FINANCIAL MARKET MODEL WITH INFLUENTIAL INFORMED INVESTORS

2005 ◽  
Vol 08 (06) ◽  
pp. 693-716 ◽  
Author(s):  
AXEL GRORUD ◽  
MONIQUE PONTIER
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Financial Market ◽  
Asset Prices ◽  
Optimization Problem ◽  
Statistical Tests ◽  
Market Model ◽  
Financial Model ◽  
Additional Information ◽  
The Interest Rate

We develop a financial model with an "influential informed" investor who has an additional information and influences asset prices by means of his strategy. The prices dynamics are supposed to be driven by a Brownian motion, the informed investor's strategies affect the risky asset trends and the interest rate. Our paper could be seen as an extension of Cuoco and Cvitanic's work [4] since, as these authors, we solve the informed influential investor's optimization problem. But our main result is the construction of statistical tests to detect if, observing asset prices and agent's strategies, this influential agent is or not an informed trader.

scholarly journals Analysis of a Four-Dimensional Hyperchaotic System Described by the Caputo–Liouville Fractional Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Derivative ◽  
Financial Market ◽  
Numerical Scheme ◽  
Hyperchaotic System ◽  
Financial Model ◽  
Investment Demand ◽  
Proposed Model ◽  
Liouville Fractional Derivative ◽  
The Interest Rate ◽  
The Stability

A new four-dimensional hyperchaotic financial model is introduced. The novelties come from the fractional-order derivative and the use of the quadric function x 4 in modeling accurately the financial market. The existence and uniqueness of its solutions have been investigated to justify the physical adequacy of the model and the numerical scheme proposed in the resolution. We offer a numerical scheme of the new four-dimensional fractional hyperchaotic financial model. We have used the Caputo–Liouville fractional derivative. The problems addressed in this paper have much importance to approach the interest rate, the investment demand, the price exponent, and the average profit margin. The validation of the chaotic, hyperchaotic, and periodic behaviors of the proposed model, the bifurcation diagrams, the Lyapunov exponents, and the stability analysis has been analyzed in detail. The proposed numerical scheme for the hyperchaotic financial model is destined to help the agents decide in the financial market. The solutions of the 4D fractional hyperchaotic financial model have been analyzed, interpreted theoretically, and represented graphically in different contexts. The present paper is mathematical modeling and is a new tool in economics and finance. We also confirm, as announced in the literature, there exist hyperchaotic systems in the fractional context, which admit one positive Lyapunov exponent.

scholarly journals Monetary Policy Effects on Energy Sector Bubbles

Energies ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 472
Author(s):  
Petre Caraiani ◽  
Adrian Călin
Keyword(s):  
Monetary Policy ◽  
Interest Rate ◽  
Asset Prices ◽  
The United States ◽  
Energy Sector ◽  
Monetary Policy Shocks ◽  
Policy Shocks ◽  
The Difference ◽  
The Interest Rate ◽  
The Impact

We investigate the effects of monetary policy shocks, including unconventional policy measures, on the bubbles of the energy sector, for the case of the United States. We estimate a time-varying Bayesian VAR model that allows for quantifying the impact of monetary policy shocks on asset prices and bubbles. The energy sector is measured through the S&P Energy Index, while bubbles are measured through the difference between asset prices and the corresponding dividends for the energy sector. We find significant differences in the impact of monetary policy shocks for the aggregate economy and for the energy sector. The findings seem sensitive to the interest rate use, i.e., whether one uses the shadow interest rate or the long-term interest rate.

scholarly journals A financial market with singular drift and no arbitrage

2020 ◽  
Author(s):  
Nacira Agram ◽  
Bernt Øksendal
Keyword(s):  
Brownian Motion ◽  
Financial Market ◽  
High Frequency ◽  
Continuous Process ◽  
Mathematical Finance ◽  
Market Model ◽  
High Frequency Trading ◽  
No Arbitrage ◽  
Drift Term ◽  
Singular Drift

AbstractWe study a financial market where the risky asset is modelled by a geometric Itô-Lévy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier. See e.g. Jarrow and Protter (J Bank Finan 29:2803–2820, 2005) for an explanation and discussion of this model in the Brownian motion case. As already pointed out by Karatzas and Shreve (Methods of Mathematical Finance, Springer, Berlin, 1998) (in the continuous setting), this allows for arbitrages in the market. However, the situation in the case of jumps is not clear. Moreover, it is not clear what happens if there is a delay in the system. In this paper we consider a jump diffusion market model with a singular drift term modelled as the local time of a given process, and with a delay $$\theta > 0$$ θ > 0 in the information flow available for the trader. We allow the stock price dynamics to depend on both a continuous process (Brownian motion) and a jump process (Poisson random measure). We believe that jumps and delays are essential in order to get more realistic financial market models. Using white noise calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as $$\theta > 0$$ θ > 0 . This implies that there is no arbitrage in the market in that case. However, when $$\theta $$ θ goes to 0, the value goes to infinity. This is in agreement with the above result that is an arbitrage when there is no delay. Our model is also relevant for high frequency trading issues. This is because high frequency trading often leads to intensive trading taking place on close to infinitesimal lengths of time, which in the limit corresponds to trading on time sets of measure 0. This may in turn lead to a singular drift in the pricing dynamics. See e.g. Lachapelle et al. (Math Finan Econom 10(3):223–262, 2016) and the references therein.

Backward Stochastic PDE and Imperfect Hedging

2003 ◽  
Vol 06 (07) ◽  
pp. 663-692 ◽  
Author(s):  
M. Mania ◽  
R. Tevzadze
Keyword(s):  
Financial Market ◽  
Asset Prices ◽  
Random Function ◽  
Value Function ◽  
Market Model ◽  
Stochastic Pde ◽  
Continuous Semimartingale ◽  
Incomplete Financial Market ◽  
Mean Variance ◽  
The Value Function

We consider a problem of minimization of a hedging error, measured by a positive convex random function, in an incomplete financial market model, where the dynamics of asset prices is given by an Rd-valued continuous semimartingale. Under some regularity assumptions we derive a backward stochastic PDE for the value function of the problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward-SDE. As an example the case of mean-variance hedging is considered.

RISK-BASED CAPITAL FOR VARIABLE ANNUITY UNDER STOCHASTIC INTEREST RATE

2020 ◽  
Vol 50 (3) ◽  
pp. 959-999
Author(s):  
JinDong Wang ◽  
Wei Xu
Keyword(s):  
Monetary Policy ◽  
Interest Rate ◽  
Mutual Fund ◽  
Risk Measures ◽  
Market Model ◽  
Model Parameters ◽  
Joint Dynamics ◽  
Contract Attributes ◽  
The Interest Rate

AbstractInterest rate is one of the main risks for the liability of the variable annuity (VA) due to its long maturity. However, most existing studies on the risk measures of the VA assume a constant interest rate. In this paper, we propose an efficient two-dimensional willow tree method to compute the liability distribution of the VA with the joint dynamics of the mutual fund and interest rate. The risk measures can then be computed by the backward induction on the tree structure. We also analyze the sensitivity and impact on the risk measures with regard to the market model parameters, contract attributes, and monetary policy changes. It illustrates that the liability of the VA is determined by the long-term interest rate whose increment leads to a decrease in the liability. The positive correlation between the interest rate and mutual fund generates a fat-tailed liability distribution. Moreover, the monetary policy change has a bigger impact on the long-term VAs than the short-term contracts.

scholarly journals Option Pricing Formulas in a New Uncertain Mean-Reverting Stock Model with Floating Interest Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhaopeng Liu
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Financial Market ◽  
American Option Pricing ◽  
European Option ◽  
Numerical Examples ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Stock Model ◽  
The Interest Rate

Options play a very important role in the financial market, and option pricing has become one of the focus issues discussed by the scholars. This paper proposes a new uncertain mean-reverting stock model with floating interest rate, where the interest rate is assumed to be the uncertain Cox-Ingersoll-Ross (CIR) model. The European option and American option pricing formulas are derived via the α -path method. In addition, some mathematical properties of the uncertain option pricing formulas are discussed. Subsequently, several numerical examples are given to illustrate the effectiveness of the proposed model.

Valuation of interest rate ceiling and floor based on the uncertain fractional differential equation in Caputo sense

2020 ◽  
pp. 1-10
Author(s):  
Ting Jin ◽  
Hui Ding ◽  
Bo Li ◽  
Hongxuan Xia ◽  
Chenxi Xue
Keyword(s):  
Interest Rate ◽  
Financial Market ◽  
Supply And Demand ◽  
Dynamic Change ◽  
Asset Price ◽  
Interest Rate Risk ◽  
Proposed Model ◽  
The Interest Rate ◽  
The Right ◽  
Predictor Corrector

As an economic lever in financial market, interest rate option is not only the function of facilitating the bank to adjust the market fund supply and demand relation indirectly, but also provides the guarantee for investors to choose whether to exercise the right at the maturity date, thereby locking in the interest rate risk. This paper mainly studies the price of the interest rate ceiling as well as floor under the uncertain environment. Firstly, from the perspective of expert reliability, rather than relying on a large amount of historical financial data, to consider interest rate trends, and further assume that the dynamic change of the interest rate conforms to the uncertain process. Secondly, since uncertain fractional-order differential equations (UFDEs) have non-locality features to reflect memory and hereditary characteristics for the asset price changes, thus is more suitable to model the real financial market. We construct the mean-reverting interest rate model based on the UFDE in Caputo type. Then, the pricing formula of the interest rate ceiling and floor are provided separately. Finally, corresponding numerical examples and algorithms are given by using the predictor-corrector method, which support the validity of the proposed model.

BROWNIAN MOTION IN THE INTEREST RATE CONSIDERED AS THE PRICE OF MONEY

1983 ◽  
Vol 18 (3) ◽  
pp. 104-104
Author(s):  
M. F. M. Osborne ◽  
Joseph E. Murphy
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
The Interest Rate

scholarly journals Jump Telegraph Processes and Financial Markets with Memory

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Nikita Ratanov
Keyword(s):  
Interest Rate ◽  
Financial Markets ◽  
Financial Market ◽  
Stock Prices ◽  
Call Option ◽  
Market Models ◽  
New Class ◽  
Risk Neutral ◽  
The Interest Rate ◽  
With Memory

The paper develops a new class of financial market models. These models are based on generalized telegraph processes with alternating velocities and jumps occurring at switching velocities. The model under consideration is arbitrage-free and complete if the directions of jumps in stock prices are in a certain correspondence with their velocity and with the behaviour of the interest rate. A risk-neutral measure and arbitrage-free formulae for a standard call option are constructed. This model has some features of models with memory, but it is more simple.

scholarly journals QUARTERLY ANALYSIS: The Progress of Monetary, Banking and Payment System Quarter III - 2011

2012 ◽  
Vol 14 (2) ◽  
pp. 103-105
Author(s):  
Author Team of Quarterly Report Bank Indonesia
Keyword(s):  
Interest Rate ◽  
Financial Market ◽  
Economic Performance ◽  
Negative Impact ◽  
The Other ◽  
Inflation Target ◽  
Inflation Expectation ◽  
Slowing Down ◽  
The Interest Rate ◽  
The Impact

The Board of Governor Meeting of Bank Indonesia on October 11, 2011 decided to lower the BI rate by 25 bps to the level of 6.5%. Bank Indonesia will also maintain the stabilization of Rupiah particularly from the impact of global financial market shock. The decision is in line with the inflation expectation of below 5% on current and next year. Furthermore, these policies are meant to anticipate and to mitigate the negative impact of the global economic and financial slowdown on Indonesian economy. Looking ahead, the Board of Governor will continue to evaluate the global economic and financial performance and use the interest rate as well as the mix of monetary and the other micro prudential policies to mitigate the possible slowing down of Indonesian economic performance, especially on achieving the inflation target of 5% + 1% in 2011 and 4.5% + 1% in 2012.

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