high-level treatment of the algorithm, describing its operation in simple terms with a minimum of formalism. In this first part, the chapter explains the algorithm so that all readers can gain an intuitive understanding of how to find the posterior distribution by sampling from it. Next, the chapter offers a somewhat more formal treatment of how MCMC is implemented mathematically. Finally, this chapter discusses implementation of Bayesian models via two routes—by using software and by writing one's own algorithm.

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