Jérôme Detemple

Option listing and stock returns: An empirical analysis

Abstract This article examines the effect of option introductions on the underlying stocks. In addition to the price increase and volatility decrease that take place when new options are listed, we obtain and explain the following new empirical results: (i) an increase in the value of the market around the listing dates of new options, (ii) an increase in the value of an industry index which excludes the optioned stocks, (iii) the dissipation of the price and volatility effects in recent periods and (iv) the existence of an announcement effect in one subperiod of our sample and its dissipation in recent periods.

Asset Prices in an Exchange Economy with Habit Formation

This paper analyzes asset prices in a representative agent exchange economy with habit-forming preferences. For a general class of utility indices and endowment processes, the authors characterize the optimal demand for consumption and derive explicit solutions for the interest rate and asset risk premia. They show that consumption smoothness may obtain even when the interest rate is stochastic. The consumption capital asset pricing model may not hold when the endowment process has stochastic coefficients; asset risk premia are larger under mild assumptions. The interest rate depends on the growth in the standard of living. Malliavin calculus is employed in the analysis. Copyright 1991 by The Econometric Society.

The Valuation of American Options on Multiple Assets

In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First, we characterize the optimal exercise regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets. Second, we derive results for American option contracts with nonconvex payoffs, such as American capped exchange options. For this option we explicitly identify the optimal exercise boundary and provide a decomposition of the price in terms of a capped exchange option with automatic exercise at the cap and an early exercise premium involving the benefits of exercising prior to reaching the cap. Besides generalizing the current literature on American option valuation our analysis has implications for the theory of investment under uncertainty. A specialization of one of our models also provides a new representation formula for an American capped option on a single underlying asset. Copyright Blackwell Publishers Inc. 1997.

Optimal consumption-portfolio choices and retirement planning

Abstract We examine consumption and investment decisions in a life-cycle model with habit formation, stochastic opportunity set, stochastic wages and labor supply flexibility. Retirement is taken into account by specifying an age at which labor earnings stop, but consumption spending continues. Explicit solutions are obtained for optimal consumption, labor supply and the financing portfolio. We examine the structure and determinants of the optimal portfolio. We also study the effects of the retirement date and of habits on optimal decisions. Finally, we conduct a preliminary analysis to assess the effects of a liquidity constraint on optimal consumption–leisure choices.

50th ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications

This paper surveys the literature on option pricing from its origins to the present. An extensive review of valuation methods for European- and American-style claims is provided. Applications to complex securities and numerical methods are surveyed. Emphasis is placed on recent trends and developments in methodology and modeling.

Further results on asset pricing with incomplete information

Abstract This paper extends the analysis of asset pricing when information is incomplete by relaxing some of the restrictive assumptions of the Gaussian model studied earlier in the literature. For the information structure considered, the posterior beliefs of the investor (the conditional distribution of the current state given the past observations) are characterized by two sets of sufficient statistics implementable in the form of a filter, (i) the vector of conditional means and (ii) a set of sufficient statistics for the conditional variance-covariance matrix. A separation theorem is demonstrated and used to produce a closed-form solution for the interest rate process when the investors utility function is logarithmic. In this context we examine the informational efficiency properties of the interest rate and analyze the stochastic shifts in the volatility of the interest rate process.

The Valuation of American Options for a Class of Diffusion Processes

We present an integral equation approach for the valuation of American-style derivatives when the underlying asset price follows a general diffusion process and the interest rate is stochastic. Our contribution is fourfold. First, we show that the exercise region is determined by a single exercise boundary under very general conditions on the interest rate and the dividend yield. Second, based on this result, we derive a recursive integral equation for the exercise boundary and provide a parametric representation of the American option price. Third, we apply the results to models with stochastic volatility or stochastic interest rate, and to American bond options in one-factor models. For the cases studied, explicit parametric valuation formulas are obtained. Finally, we extend results on American capped options to general diffusion prices. Numerical schemes based on approximations of the optimal stopping time (such as approximations based on a lower bound, or on a combination of lower and upper bounds) are shown to be valid in this context.

Representation formulas for Malliavin derivatives of diffusion processes

Abstract.We provide new representation formulas for Malliavin derivatives of diffusions, based on a transformation of the underlying processes. Both the univariate and the multivariate cases are considered. First order as well as higher order Malliavin derivatives are characterized. Numerical illustrations of the benefits of the transformation are provided.

Financial Innovation, Values and Volatilities when Markets Are Incomplete

The traditional pricing methodology in finance values derivative securities as redundant assets that have no impact on equilibrium prices and allocations. This paper considers a model with incomplete markets in which the valuation of derivative securities cannot be treated independently from the valuation of the primary securities. The model constitutes a framework for the analysis of the consequences of financial innovation (creation of new contracts or modification of existing contracts). We provide a numerical counterexample to the popular belief that financial innovations that increase the volatilities of traded securities are “bad”. In this example the introduction of an option increases the volatility of the rate of return on the underlying stock, yet the creation of this asset is unanimously supported by investors.

Non-addictive habits: optimal consumption-portfolio policies

Abstract We formulate a model of preferences with non-addictive habits, where consumption is required to be non-negative at all times, but can fall below a “standard of living” index that aggregates past consumption. We study the consumption-portfolio problem taking account of the non-negativity constraint on consumption, and provide a constructive proof for the existence of an optimal policy on a finite time-horizon [0,T]. We show that the consumption constraint binds up to an endogenous stopping time τ ∗ ∈[0,T] , after which it remains slack until T. A decomposition of constrained consumption involving an Asian average-strike capped call-option is demonstrated.