An alternative approach to the valuation of American options and applications

In this paper we examine the structure of American option valuation problems and derive the analytic valuation formulas under general underlying security price processes by an alternative but intuitive method. For alternative diffusion processes, we derive closed-form analytic valuation formulas and analyze the implications of asset price dynamics on the early exercise premiums of American options. In this regard, we introduce useful and interesting diffusion processes into American option-pricing literature, thus providing a wide range of choices of pricing models for various American-type derivative assets. This work offers a useful analytic framework for empirical testing and practical applications such as the valuation of corporate securities and examining the impact of options trading on market micro-structure.     

On the valuation of American call options on stocks with known dividends

Both the Roll and the Geske equations for the valuation of the American call option on a stock with known dividends are incorrectly specified. This note presents the corrected valuation formula, explains the misspecifications and provides a numerical example.     

Valuation of American Futures Options: Theory and Empirical Tests

This paper reviews the theory of futures option pricing and tests the valuation principles on transaction prices from the S&P 500 equity futures option market. The American futures option valuation equations are shown to generate mispricing errors which are systematically related to the degree the option is in-the-money and to the option's time to expiration. The models are also shown to generate abnormal risk-adjusted rates of return after transaction costs. The joint hypothesis that the American futures option pricing models are correctly specified and that the S&P 500 futures option market is efficient is refuted, at least for the sample period January 28, 1983 through December 30, 1983.     

DIVIDENDS, DIVIDEND POLICY AND OPTION VALUATION: A NEW PERSPECTIVE

This paper develops a model which explicitly incorporates the impact of the payment of dividends on the underlying stock into the valuation of both American and European calls and puts. Unlike earlier models, what we call the Dividend Adjustment Merton (DAM) model neither assumes arbitrary continuous dividends nor uses ad hoc methods to adjust for discrete dividend payments. Instead, it assumes the existence of a Miller and Modigliani (1961) valuation neutral dividend policy and adjusts Merton's constant proportional dividend model to incorporate any known schedule of discrete cash dividends of this type. The DAM model produces results which are equal to or superior to those of the separate models now used to value American calls (the Roll-Geske-Whaley model) and American puts (the Geske-Johnson model) on dividend paying stocks. It has the virtue of being internally consistent in that the same model can be used to value both calls and puts. In developing the DAM model, the paper clarifies the role of dividends and dividend policy in determining option values. It also produces significantly tightened boundary conditions for option values.     

Valuation of American partial barrier options

This paper concerns barrier options of American type where the underlying asset price is monitored for barrier hits during a part of the option’s lifetime. Analytic valuation formulas of the American partial barrier options are provided as the finite sum of bivariate normal distribution functions. This approximation method is based on barrier options along with constant early exercise policies. In addition, numerical results are given to show the accuracy of the approximating price. Our explicit formulas provide a very tight lower bound for the option values, and moreover, this method is superior in speed and its simplicity.     

How different GAAPS affect performance of valuation models: Evidence from Asia-based companies

Use of accounting information to assess a firm's value is a very important subject for financial analysts, investors, lenders, policy-makers, and other market participants. Given the current worldwide movement toward adoption of IFRS, understanding how it compares to other GAAPs and affects valuation models is an important matter. This study compares the relative performance of three valuation models based on a sample of all relevant American Depositary Shares (ADRs) from selected Asian countries and a matched sample of US counterparts, using accounting variables reported under International Financial Reporting Standards (IFRS), US generally accepted accounting principles (GAAP), and non-IFRS/US GAAP. Results indicate that there are substantial differences between the three models' explanatory power and that the dominant (most explanatory) valuation model will vary depending on which GAAP (IFRS, US GAAP, and non-IFRS/US GAAP) is used.     

A risk-based approach for pricing American options under a generalized Markov regime-switching model

This paper considers a risk-based approach for pricing an American contingent claim in an incomplete market described by a continuous-time, Markov, regime-switching jump-diffusion model. We formulate the valuation problem as a stochastic differential game and use dynamic programming. Verification theorems for the Hamilton–Jacobi–Bellman–Issacs (HJBI) variational inequalities of the games are used to determine the seller's and buyer's prices and optimal exercise strategies.     

The valuation of American call options and the expected ex-dividend stock price decline

This study focuses on the ex-dividend stock price decline implicit within the valuation of American call options on dividend-paying stocks. The Roll (1977) American call option pricing formula and the observed structure of CBOE call option transaction prices are used to infer the expected ex-dividend stock price decline as a proportion of the amount of the dividend. The relative decline is shown to be not meaningfully different from one, confirming some recent evidence from studies which examined stock prices in the days surrounding ex-dividend.     

Tight bounds on American option prices

In contrast to the constant exercise boundary assumed by Broadie and Detemple (1996) [Broadie, M., Detemple, J., 1996. American option valuation: New bounds, approximations, and comparison of existing methods. Review of Financial Studies 9, 1211–1250], we use an exponential function to approximate the early exercise boundary. Then, we obtain lower bounds for American option prices and the optimal exercise boundary which improve the bounds of Broadie and Detemple (1996). With the tight lower bound for the optimal exercise boundary, we further derive a tight upper bound for the American option price using the early exercise premium integral of Kim (1990) [Kim, I.J., 1990. The analytic valuation of American options. Review of Financial Studies 3, 547–572]. The numerical results show that our lower and upper bounds are very tight and can improve the pricing errors of the lower bound and upper bound of Broadie and Detemple (1996) by 83.0% and 87.5%, respectively. The tightness of our upper bounds is comparable to some best accurate/efficient methods in the literature for pricing American options. Moreover, the results also indicate that the hedge ratios (deltas and gammas) of our bounds are close to the accurate values of American options.     

The use of earnings and cash flows in investment decisions in the U.S. and Mexico: Experimental evidence

In this study, we investigate which of two accounting performance measures, earnings or cash flows, is used more in valuation decisions by non-professional investors in the United States and in Mexico. This issue is relevant for the Mexican Stock Market (Bolsa Mexicana de Valores) because the Bolsa's growth has stagnated compared with markets of other Latin American countries. Results of the study reveal that the majority of participants in the U.S. rely on earnings while the majority of participants in Mexico rely on cash flows. Results also suggest that the users’ predisposition can be dysfunctional to the extent that they do not consider using the other accounting measure, even when doing so made it easier to arrive at the correct valuation result (i.e. they did not choose to use the more persistent and therefore easier to forecast accounting measure). However, results are mixed for participants using earnings, since we document a higher chance of forecasting errors for participants in both countries when using earnings rather than cash flows in their calculations for the failure of these participants to adjust earnings for depreciation.This study extends the existing international literature by documenting a country-specific predisposition to use cash flows or earnings as a valuation tool by non-professional investors. Moreover, this study also shows that this predisposition can be dysfunctional, leading participants to make incorrect valuation decisions as a result of their failure to consider the differential persistence of the two accounting measures presented in the experiment.     

Valuation of American options in the presence of event risk

This paper studies the valuation of American options in the presence of external/non-hedgeable event risk. When the event occurs, the American option is terminated and a rebate is paid instead of the promised pay-off profile. Consequently, the presence of event risk influences the exercise strategy of the option holder. For the financial market in a diffusion setting, the probabilistic structure in terms of equivalent martingale measures is briefly analysed. Then, for a given equivalent martingale measure the optimal stopping problem of the American option is solved. As a main result, no-arbitrage bounds for American option values in the presence of event risk are derived, as well as hedging strategies corresponding to the no-arbitrage bounds.Received: May 2004, Mathematics Subject Classification: 90C47, 60H30, 60G40JEL Classification: G13, D52, D81The author thanks John Gould and Ross Maller for useful discussions. The author is also grateful to a referee for helpful comments. This research was partially supported by University of Western Australia Research Grant RA/1/485.     

The practice of investment valuation in emerging markets: Evidence from Argentina

This paper discusses the challenges of applying traditional valuation techniques to emerging markets, and reports on how CFOs, financial advisors and private equity funds meet those challenges in Argentina, a major Latin American emerging economy. On many fronts, our findings show that there is substantial alignment with U.S. valuation practices. We find that: (a) discounted cashflow techniques like NPV, IRR and payback are very popular among corporations and financial advisors; (b) the CAPM is the most popular asset pricing model, yet it is frequently modified to account for country-specific risk; (c) capital budgeting analyses are performed in U.S. dollars by non-dollar companies; (d) financial advisors tend to apply U.S. betas to the emerging market, yet they rarely adjust betas for cross-border asymmetries; and (e) corporations tend to disregard the effects of small size and illiquidity. We provide tentative explanations for our findings.     

Markov-switching in target stocks during takeover bids

This paper examines shifts in the market betas and the conditional volatility of stock prices of takeover targets. Using daily stock prices of five European and American targets, we find that adequately specified Markov-switching GARCH models are capable of detecting statistically significant regime-switches in all takeover deal-types (in cash bids, pure share-exchange bids, mixed bids). In particular, conditional volatility regime-switches are found to be most clear-cut for cash bids. Our econometric findings have implications for a broad range of financial applications such as the valuation of target stock options.     

An investigation of SEC “Speech GAAP”

This study investigates the financial reporting regulation effects of the Securities and Exchange Commission (SEC) staff comments made during the American Institute of Certified Public Accountants (AICPA) Annual Current SEC & Public Company Oversight Board (PCAOB) Developments Conference in Washington, D.C. (SEC Conference). At this conference, the SEC staff communicates its preferences about areas where it believes companies are misapplying GAAP (Generally Accepted Accounting Principles). We call this communication SEC Speech GAAP. One outcome of the SEC Conference may be that companies re-evaluate their previous financial reporting by restating their financial statements. We find, first, that firms with restatement issues similar to those covered at the SEC Conference experience a decrease in the association between earnings and future cash flows after the restatement. Second, we find little market reaction to the disclosure of restatements related to SEC Conference issues, but the disclosure of non-conference related restatement issues has a significantly negative affect on investors’ valuation decisions. Our findings suggest that SEC Speech GAAP is associated with financial statements that are less informative to investors and investors find the valuation consequences of restatements prompted by SEC Speech GAAP to be less important than the valuation consequences for restatements prompted for other reasons.     

A closed-form solution to American options under general diffusion processes

This paper investigates American option pricing under general diffusion processes. Specifically, the underlying asset price is assumed to follow a diffusion process in which both the dividend yield and volatility are functions of time and the underlying asset price. Using the generalized homotopy analysis method, the determination of the early exercise boundary is separated from the valuation procedure of American options. Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. In addition, the corresponding optimal early exercise boundary and the Greeks are obtained in closed-form solutions. A nonlinear sequence transformation, the Padé technique, is used to effectively accelerate the convergence of the partial sums of the infinite series. As the homotopy constructed in this paper is based on a generalized deformation with a shape parameter and kernel function, the error of the homotopic approximation could be reduced further for a fixed order. Numerical examples demonstrate the validity, effectiveness, and flexibility of the proposed approach.     

American Parisian options

In this article, we describe the various sorts of American Parisian options and propose valuation formulae. Although there is no closed-form valuation for these products in the non-perpetual case, we have been able to reformulate their price as a function of the exercise frontier. In the perpetual case, closed-form solutions or approximations are obtained by relying on excursion theory. We derive the Laplace transform of the first instant Brownian motion reaches a positive level or, without interruption, spends a given amount of time below zero. We perform a detailed comparison of perpetual standard, barrier and Parisian options.     

Commodity Spread Option with Cointegration

We derive the valuation formula of a European call option on the spread of two cointegrated commodity futures prices, based on the Gibson–Schwartz with cointegration (GSC) model. We also analyze the American commodity spread option including the early exercise premium representation and an analytical approximation valuation formulae with cointegration. In the numerical analysis, we compare the spread option values calculated by the GSC model and the Gibson–Schwartz (GS) model that ignores cointegration. Consistent with the intuition that the cointegration prevents the prices from diverging, the GSC model prices the commodity spread option lower than the GS model which have longer maturity of more than 6 years. In other words, the GS model may overprice the commodity spread options for those with longer maturity without taking account of cointegration. Thus, incorporating cointegration is important for valuation and hedging of long-term commodity spread options such as large scale oil refining plant developments.     

An exact and explicit solution for the valuation of American put options

In this paper, an exact and explicit solution of the well-known Black–Scholes equation for the valuation of American put options is presented for the first time. To the best of the author's knowledge, a closed-form analytical formula has never been found for the valuation of American options of finite maturity, although there have been quite a few approximate solutions and numerical approaches proposed. The closed-form exact solution presented here is written in the form of a Taylor's series expansion, which contains infinitely many terms. However, only about 30 terms are actually needed to generate a convergent numerical solution if the solution of the corresponding European option is taken as the initial guess of the solution series. The optimal exercise boundary, which is the main difficulty of the problem, is found as an explicit function of the risk-free interest rate, the volatility and the time to expiration. A key feature of our solution procedure, which is based on the homotopy-analysis method, is the optimal exercise boundary being elegantly and temporarily removed in the solution process of each order, and, consequently, the solution of a linear problem can be analytically worked out at each order, resulting in a completely analytical and exact series-expansion solution for the optimal exercise boundary and the option price of American put options.     

A novel approach to the valuation of American options

We introduce a practical numerical method to the valuation of American options. The new feature is the exact reformulation of the problems over very small regions. Numerical examples and analyses show that our algorithm leads to very fast and highly accurate results.     

The Determinants of Stock Price Exposure: Financial Engineering and the Gold Mining Industry

This paper studies the exposure of North American gold mining firms to changes in the price of gold. The average mining stock moves 2 percent for each 1 percent change in gold prices, but exposures vary considerably over time and across firms. As predicted by valuation models, gold firm exposures are significantly negatively related to the firm's hedging and diversification activities and to gold prices and gold return volatility, and are positively related to firm leverage. Simple discounted cash flow models produce useful exposure predictions but they systematically overestimate exposures, possibly due to their failure to reflect managerial flexibility.