Search

Since 1996, the Central Bank of México issues a put option in order to buy American Dollars as a way of increasing its international reserves. This is an exotic option that gives the right to the Mexican banks to sell this currency to the Central Bank at the price of the day before the date of exercise. The option has a maturity of one month and can be exercised on any day during this period, subject to an additional condition that depends on the average price of the Dollar during the previous 20 days. In this work we study the valuation and the optimal time of exercise of this option under the Binomial and the Black--Scholes Models. The optimal time of exercise is found for the Binomial model and a rule of exercise is proposed for the Black--Scholes Model. Numerical results are included to illustrate the performance of this rule of exercise. [ABSTRACT FROM AUTHOR]

We study whether default options are mispriced in equity values by employing a structural equity valuation model that explicitly takes into account the value of the option to default (or abandon the firm) and uses firm‐specific inputs. We implement our model on the entire cross section of stocks and identify both over‐ and underpriced equities. An investment strategy that buys undervalued stocks and shorts overvalued stocks generates an annual four‐factor alpha of about 11% for U.S. stocks. The model's performance is stronger for stocks with a higher value of the default option, such as distressed or highly volatile stocks. [ABSTRACT FROM AUTHOR]

We investigate the overconfidence theory and inflation-illusion hypothesis of asset mispricing. Both concepts address subjective asset valuation but place the impetus on differing explanations within the standard dividend-growth model. We find that one of the theoretical outcomes of overconfidence-asset turnover-consistently explains mispricing in U.S. housing markets. Further, we find that asset turnover subsumes expected inflation in certain specifications, suggesting that dispersion in investors' beliefs is a better explanation of asset mispricing than the investors' inability to properly discount future cash flows. [ABSTRACT FROM AUTHOR]

This paper is a compendium of results--theoretical and computational--from a series of recent papers developing a new American option valuation technique based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given, as is the analysis needed to solve the inverse problem of determining local (one-factor) volatility from market data. The ideas behind a fast accurate revised simplex method, whose performance is linear in time and space discretizations, are described and the practicalities of fitting the volatility smile are discussed. Numerical results are presented which show the LP valuation technique to be extremely fast--lattice speed with PDE accuracy. American options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We consider the problem of pricing path-dependent contingent claims. Classically, this problem can be cast into the Black-Scholes valuation framework through inclusion of the path-dependent variables into the state space. This leads to solving a degenerate advection-diffusion partial differential equation (PDE). We first establish necessary and sufficient conditions under which degenerate diffusions can be reduced to lower-dimensional nondegenerate diffusions. We apply these results to path-dependent options. Then, we describe a new numerical technique, called forward shooting grid (FSG) method, that efficiently copes with degenerate diffusion PDEs. Finally, we show that the FSG method is unconditionally stable and convergent. The FSG method is the first capable of dealing with the early exercise condition of American options. Several numerical examples are presented and discussed. [ABSTRACT FROM AUTHOR]

Reports on the development of lower and upper bounds on the prices of call and put options in the United States that are written on a dividend-paying asset. Two option price approximations; Modifications of the procedures for American put options; Comparison of several American option pricing methods on the basis of the speed of computation and the accuracy of the results.