Complete Financial Market Research Articles

Risk Spillovers and Hedging: Why Do Firms Invest Too Much in Systemic Risk

In this paper we show that free entry decisions may be socially inefficient, even in a perfectly competitive homogeneous goods market with non-lumpy investments. In our model, inefficient entry decisions are the result of risk-aversion of incumbent producers and consumers, combined with incomplete financial markets which limit risk-sharing between market actors. Investments in productive assets affect the distribution of equilibrium prices and quantities, and create risk spillovers. From a societal perspective, entrants under-invest in technologies that would reduce systemic sector risk, and may over-invest in risk-increasing technologies. The inefficiency is shown to disappear when a complete financial market of tradable risk-sharing instruments is available, although the introduction of any individual tradable instrument may actually decrease efficiency. We therefore believe that sectors without well-developed financial markets will benefit from sector-specific regulation of investment decisions.

Risk Spillovers and Hedging: Why Do Firms Invest Too Much in Systemic Risk?

In this paper we show that free entry decisions may be socially inefficient, even in a perfectly competitive homogeneous goods market with non-lumpy investments. In our model, inefficient entry decisions are the result of risk-aversion of incumbent producers and consumers, combined with incomplete financial markets which limit risk-sharing between market actors. Investments in productive assets affect the distribution of equilibrium prices and quantities, and create risk spillovers. From a societal perspective, entrants under-invest in technologies that would reduce systemic sector risk, and may over-invest in risk-increasing technologies. The inefficiency is shown to disappear when a complete financial market of tradable risk-sharing instruments is available, although the introduction of any individual tradable instrument may actually decrease efficiency. We therefore believe that sectors without well-developed financial markets will benefit from sector-specific regulation of investment decisions.

DISCRETE TIME HEDGING OF THE AMERICAN OPTION

In a complete financial market we consider the discrete time hedging of the American option with a convex payoff. It is well known that for the perfect hedging the writer of the option must trade continuously in time, which is impossible in practice. In reality, the writer hedges only at some discrete time instants. The perfect hedging requires the knowledge of the partial derivative of the value function of the American option in the underlying asset, the explicit form of which is unknown in most cases of practical importance. Several approximation methods have been developed for the calculation of the value function of the American option. We claim in this paper that having at hand any uniform approximation of the American option value function at equidistant discrete rebalancing times it is possible to construct a discrete time hedging portfolio, the value process of which uniformly approximates the value process of the continuous time perfect delta-hedging portfolio. We are able to estimate the corresponding discrete time hedging error that leads to a complete justification of our hedging method for nonincreasing convex payoff functions including the important case of the American put. This method is essentially based on a new type square integral estimate for the derivative of an arbitrary convex function recently found by Shashiashvili.

Numerical Approximation of Black-Scholes Equation

This study deals with well-known Black-Scholes model in a complete financial market. We obtain numerical methods for european and exotic options, for one asset and for two assets models. Introduction. Options are used on markets and exchanges. The Black- Scholes model is a convenient way to calculate the price of an option. In this study numerical methods will be processed to solve that equation. The numerical methods are based on finite differences. We test fully implicit, semi-implicit and explicit methods. For the discretized problem, a linear algebraic system, we test direct and iterative methods. This way we intend to create a general numerical scheme for different types of options. Section 1 deals with the Black-Scholes model. In this part we show some options used, European call and put option, and the mathematical properties of these options. Section 2 shows our numerical setup for the equation presented in Sec- tion 1. This section deals with the space discretization of the parabolic differential equation with one underlying asset, using finite difference meth- ods. We obtain an explicit and two implicit methods (fully implicit and semi-implicit method) to solve the discretized system. Numerical experi- ments are related for each method.

Universalizing Complete Access to Finance: Key Conceptual Issues

In this paper, we present two stylized models of the financial system. We make the case that in order to realize the potential of a well-functioning complete financial market, financial system designers and financial service providers will need to think about ways to deliver financial propositions that are customized to individual households by responding to their unique circumstances. This will entail the presence of proximate, well-trained providers that intermediate between the customer and those large “product manufacturers” whose goal is financial well being and not merely product sales. These providers would need to use expertise in financial advice or wealth management to develop integrated financial propositions for clients. We also highlight some of the important debates that arise in making this stylized financial system a reality.

On Modelling Long Term Stock Returns with Ergodic Diffusion Processes: Arbitrage and Arbitrage‐Free Specifications

We investigate the arbitrage‐free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset‐liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.

Stochastic optimal control of DC pension funds

In this paper, we study the portfolio problem of a pension fund manager who wants to maximize the expected utility of the terminal wealth in a complete financial market with the stochastic interest rate. Using the method of stochastic optimal control, we derive a non-linear second-order partial differential equation for the value function. As it is difficult to find a closed form solution, we transform the primary problem into a dual one by applying a Legendre transform and dual theory, and try to find an explicit solution for the optimal investment strategy under the logarithm utility function. Finally, a numerical simulation is presented to characterize the dynamic behavior of the optimal portfolio strategy.

Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences

This paper investigates the dynamic consumption and portfolio choice of an investor with habit formation in preferences and access to a complete financial market with time-varying investment opportunities. An exact and simple characterization of the optimal behavior under general, possibly non-Markov, dynamics of market prices is derived. Relative to the benchmark case of time-additive power utility, habit formation affects the hedge component of the optimal portfolio differently than the speculative component. The quantitative effects of habit formation are studied in three concrete settings. Firstly, a closed-form solution of the optimal consumption and portfolio choice with mean-reverting stock returns is derived. Secondly, with Cox–Ingersoll–Ross interest rate dynamics the optimal strategies are expressed in terms of the solution to a partial differential equation, which has an explicit solution for time-additive utility, but not with habit formation. Thirdly, a new model with both mean-reverting stock returns and stochastic interest rates is studied. Overall, the numerical examples show that, while hedging demands for various assets are affected differently by habit persistence, the main effect on relative asset allocations stems from the fact that some assets (bonds and cash) are better investment objects than others (stocks) when it comes to ensuring that future consumption will not fall below the habit level.

On Modelling Long Term Stock Returns with Ergodic Diffusion Processes: Arbitrage and Arbitrage-Free Specifications

We investigate the arbitrage-free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for insurer asset-liability management as they allow the modelling of long term stock returns with heavy tailed ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market. Unfortunately the standard specification of these models in the literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities, and consequently construct a modification that is arbitrage free.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multiperiod inventory models as well as multiperiod models that coordinate inventory and pricing strategies. We show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. These structural results are extended to models in which the decision maker has access to a (partially) complete financial market and can hedge its operational risk through trading financial securities. Computational results demonstrate that the optimal policy is relatively insensitive to small changes in the decision-maker's level of risk aversion.

Pricing and hedging in the presence of extraneous risks

Given an underlying complete financial market, we study contingent claims whose payoffs may depend on the occurrence of nonmarket events. We first investigate the almost-sure hedging of such claims. In particular, we obtain new representations of the hedging prices and provide necessary and sufficient conditions for a claim to be marketed. The analysis of various examples then leads us to investigate alternative pricing rules. We choose to embed the pricing problem into the agent’s portfolio decision and study reservation prices. We establish the existence and consistency of this pricing rule in a semimartingale model. We characterize the nonlinear dependence of the reservation price with respect to both the agent’s initial capital and the size of her position. The fair price arises as a limiting case.

Delegated dynamic portfolio management under mean-variance preferences

We consider a complete financial market with deterministic parameters where an investor and a fund manager have mean-variance preferences. The investor is allowed to borrow with risk-free rate and dynamically allocate his wealth in the fund provided his holdings stay nonnegative. The manager gets proportional fees instantaneously for her management services. We show that the manager can eliminate all her risk, at least in the constant coefficients case. Her own portfolio is a proportion of the amount the investor holds in the fund. The equilibrium optimal strategies are independent of the fee rate although the portfolio of each agent depends on it. An optimal fund weight is obtained by the numerical solution of a nonlinear equation and is not unique in general. In one-dimensional case, the investor's risk is inversely proportional to the weight of the risky asset in the fund. We also generalize the problem to the case of multiple managers and provide some examples.

Optimal portfolio strategies benchmarking the stock market

The paper investigates the impact of adding a shortfall risk constraint to the problem of a portfolio manager who wishes to maximize his utility from the portfolios terminal wealth. Since portfolio managers are often evaluated relative to benchmarks which depend on the stock market we capture risk management considerations by allowing a prespecified risk of falling short such a benchmark. This risk is measured by the expected loss in utility. Using the Black–Scholes model of a complete financial market and applying martingale methods, explicit analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.

Hedging life insurance contracts in a Lévy process financial market

Starting from the model of Møller [Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin 28 (1998) 17–47] we derive analogously, but for an incomplete financial market, a (locally) risk-minimizing hedging strategy for unit-linked life insurance contracts represented by the pure endowment and the term insurance. The incomplete financial market is exemplarily given by a general Lévy-driven model. We investigate the Föllmer–Schweizer decomposition of their intrinsic value. Additionally, we compare our results to the ones obtained by Møller [Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin 28 (1998) 17–47] and show how they are affected by replacing the complete financial market by an incomplete one.

Dynamic utility maximization with bounded shortfall risks

AbstractWe address the dynamic portfolio optimization problem where the expected utility from terminal wealth has to be maximized. The special feature of this paper is an additional constraint on the portfolio strategy modeling bounded shortfall risks. We consider the risk, that the terminal wealth of the portfolio falls short of a certain benchmark. This benchmark is chosen to be proportional to the stock price. The risk is measured by the Expected Utility Loss.Using a continuous‐time model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamic Portfolio Optimization with Bounded Shortfall Risks

We address a dynamic portfolio optimization problem where the expected utility from terminal wealth has to be maximized. The special feature of this paper is an additional constraint on the portfolio strategy modeling bounded shortfall risks, which are measured by value at risk or expected loss. Using a continuous-time model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Finally, some numerical results are presented.

Dynamic Minimization of Worst Conditional Expectation of Shortfall

In a complete financial market model, the shortfall‐risk minimization problem at the terminal date is treated for the seller of a derivative security F. The worst conditional expectation of the shortfall is adopted as the measure of this risk, ensuring that the minimized risk satisfies certain desirable properties as the dynamic measure of risk, as proposed by Cvitanić and Karatzas (1999). The terminal value of the optimized portfolio is a binary functional dependent on F and the Radon‐Nikodym density of the equivalent local martingale measure. In particular, it is observed that there exists a positive number x* that is less than the replicating cost xF of F, and that the strategy minimizing the expectation of the shortfall is optimal if the hedger's capital is in the range [x*, xF].

A class of complete benchmark models with intensity-based jumps

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

A class of complete benchmark models with intensity-based jumps

This paper proposes a class of complete financial market models, the benchmark models, with security price processes that exhibit intensity-based jumps. The benchmark or reference unit is chosen to be the growth-optimal portfolio. Primary security account prices, when expressed in units of the benchmark, turn out to be local martingales. In the proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair derivative prices are obtained as conditional expectations of future benchmarked prices under the real-world probability measure. This concept of fair pricing generalizes the classical risk-neutral approach and the actuarial present-value pricing methodology.

Optimal pension management in a stochastic framework

We consider a stochastic model for a defined-contribution pension fund in continuous time. In particular, we focus on the portfolio problem of a fund manager who wants to maximize the expected utility of his terminal wealth in a complete financial market with stochastic interest rate. The fund manager must cope with two background risks: the salary risk and the inflation risk. We find a closed form solution for the asset allocation problem and so we are able to analyze in detail the behavior of the optimal portfolio with respect to salary and inflation. Finally, a numerical simulation is presented.