Incomplete Market Setting Research Articles

Risk Shifting, Technology Policy and Sales Contingent Claims: When is Launch Aid to the Aerospace Industry a Subsidy?

This paper studies the criteria with which the presence or absence of 'subsidy' in sales contingent Launch Aid R&D support may be determined when payoff-relevant market incompleteness limits the precision of market-based pricing to non-trivial intervals. Existing criteria correctly account for the opportunity cost of capital when markets are complete and frictionless, but fail when the interval between bid and ask prices may not be finessed away. An economic definition of subsidy must necessarily capture opportunity cost, and we develop a definition that fully incorporates government's opportunity cost in both complete and incomplete market settings.

On Pricing Derivatives Under GARCH Models: A Dynamic Gerber-Shiu Approach

This paper proposes a method for pricing derivatives under the generalized autoregressive conditional heteroskedasticity (GARCH) assumption for underlying assets in the context of a "dynamic" version of Gerber and Shiu's (1994) option-pricing model. Instead of adopting the notion of a local risk-neutral valuation relationship (LRNVR), introduced by Duan (1995), the authors here employ the concept of conditional Esscher transforms introduced by Bühlmann et al. (1996) to identify a martingale measure under the incomplete market setting. One advantage of this model is that it provides a unified and convenient approach to deal with different parametric models for the innovation of the GARCH stock-price process. Under the conditional normality assumption for stock innovation, our pricing result is consistent with that of Duan (1995). In line with the celebrated Gerber-Shiu option pricing model, the pricing result can be justified within the dynamic framework of utility maximization problems, which makes the economic intuition of the pricing result more appealing. In fact, the use of the Esscher transform for option valuation can also be justified by the minimization of the relative entropy between the statistical probability and the risk-neutralized pricing probability. Numerical results for comparing the model with the Black-Scholes optionpricing model are also presented.

A Fair Pricing Approach to Weather Derivatives

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of the value of the growth optimal portfolio, it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed.

Quadratic Hedging and Mean-Variance Portfolio Selection with Random Parameters in an Incomplete Market

This paper concerns the problems of quadratic hedging and pricing, and mean-variance portfolio selection in an incomplete market setting with continuous trading, multiple assets, and Brownian information. In particular, we assume throughout that the parameters describing the market model may be random processes. We approach these problems from the perspective of linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs); that is, we focus on the so-called stochastic Riccati equation (SRE) associated with the problem. Excepting certain special cases, solvability of the SRE remains an open question. Our primary theoretical contribution is a proof of existence and uniqueness of solutions of the SRE associated with the quadratic hedging and mean-variance problems. In addition, we derive closed-form expressions for the optimal portfolios and efficient frontier in terms of the solution of the SRE. A generalization of the Mutual Fund Theorem is also obtained.

Managing Electricity Risk

In this paper we propose an algorithm for pricing derivatives written about electricity in an incomplete market setting. A discrete time model for price dynamics which embodies the main features of electricity price revealed by simple time series analysis is considered. We use, jointly, Binomial and Monte Carlo methods for pricing under a risk–neutral measure of which we prove the existence.

Mean Variance Portfolio and Hedging Strategies in Incomplete Markets

We address two mean-variance asset allocation and hedging problems in continuous-time incomplete markets. The resolution emphasizes the geometric properties of mean-variance portfolios and underlines the role of two specific portfolios: The minimum norm and the minimum variance portfolios. We extend the portfolio strategies of Bajeux-Besnainou and Portait (1998) to the incomplete market setting and provide a set of fictitious assets that can complement the market without being traded. Moreover, the fictitious assets can be chosen independently of the investor's level of risk aversion. As importantly, we show that the fictitious completion is irrelevent in mean-variance portfolio problems. Taking the orthogonal projection of fictitious portfolio distributions on the space of attainable distributions provides the required attainable portfolio. This approach is applied successfully in the imperfect hedging problem of Duffie and Richardson (1991) where the least favorable completion cannot be explicited.

Portfolio Choice under Inflation: Are Popular Recommendations Consistent with Rational Behavior?

We consider the optimal asset allocation choice of an investor who can invest in cash (a money market bank account), nominal bonds, and stocks (the stock index). The investor faces an incomplete market setting and is not able to perfectly hedge long run real interest rate risk using the available securities. The optimal investment strategy is consistent with the following features of popular investment advice which have been pointed out as puzzles: (i) a decreasing fraction of stocks in the portfolio as time passes towards the investment horizon, and (ii) a higher bond to stock ratio for more (less risk tolerant) investors (Canner, Mankiw and Weil, 1997). The model for asset price dynamics is calibrated to US market data and, furthermore, risk aversion parameters and time horizons are calibrated so as to obtain a match between the optimal asset allocations and observed investment recommendations for aggressive, moderate, and conservative investor groups with different investment horizons.

Modelling the Stochastic Dynamics of Volatility for Equity Indices

The paper is based on the observations that stockk index returns of major equity markets are likely to be Student t distributed. It then develops a class of continuous time stochastic volatility models that is consistent with such empirical findings. Furthermore, applying the criterion of local risk minimisation in an incomplete market setting, option prices are computed. Finally it is shown that implied volatility smile and skew patterns of the type observed in the markets can be recovered from the resulting stochastic volatility model.

Risk Aversion and Arbitrage

ABSTRACTThis paper characterizes conditions under which asset returns and consumption are consistent with risk‐averse preferences. It is shown that risk aversion is equivalent to “zero arbitrage” on a transformation of the payoff space. The implicit state prices which are dual to this no‐arbitrage condition can be interpreted as prices of “pure consumption hedges.” This zero‐arbitrage restriction implies the usual restrictions associated with nonsatiation. The analysis holds in both complete and incomplete market settings.