scholarly journals Pricing Interval European Option with the Principle of Maximum Entropy

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 788 ◽  
Author(s):  
Xiao Liu ◽  
Rongxi Zhou ◽  
Yahui Xiong ◽  
Yuexiang Yang
Keyword(s):  
Maximum Entropy ◽  
Stock Exchange ◽  
The United States ◽  
Stock Option ◽  
European Option ◽  
Entropy Model ◽  
Underlying Asset ◽  
European Option Pricing ◽  
Asset Distribution ◽  
Principle Of Maximum

This paper develops the interval maximum entropy model for the interval European option valuation by estimating an underlying asset distribution. The refined solution for the model is obtained by the Lagrange multiplier. The particle swarm optimization algorithm is applied to calculate the density function of the underlying asset, which can be utilized to price the Shanghai Stock Exchange (SSE) 50 Exchange Trades Funds (ETF) option of China and the Boeing stock option of the United States. Results show that maximum entropy distribution provides precise estimations for the underlying asset of interval number situations. In this way, we can get the distribution of the underlying assets and apply it to the interval European option pricing in the financial market.

scholarly journals A Maximum Entropy Model of Phonotactics and Phonotactic Learning

2008 ◽  
Vol 39 (3) ◽  
pp. 379-440 ◽  
Author(s):  
Bruce Hayes ◽  
Colin Wilson
Keyword(s):  
Maximum Entropy ◽  
Learning Algorithm ◽  
Universal Grammar ◽  
Vowel Harmony ◽  
Baseline Model ◽  
Entropy Model ◽  
Principle Of Maximum Entropy ◽  
Phonotactic Learning ◽  
As Stress ◽  
Principle Of Maximum

The study of phonotactics is a central topic in phonology. We propose a theory of phonotactic grammars and a learning algorithm that constructs such grammars from positive evidence. Our grammars consist of constraints that are assigned numerical weights according to the principle of maximum entropy. The grammars assess possible words on the basis of the weighted sum of their constraint violations. The learning algorithm yields grammars that can capture both categorical and gradient phonotactic patterns. The algorithm is not provided with constraints in advance, but uses its own resources to form constraints and weight them. A baseline model, in which Universal Grammar is reduced to a feature set and an SPE-style constraint format, suffices to learn many phonotactic phenomena. In order for the model to learn nonlocal phenomena such as stress and vowel harmony, it must be augmented with autosegmental tiers and metrical grids. Our results thus offer novel, learning-theoretic support for such representations. We apply the model in a variety of learning simulations, showing that the learned grammars capture the distributional generalizations of these languages and accurately predict the findings of a phonotactic experiment.

scholarly journals Proactive Hedging European Call Option Pricing with Linear Position Strategy

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Meng Li ◽  
Xuefeng Wang ◽  
Fangfang Sun
Keyword(s):  
Asset Price ◽  
Stock Option ◽  
Call Option ◽  
European Option ◽  
Price Movement ◽  
Underlying Asset ◽  
European Call Option ◽  
Exotic Option ◽  
Risk Of Exposure ◽  
Geometric Fractional Brownian Motion

Proactive hedging option is an exotic European stock option designed for hedgers. Such option requires option holders to buy in (or sell out) the underlying asset (stock) and allows them to adjust the holdings of the underlying asset per its price changes within an option period. The proactive hedging option is an attractive choice for hedgers because its price is lower than that of classical options and because it completely hedges the risk of exposure for option holders. In this study, the underlying asset price movement is assumed to follow geometric fractional Brownian motion. The pricing formula for proactive hedging call options is derived with a linear position strategy by applying the risk-neutral evaluation principle. We use simulations to confirm that the price of this exotic option is always no more than that of the classical European option under the same parameters.

scholarly journals European Option Pricing Formula in Risk-Aversive Markets

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Shujin Wu ◽  
Shiyu Wang
Keyword(s):  
Risk Measure ◽  
European Option ◽  
Underlying Asset ◽  
No Arbitrage ◽  
European Option Pricing ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Risk Neutral ◽  
Arbitrage Opportunity ◽  
Weaker Conditions

In this study, using the method of discounting the terminal expectation value into its initial value, the pricing formulas for European options are obtained under the assumptions that the financial market is risk-aversive, the risk measure is standard deviation, and the price process of underlying asset follows a geometric Brownian motion. In particular, assuming the option writer does not need the risk compensation in a risk-neutral market, then the obtained results are degenerated into the famous Black–Scholes model (1973); furthermore, the obtained results need much weaker conditions than those of the Black–Scholes model. As a by-product, the obtained results show that the value of European option depends on the drift coefficient μ of its underlying asset, which does not display in the Black–Scholes model only because μ = r in a risk-neutral market according to the no-arbitrage opportunity principle. At last, empirical analyses on Shanghai 50 ETF options and S&P 500 options show that the fitting effect of obtained pricing formulas is superior to that of the Black–Scholes model.

Risk and Return of Retail Sukuk and Retail Bond in Indonesia Period 2008-2017 (Comparative Study)

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Rahma Yudi Astuti ◽  
Asad Arsya Brilliant Fani
Keyword(s):  
Standard Deviation ◽  
Comparative Study ◽  
Stock Exchange ◽  
Secondary Data ◽  
Bond Market ◽  
Bond Pricing ◽  
Risk And Return ◽  
Underlying Asset ◽  
The Real ◽  
The World

Sukuk and Bonds has differences and similarities. Fundamental differences between sukuk and bonds are first, underlying asset in every sukuk issuance, concept of profit loss sharing and the use of Islamic contracts. Whereas conducted research in practice of differences between sukuk and bonds are still an on-going discussion. This study aims to add the evidence in the discussion regarding whether there is differences between sukuk and bonds in the world of practice, provide investment preferences as well as educating investors in choosing sukuk or bonds as a sustainable and smooth instrument. The method used is Mann Whitney U-Test to test whether there is a different between yield to maturity (return) and standard deviation (risk) of both instruments. Using secondary data of Retail Sukuk (SR) and Retail Bonds (ORI) period 2008-2017 obtained from Indonesia Stock Exchange, Indonesia Bond Market Directory and Indonesia Bond Pricing Agency. The result shows that there is no significance difference of retail sukuk return and risk with retail bonds in Indonesia. Besides retail bonds are show higher return than retail sukuk because of higher coupon and longest mature date. While, retail sukuk is more stable rather than bonds as it backed up by the real underlying asset. Keywords: Retail Sukuk (SR), Retail Bonds (ORI), Yield to Maturity

The Nexus Between Johannesburg Stock Exchange and the United States Unemployment Rate Announcement: An Impulse Response Analysis

2018 ◽  
Vol 10 (3(J)) ◽  
pp. 160-168
Author(s):  
Misheck Mutize ◽  
Victor Virimai Mugobo
Keyword(s):  
United States ◽  
South African ◽  
Impulse Response ◽  
Unemployment Rate ◽  
Stock Prices ◽  
Stock Exchange ◽  
The United States ◽  
Response Analysis ◽  
Johannesburg Stock Exchange ◽  
The Us

The study explores the relationship between the unemployment rate in the United States and South Africa’s stock prices from the beginning of 2013 to the last day 2017. The objective of this paper is to examine the impact of the US unemployment rate announcement on the South African financial market. Results of Impulse Response analysis show that there is a very minimal impact from the US unemployment announcement to South Africa’s stock prices which disappears within two days of the announcement. In addition, the Johannesburg stock exchange index marginally responds to own shocks, which marginally fades away within two days. These findings imply that the changes in the US employment policies have a direct ripple effect on the South African macroeconomic environment, its investing public sentiments and corporate confidence on the future prospects of businesses.

scholarly journals Pairwise maximum entropy model explains the role of white matter structure in shaping emergent co-activation states

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Arian Ashourvan ◽  
Preya Shah ◽  
Adam Pines ◽  
Shi Gu ◽  
Christopher W. Lynn ◽  
...  
Keyword(s):  
White Matter ◽  
Maximum Entropy ◽  
Large Scale ◽  
Structural Connectivity ◽  
Quantitative Relationship ◽  
Brain Regions ◽  
Maximum Entropy Model ◽  
Entropy Model ◽  
Activation Patterns ◽  
Co Activation

AbstractA major challenge in neuroscience is determining a quantitative relationship between the brain’s white matter structural connectivity and emergent activity. We seek to uncover the intrinsic relationship among brain regions fundamental to their functional activity by constructing a pairwise maximum entropy model (MEM) of the inter-ictal activation patterns of five patients with medically refractory epilepsy over an average of ~14 hours of band-passed intracranial EEG (iEEG) recordings per patient. We find that the pairwise MEM accurately predicts iEEG electrodes’ activation patterns’ probability and their pairwise correlations. We demonstrate that the estimated pairwise MEM’s interaction weights predict structural connectivity and its strength over several frequencies significantly beyond what is expected based solely on sampled regions’ distance in most patients. Together, the pairwise MEM offers a framework for explaining iEEG functional connectivity and provides insight into how the brain’s structural connectome gives rise to large-scale activation patterns by promoting co-activation between connected structures.

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