scholarly journals An Interval of No-Arbitrage Prices in Financial Markets with Volatility Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hanlei Hu ◽  
Zheng Yin ◽  
Weipeng Yuan
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Stock Price ◽  
Contingent Claims ◽  
Price Dynamics ◽  
Complex Situation ◽  
No Arbitrage ◽  
Price Process ◽  
Arbitrage Opportunities

In financial markets with volatility uncertainty, we assume that their risks are caused by uncertain volatilities and their assets are effectively allocated in the risk-free asset and a risky stock, whose price process is supposed to follow a geometric G-Brownian motion rather than a classical Brownian motion. The concept of arbitrage is used to deal with this complex situation and we consider stock price dynamics with no-arbitrage opportunities. For general European contingent claims, we deduce the interval of no-arbitrage price and the clear results are derived in the Markovian case.

scholarly journals PRICING DERIVATIVES IN HERMITE MARKETS

2019 ◽  
Vol 22 (06) ◽  
pp. 1950031
Author(s):  
STOYAN V. STOYANOV ◽  
SVETLOZAR T. RACHEV ◽  
STEFAN MITTNIK ◽  
FRANK J. FABOZZI
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Fractional Brownian Motion ◽  
Trading Strategies ◽  
Risky Assets ◽  
No Arbitrage ◽  
Arbitrage Opportunities ◽  
Black Scholes ◽  
Hedging Portfolio ◽  
New Framework

We present a new framework for Hermite fractional financial markets, generalizing the fractional Brownian motion (FBM) and fractional Rosenblatt markets. Considering pure and mixed Hermite markets, we introduce a strategy-specific arbitrage tax on the rate of transaction volume acceleration of the hedging portfolio as the prices of risky assets change, allowing us to transform Hermite markets with arbitrage opportunities to markets with no arbitrage opportunities within the class of Markov trading strategies. We derive PDEs for the price of such strategies in the presence of an arbitrage tax in pure Hermite, mixed Hermite, and Black–Scholes–Merton diffusion markets.

Time-changed generalized mixed fractional Brownian motion and application to arithmetic average Asian option pricing

2017 ◽  
Vol 6 (3) ◽  
pp. 85
Author(s):  
ömer önalan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Long Range Dependence ◽  
Price Process ◽  
Inverse Gamma ◽  
Proposed Model ◽  
Mixed Fractional Brownian Motion ◽  
Time Periods

In this paper we present a novel model to analyze the behavior of random asset price process under the assumption that the stock price pro-cess is governed by time-changed generalized mixed fractional Brownian motion with an inverse gamma subordinator. This model is con-structed by introducing random time changes into generalized mixed fractional Brownian motion process. In practice it has been observed that many different time series have long-range dependence property and constant time periods. Fractional Brownian motion provides a very general model for long-term dependent and anomalous diffusion regimes. Motivated by this facts in this paper we investigated the long-range dependence structure and trapping events (periods of prices stay motionless) of CSCO stock price return series. The constant time periods phenomena are modeled using an inverse gamma process as a subordinator. Proposed model include the jump behavior of price process because the gamma process is a pure jump Levy process and hence the subordinated process also has jumps so our model can be capture the random variations in volatility. To show the effectiveness of proposed model, we applied the model to calculate the price of an average arithmetic Asian call option that is written on Cisco stock. In this empirical study first the statistical properties of real financial time series is investigated and then the estimated model parameters from an observed data. The results of empirical study which is performed based on the real data indicated that the results of our model are more accuracy than the results based on traditional models.

CORRIGENDUM: “PRICING AND VALUATION UNDER THE REAL-WORLD MEASURE”

2018 ◽  
Vol 21 (04) ◽  
pp. 1892001 ◽  
Author(s):  
GABRIEL FRAHM
Keyword(s):  
Banach Space ◽  
Asset Pricing ◽  
Financial Markets ◽  
Real World ◽  
Fundamental Theorem ◽  
Contingent Claims ◽  
Henri Poincaré ◽  
The Real ◽  
The Third ◽  
Price Process

In order to prove the third fundamental theorem of asset pricing for financial markets with infinite lifetime [G. Frahm (2016) Pricing and valuation under the real-world measure, International Journal of Theoretical and Applied Finance 19, 1650006], we shall assume that the discounted price process is locally bounded. Otherwise, some principal results developed by [F. Delbaen & W. Schachermayer (1997) The Banach space of workable contingent claims in arbitrage theory, Annales de l’Institut Henri Poincaré 1, 114–144] cannot be applied.

TRADER SPECIES WITH DIFFERENT DECISION STRATEGIES AND PRICE DYNAMICS IN FINANCIAL MARKETS: AN AGENT-BASED MODELING PERSPECTIVE

2010 ◽  
Vol 09 (02) ◽  
pp. 327-344 ◽  
Author(s):  
WEI ZHANG ◽  
GEN LI ◽  
XIONG XIONG ◽  
YONG JIE ZHANG
Keyword(s):  
Financial Markets ◽  
Asset Price ◽  
Agent Based Modeling ◽  
Price Dynamics ◽  
Trading Behavior ◽  
Agent Based ◽  
Price Process ◽  
Trading Decisions ◽  
The Individual ◽  
Analytical Approaches

Investors with different trading strategies can be viewed as different "species" in financial markets. Since the asset price is ultimately determined by the individual trading decisions, the combination and evolution of different trader species in financial market ecology will have great impact to the price dynamics. Considering the limitations and shortcomings of traditional analytical approaches in financial economics in dealing with this issue, an agent-based computational model is introduced in this paper. With the co-existence of 3-type trader species that make different decisions based on their own beliefs and constrains, it is found that although rational speculation destabilizes the price process with the presence of positive feedback strategy, as suggested in the literature, introducing extra noise trading behavior to the market will make the price process back to a more stationary situation, meaning that the market will be healthier if more diversified trader species co-exist in the markets.

OPTION PRICING FOR PROCESSES DRIVEN BY MIXED FRACTIONAL BROWNIAN MOTION WITH SUPERIMPOSED JUMPS

2015 ◽  
Vol 29 (4) ◽  
pp. 589-596 ◽  
Author(s):  
B.L.S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Option Price ◽  
Motion Model ◽  
Price Process ◽  
European Call Option ◽  
Mixed Fractional Brownian Motion ◽  
Special Cases ◽  
Brownian Motion Model

We propose a geometric mixed fractional Brownian motion model for the stock price process with possible jumps superimposed by an independent Poisson process. Option price of the European call option is computed for such a model. Some special cases are studied in detail.

scholarly journals CONSISTENT UPPER PRICE BOUNDS FOR EXOTIC OPTIONS

2021 ◽  
pp. 2150011
Author(s):  
NICOLE BÄUERLE ◽  
DANIEL SCHMITHALS
Keyword(s):  
Stock Prices ◽  
Stock Price ◽  
Exotic Options ◽  
Asian Option ◽  
Worst Case ◽  
No Arbitrage ◽  
Price Process ◽  
Model Free ◽  
Marginal Pricing ◽  
Predetermined Time

We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.

FINANCIAL MARKETS WITH NO RISKLESS (SAFE) ASSET

2017 ◽  
Vol 20 (08) ◽  
pp. 1750054
Author(s):  
SVETLOZAR T. RACHEV ◽  
STOYAN V. STOYANOV ◽  
FRANK J. FABOZZI
Keyword(s):  
Option Pricing ◽  
Financial Markets ◽  
Price Dynamics ◽  
Jump Diffusions ◽  
Risky Assets ◽  
No Arbitrage ◽  
Market Completeness ◽  
Black Scholes ◽  
Stochastic Volatilities

We study markets with no riskless (safe) asset. We derive the corresponding Black–Scholes–Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geometric fractional Brownian and Rosenblatt motions. No-arbitrage and market-completeness conditions are derived in all four cases.

OPTIMAL TRADE EXECUTION UNDER GEOMETRIC BROWNIAN MOTION IN THE ALMGREN AND CHRISS FRAMEWORK

2011 ◽  
Vol 14 (03) ◽  
pp. 353-368 ◽  
Author(s):  
JIM GATHERAL ◽  
ALEXANDER SCHIED
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Closed Form Solution ◽  
Form Solution ◽  
Geometric Brownian Motion ◽  
Price Process ◽  
Risk Criterion ◽  
Execution Strategy ◽  
Optimal Trade Execution ◽  
Alternative Choice

With an alternative choice of risk criterion, we solve the HJB equation explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren–Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.

scholarly journals WEAK AND STRONG NO-ARBITRAGE CONDITIONS FOR CONTINUOUS FINANCIAL MARKETS

2015 ◽  
Vol 18 (01) ◽  
pp. 1550005 ◽  
Author(s):  
CLAUDIO FONTANA
Keyword(s):  
Financial Markets ◽  
Financial Market ◽  
Asset Price ◽  
Complete Characterization ◽  
Free Lunch ◽  
No Arbitrage ◽  
Price Process ◽  
Arbitrage Opportunity ◽  
No Free Lunch

We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage opportunity (NA) and No Free Lunch with Vanishing Risk (NFLVR). We provide a complete characterization of the considered no-arbitrage conditions, linking their validity to the characteristics of the discounted asset price process and to the existence and the properties of (weak) martingale deflators, and review classical as well as recent results.

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