On Valuing American Call Options with the Black-Scholes European Formula

Empirical papers on option pricing have uncovered systematic differences between market prices and values produced by the Black-Scholes European formula. Such “biases” have been found related to the exercise price, the time to maturity, and the variance. We argue here that the American option variant of the Black-Scholes formula has the potential to explain the first two biases and may partly explain the third. It can also be used to understand the empirical finding that the striking price bias reverses itself in different sample periods. The expected form of the striking price bias is explained in detail and is shown to be closely related to past empirical findings.     

Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models

To value mortgage-backed securities and options on fixed-income securities, it is necessary to make assumptions regarding the term structure of interest rates. We assume that the multi-factor fixed parameter term structure model accurately represents the actual term structure of interest rates, and that the values of mortgage-backed securities and discount bond options derived from such a term structure model are correct. Differences in the prices of interest rate derivative securities based on single-factor term structure models are therefore due to pricing bias resulting from the term structure model. The price biases that result from the use of single-factor models are compared and attributed to differences in the underlying models and implications for the selection of alternative term structure models are considered.     

An Empirical Comparison of Forward-Rate and Spot-Rate Models for Valuing Interest-Rate Options

Our main goal is to investigate the question of which interest-rate options valuation models are better suited to support the management of interest-rate risk. We use the German market to test seven spot-rate and forward-rate models with one and two factors for interest-rate warrants for the period from 1990 to 1993. We identify a one-factor forward-rate model and two spot-rate models with two factors that are not significantly outperformed by any of the other four models. Further rankings are possible if additional criteria are applied.     

Early Exercise of Put Options on Stocks

U.S. exchange‐traded stock options are exercisable before expiration. While put options should frequently be exercised early to earn interest, they are not. In this paper, we derive an early exercise decision rule and then examine actual exercise behavior during the period January 1996 through September 2008. We find that more than 3.96 million puts that should have been exercised early remain unexercised, representing over 3.7% of all outstanding puts. We also find that failure to exercise cost put option holders $1.9 billion in forgone interest income and that this interest is systematically captured by market makers and proprietary firms.     

Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data

This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects might have a better fit with actual prices. We perform dominant tests and calculate average percent mean squared errors of model prices. Our findings indicate that the Black-Scholes model outperforms the GARCH models. An implication of this result is that participants in the currency call options market do not seem to price volatility clusters in the underlying process.     

Valuing and Pricing Retail Leases with Renewal and Overage Options

We consider retail leases with landlord overages options, with tenant renewal options, with both and with neither. We illustrate how the ratio of initial expected sales to the sales threshold can be manipulated to equate the value of the landlord overage options to that of the tenant renewal option at the same initial rent. Not only are the values equal, but the cumulative distributions of potential IRRs on the two leases are nearly identical, suggesting that these leases are equally attractive to risk-averse investors and thus that the same risky discount rate can be used in valuing the leases. In contrast, the appropriate risky discount rate for the overage lease is calculated to be 75–160 basis points greater than that for the renewal lease.     

Computing a Multivariate Normal Integral for Valuing Compound Real Options

We extend the Geske (1979) model to a multivariate normal integral for the valuation of a compound real option. We compared the computing speeds and errors of three numerical integration methods, namely, Drezner's improved Gauss quadrature method, Monte Carlo method and Lattice method, together with appropriate critical value finding methods. It is found that secant method for finding critical values combined with Lattice method and run by Fortran took merely one second, Monte Carlo method 120 seconds. It is also found that the real option decreases with interest rate, not necessarily positively correlated with volatility , a result different from that anticipated under financial option theory. This is mainly because the underlying of real option is a non-traded asset, which brings dividend-like yield into the formula of compound real options. Dividend-like yield rises with the multiplication of correlation coefficient and . High indicates the poor diversification advantage of the new investment project in relation to the existing market portfolio, and the value of real call option decreases with . Conversely, when is low, the proposed project provides better diversification advantage and the real call option rises with . Irrespective of the value of , when interest rate increases, the value of real call option drops, especially when is high, the value of the project is dominated by interest rate.     

The Joint Cross Section of Stocks and Options

Stocks with large increases in call (put) implied volatilities over the previous month tend to have high (low) future returns. Sorting stocks ranked into decile portfolios by past call implied volatilities produces spreads in average returns of approximately 1% per month, and the return differences persist up to six months. The cross section of stock returns also predicts option implied volatilities, with stocks with high past returns tending to have call and put option contracts that exhibit increases in implied volatility over the next month, but with decreasing realized volatility. These predictability patterns are consistent with rational models of informed trading.     

The Impact of Dividends, Debt and Investment on Valuation Models

The reliability of a basic earnings and equity model of value is tested using 8,287 cases drawn from UK industrial and commercial firms reporting during 1987–1995. A respecification of this model is used to investigate the value relevance of dividends, capital structure and capital expenditure. Both the dividend and capital expenditure signals appear to be significant and the impact of the former is surprisingly strong. There is no convincing evidence that equity value is affected by the level of debt. Further investigation of dividends confirms that they are less influential in large firms or in firms with high return on equity.     

Empirical Tests of Boundary Conditions for Toronto Stock Exchange Options

Using option and stock transaction data for the period 1978–1979, three issues were investigated: first, the conformance of observed prices to various boundary conditions; second, the evolution of the market over time, as the volume of trading and the number of listed options increased; and third, to test the efficiency of the market. It was found that violations did occur. Using a trading rule based on the signal of observed violations, the results suggest that even after transaction costs the market was inefficient over the sample period.     

Options on Leveraged Equity: Theory and Empirical Tests

We develop an option pricing model for calls and puts written on leveraged equity in an economy with corporate taxes and bankruptcy costs. The model explains implied Black-Scholes volatility biases by relating them to the firm's structural characteristics such as leverage and debt covenants. We test the model by comparing predicted pricing biases with biases observed in a large cross-section of firms with liquid exchange traded option contracts. Our empirical study detects leverage related pricing biases. The magnitudes of these biases correspond to those predicted by our model. We also find significant pricing biases for firms financed primarily by short-term debt. This supports our model because short-term debt introduces net-worth hurdles similar to net-worth covenants.     

The Information Content of Insider Call Options Trading

We examine the information content of two forms of insider trading, insider buy-, and sell-call transactions. We find that the information carried by stand-alone call purchases has only a short-term impact on stock prices, but over a longer term, call purchases accompanied by stock purchases have a positive impact. Call purchases accompanied by stock sales signal negative information about the firm, suggesting that some insiders use complicated trading strategies to manipulate the market. Insider sell-call transactions are followed by negative returns, indicating these transactions are driven by negative information about the firm.     

Share Repurchases,Dividends and Executive Options: the Effect of Dividend Protection

We study the determinants of share repurchases and dividends in Finland. We find that higher foreign ownership serves as a determinant of share repurchases and suggest that this is explained by the different tax treatment of foreign and domestic investors. Further, we also find support for the signalling and agency cost hypotheses for cash distributions. The fact that 41% of the option programmes in our sample are dividend protected allows us to test more directly the ‘substitution/managerial wealth’ hypothesis for the choice of distribution method. When options are dividend protected, the relationship between dividend distributions and the scope of the options programme turns to a significantly positive one instead of the negative one documented in US data.     

Semi-Parametric Specification Tests for Discrete Probability Models

Loss functions play an important role in analyzing insurance portfolios. A fundamental issue in the study of loss functions involves the selection of probability models for claim frequencies. In this article, we propose a semi‐parametric approach based on the generalized method of moments (GMM) to solve the specification problems concerning claim frequency distributions. The GMM‐based testing procedure provides a general framework that encompasses many specification problems of interest in actuarial applications. As an alternative approach to the Pearson χ² and other goodness‐of‐fit tests, it is easy to implement and should be of practical use in applications involving selecting and validating probability models with complex characteristics.     

Efficiency Tests of the Foreign Currency Options Market

Based on a new options transactions data base from the Philadelphia Stock Exchange Foreign Currency Options Market, this paper examines the importance of the effect of nonsynchronous prices and transaction costs on the usual option market efficiency tests. The tests conducted are based on the transaction cost adjusted early exercise and put-call parity pricing boundaries applicable to the American foreign currency options market. The test results show that the put-call parity boundary tests are sensitive to both nonsynchronous prices and transaction costs. The early exercise boundary tests are sensitive to transaction costs but are not very sensitive to simultaneity of the option price and the underlying spot price. Under the no-transaction costs scenario, a large number of early exercise boundary violations is found even when simultaneous spot and option prices are used. These violations disappear when actual transaction costs are taken into account.     

Portfolio Construction for Tests of Asset Pricing Models

Portfolios are commonly used in finance literature to study asset‐pricing models. In business practice portfolios are used to detect abnormal performance in certain asset groups or to construct reference assets. However, analyses on practical issues related to portfolio construction are surprisingly few. This paper presents and discusses issues related to portfolio return calculation from theoretical and practical perspectives. Special attention is given both to smaller and emerging stock markets. These stock markets often share common features like low liquidity, multiple stock series, and changes in foreign ownership restrictions that greatly affect portfolio construction.