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This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part.
Abstract
Purpose
This paper aims to study the conditions for the hedging portfolio of any contingent claim on bonds to have no bank account part.
Design/methodology/approach
Hedging and Malliavin calculus techniques recently developed under a stochastic string framework are applied.
Findings
A necessary and sufficient condition for the hedging portfolio to have no bank account part is found. This condition is applied to a barrier option, and an example of a contingent claim whose hedging portfolio has a bank account part different from zero is provided.
Originality/value
To the best of the authors’ knowledge, this is the first time that this issue has been addressed in the literature.
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The purpose of this paper is to study the problem of optimal Ramsey taxation in a finite-planning-horizon, representative-agent endogenous growth model including government…
Abstract
Purpose
The purpose of this paper is to study the problem of optimal Ramsey taxation in a finite-planning-horizon, representative-agent endogenous growth model including government expenditures as a productive input in capital formation and also with hidden actions.
Design/methodology/approach
Technically, Malliavin calculus and forward integrals are naturally introduced into the macroeconomic theory when economic agents are faced with different information structures arising from a non-Markovian environment.
Findings
The major result shows that the well-known Judd-Chamley Theorem holds almost surely if the depreciation rate is strictly positive, otherwise Judd-Chamley Theorem only holds for a knife-edge case or on a Lebesgue measure-zero set when the physical capital is completely sustainable.
Originality/value
The author believes that the approach developed as well as the major result established is new and relevant.
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Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper…
Abstract
Empirical findings on interest rate dynamics imply that short rates show some long memories and non-Markovian. It is well-known that fractional Brownian motion (IBm) is a proper candidate for modelling this empirical phenomena. IBm. however. is not a semimartingale process. For this reason. it is very hard to apply such processes for asset price modelling.
Without using Ito formula, we investigate the IBm interest rate theory‘ We obtain a pure discount bond price. and Greeks by using Malllavin calculus.
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I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to…
Abstract
I survey applications of Markov switching models to the asset pricing and portfolio choice literatures. In particular, I discuss the potential that Markov switching models have to fit financial time series and at the same time provide powerful tools to test hypotheses formulated in the light of financial theories, and to generate positive economic value, as measured by risk-adjusted performances, in dynamic asset allocation applications. The chapter also reviews the role of Markov switching dynamics in modern asset pricing models in which the no-arbitrage principle is used to characterize the properties of the fundamental pricing measure in the presence of regimes.
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Rim Amami, Monique Pontier and Hani Abidi
The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These…
Abstract
Purpose
The purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.
Design/methodology/approach
The main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.
Findings
In this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.
Originality/value
In this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.
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Youssef El-Khatib and Abdulnasser Hatemi-J
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. The purpose of this…
Abstract
Purpose
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. The purpose of this paper is to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time.
Design/methodology/approach
The authors consider a market suffering from a financial crisis. The authors provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. Furthermore, the underlying price sensitivities are derived.
Findings
The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during a financial crisis more precise. A numerical application is provided for determining the premium for a call and a put European option along with the underlying price sensitivities for each option.
Originality/value
An alternative option pricing model is introduced that performs better than existing ones, especially during a financial crisis.
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The purpose of this paper is to review the life of the famous mathematician Kiyosi Itô and discuss his influence on the study of agricultural finance and agricultural economics.
Abstract
Purpose
The purpose of this paper is to review the life of the famous mathematician Kiyosi Itô and discuss his influence on the study of agricultural finance and agricultural economics.
Design/methodology/approach
This paper is a qualitative historical review.
Findings
The paper provides a biographical stretch of Itô's life. It is shown that his influence started to infiltrate the agricultural economics profession at around 1985 and is currently a major influence of a range of economic issues from farm policy to agricultural investments.
Research limitations/implications
The biography is limited to a review of Itô's academic life and influence.
Practical implications
The paper offers a historical perspective on how probability emerged as a critical piece of the economic puzzle. For scholars and practitioners of agricultural finance, the paper provides an in depth review of how Itô processes have, and can, be used.
Originality/value
This paper provides a historical perspective on Itô that is of use to students and scholars of rural credit. This is the first “biography” of Itô to discuss his influence on agricultural finance and agricultural economics.
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This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50…
Abstract
Purpose
This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation.
Design/methodology/approach
This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap.
Findings
The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap.
Research limitations/implications
The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model.
Originality/value
This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.
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The paper aims to compare and clarify the differences and between the two well-known decomposition spectral techniques; the Winer–Chaos expansion (WCE) and the Winer–Hermite…
Abstract
Purpose
The paper aims to compare and clarify the differences and between the two well-known decomposition spectral techniques; the Winer–Chaos expansion (WCE) and the Winer–Hermite expansion (WHE). The details of the two decompositions are outlined. The difficulties arise when using the two techniques are also mentioned along with the convergence orders. The reader can also find a collection of references to understand the two decompositions with their origins. The geometrical Brownian motion is considered as an example for an important process with exact solution for the sake of comparison. The two decompositions are found practical in analysing the SDEs. The WCE is, in general, simpler, while WHE is more efficient as it is the limit of WCE when using infinite number of random variables. The Burgers turbulence is considered as a nonlinear example and WHE is shown to be more efficient in detecting the turbulence. In general, WHE is more efficient especially in case of nonlinear and/or non-Gaussian processes.
Design/methodology/approach
The paper outlined the technical and literature review of the WCE and WHE techniques. Linear and nonlinear processes are compared to outline the comparison along with the convergence of both techniques.
Findings
The paper shows that both decompositions are practical in solving the stochastic differential equations. The WCE is found simpler and WHE is the limit when using infinite number of random variables in WCE. The WHE is more efficient especially in case of nonlinear problems.
Research limitations/implications
Applicable for SDEs with square integrable processes and coefficients satisfying Lipschitz conditions.
Originality/value
This paper fulfils a comparison required by the researchers in the stochastic analysis area. It also introduces a simple efficient technique to model the flow turbulence in the physical domain.
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This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models.
Abstract
Purpose
This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models.
Design/methodology/approach
The paper uses theory of forecasting to find criteria of predictability of market parameters such as volatilities and the appreciation rates.
Findings
It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into an incomplete one. The paper shows that market incompleteness is also non-robust: for any incomplete market from a wide class of models, there exists a complete market model with arbitrarily close paths of the stock prices and the market parameters.
Originality/value
The paper results lead to a counterintuitive conclusion that the incomplete markets are indistinguishable in the terms of the market statistics.
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