Abstract In this article we establish cautiousness as a new downside risk aversion measure, using a portfolio problem with a risk-free bond, a stock, and an option. We show that, an investor has higher cautiousness (i) if and only if she is always more likely to buy the option; and (ii) if and only if she always demands more options per share. As an option’s payoff is a convex function, increasing positions in the option increases the convexity of a portfolio, which leads to an increase in skewness. Thus the results in this article establish the link between cautiousness and skewness preference.

Abstract An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownian motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownian motion for the forward price of the underlying asset, so that the Black–Scholes formula correctly prices options on the asset. In contrast, declining elasticity implies that the forward price process is no longer a Brownian motion: it has higher volatility and exhibits autocorrelation. In this case, the Black–Scholes formula underprices all options.

In this article, we suggest an efficient method of approximating a general, multivariate log-normal distribution by a multivariate binomial process. There are two important features of such multivariate distributions. First, the state variables may have volatilities that change over time. Second, the two or more relevant state variables involved may covary with each other in a specified manner, with a time-varying covariance structure. We discuss the asymptotic properties of the resulting processes and show how the methodology can be used to value a complex, multiple exercisable option whose payoff depends on the prices of two assets. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

We value American options on bonds using a generalization of the Geske–Johnson (Geske, R., Johnson, H., 1984. Journal of Finance 39, 1151–1542) (GJ) technique. The method requires the valuation of European options, and options with multiple exercise dates. It is shown that a risk-neutral valuation relationship (RNVR) along the lines of Black–Scholes (Black, F., Scholes, M., 1973. Journal of Political Economy 81, 637–659) model holds for options exercisable on multiple dates, even under stochastic interest rates, when the price of the underlying asset is lognormally distributed. The proposed computational procedure uses the maximized value of these options, where the maximization is over all possible exercise dates. The value of the American option is then computed by Richardson extrapolation. The volatility of the underlying default-free bond is modeled using a two-factor model, with a short-term and a long-term interest rate factor. We report the results of simulations of American option values using our method and show how they vary with the key parameter inputs, such as the maturity of the bond, its volatility, and the option strike price.

The Geske–Johnson approach provides an efficient and intuitively appealing technique for the valuation and hedging of American-style contingent claims. Here, we generalize their approach to a stochastic interest rate economy. The method is implemented using options exercisable on one of a finite number of dates. We illustrate how the value of an American-style option increases with interest rate volatility. The magnitude of this effect depends on the extent to which the option is in the money, the volatilities of the underlying asset and the interest rates, as well as the correlation between them.