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Warrant Pricing: Jump-Diffusion vs. Black-Scholes

Journal of Financial and Quantitative Analysis 1993 28(2), 255
This paper investigates the warrant pricing abilities of dilution-adjusted versions of the Black-Scholes and Jump-Diffusion option pricing models. Because of the typically long lives of warrants, their pricing is hypothesized to benefit from use of the Jump-Diffusion model, which relaxes the Black-Scholes restriction against stock price jumps. Empirical results indicate that while the Black-Scholes model almost uniformly provides more efficient estimates, the Jump-Diffusion model generally provides less biased estimates of market value. Particularly for the valuation of out-of-the-money warrants and warrants on stocks with a history of large and/or frequent jumps, the Jump-Diffusion model may be preferred.

Another look at time-varying risk and return in a long-horizon contrarian strategy

Journal of Financial Economics 1993 33(1), 119-144
This paper reconciles the relative pricing controversy between DeBondt and Thaler (1985, 1987), Chan (1988), and Ball and Kothari (1989). The negative autocorrelation in long-horizon index returns, along with the selection criterion of the contrarian strategy, can explain the positive covariance between time-varying betas and risk premiums. However, test-period beta estimates reflect the reversal of earnings expectations associated with underlying factors. The controversy thus reduces to the debate of Fama and French (1988) and Poterba and Summers (1988) over the source of the temporary price components in the market index. Rational changes in expected returns and cash flows explain most of the cross-sectional variation in returns.

New Evidence on SFAS No. 69 and the Components of the Change in Reserve Value.

The Accounting Review 1993 68(3), 639-656
The purpose of this article is to investigate the information content of the change in the standardized measure (CSM) disclosure reported by oil and gas producers as assessed by market participants. Previous research by Doran et al. (1988) suggests that selected components of the CSM disclosure have a modest influence on share prices. This study reexamines this issue with a more homogeneous sample of oil and gas producers (e.g., excluding Canadian firms), and investigates all ten components of the CSM that firms must currently report. It provides evidence on the usefulness of one of the major supplemental disclosures for oil and gas producers. In particular, it shows that disaggregating the change in reserve value into the required components provides additional information over reporting only the CSM, and that six components provide incremental information relative to the other components and to net income: (1) production; (2) discoveries; (3) purchases of reserves; (4) quantity revisions; (5) price changes; and (6) the change in income taxes. In the early 1980s, the Financial Accounting Standards Board (FASB) and the Securities Exchange Commission (SEC) decided that, although reserve value accounting data would not be reported in the financial statements, supplemental disclosures of reserve values and changes therein (i.e., the CSM disclosure) would be required because such information is not reflected in historical cost financial statements (see FASB 1982; SEC 1982). Thus, this study also contributes to the more general area regarding the incremental information in footnotes relative to information such as net income reported in the financial statements (e.g., see Beaver et al. 1982; Imhoff et al. 1992). Doran et al. (1988) tested for the incremental information content, relative to historical cost earnings, of three reserve value-based measures: (1) the total annual change in reserve value (less reserve purchases and sales), as well as the change in reserve value attributable to (2) discoveries and (3) revisions in price and quantity estimates. They calculated the variables using data filed under Statement of Financial Accounting Standards No. 69 (SFAS No. 69, FASB 1982) for 1982-1984 and found that only the revisions variable provided information on producers and that earnings did not. This study replicates their tests using SFAS No. 69 data over the same period with consistent results. The analyses of Doran et al. are then expanded by investigating the information content of the ten components of the change in reserve value required by SFAS No. 69. The set of information Items currently required are more disaggregated than the set that was required prior to SFAS No. 69. The study results offer new insights and provide the first evidence that gross profits from production are positively associated with returns. In addition, the findings suggest that discoveries and purchases of reserves are negatively associated with returns during the test period. Although this appears to be counterintuitive, it is consistent with analyses of the oil and gas industry by McConnell and Muscarella (1985), Picchi (1985), and Jensen (1986a, 1986b) that the market reacted negatively to oil firms investing in exploration and development (E & D) during this time period. They describe the period as one in which oil prices were declining, and firms were spending too much on E & D, and had excessive levels of reserves. Thus, additions to reserves as measured by CSM components such as discoveries need not be positively associated with returns. In addition, there is some evidence that the tax change component reflects a tax adjustment to the values of the other components. The analysis of the CSM components is replicated using abnormal returns estimated from a market model that includes industry and market indexes. The results show that net income is positively related to abnormal returns, which indicates that earnings do provide information about firm-specific events for producers. The results also indicate that the six CSM components described above are associated with the dual-index returns.

New Evidence on SFAS No. 69 and the Components of the Change in Reserve Value

The Accounting Review 1993 68(3), 639-656
[The purpose of this article is to investigate the information content of the change in the standardized measure (CSM) disclosure reported by oil and gas producers as assessed by market participants. Previous research by Doran et al. (1988) suggests that selected components of the CSM disclosure have a modest influence on share prices. This study reexamines this issue with a more homogeneous sample of oil and gas producers (e.g., excluding Canadian firms), and investigates all ten components of the CSM that firms must currently report. It provides evidence on the usefulness of one of the major supplemental disclosures for oil and gas producers. In particular, it shows that disaggregating the change in reserve value into the required components provides additional information over reporting only the CSM, and that six components provide incremental information relative to the other components and to net income: (1) production; (2) discoveries; (3) purchases of reserves; (4) quantity revisions; (5) price changes; and (6) the change in income taxes. In the early 1980s, the Financial Accounting Standards Board (FASB) and the Securities Exchange Commission (SEC) decided that, although reserve value accounting data would not be reported in the financial statements, supplemental disclosures of reserve values and changes therein (i.e., the CSM disclosure) would be required because such information is not reflected in historical cost financial statements (see FASB 1982; SEC 1982). Thus, this study also contributes to the more general area regarding the incremental information in footnotes relative to information such as net income reported in the financial statements (e.g., see Beaver et al. 1982; Imhoff et al. 1992). Doran et al. (1988) tested for the incremental information content, relative to historical cost earnings, of three reserve value-based measures: (1) the total annual change in reserve value (less reserve purchases and sales), as well as the change in reserve value attributable to (2) discoveries and (3) revisions in price and quantity estimates. They calculated the variables using data filed under Statement of Financial Accounting Standards No. 69 (SFAS No. 69, FASB 1982) for 1982-1984 and found that only the revisions variable provided information on producers and that earnings did not. This study replicates their tests using SFAS No. 69 data over the same period with consistent results. The analyses of Doran et al. are then expanded by investigating the information content of the ten components of the change in reserve value required by SFAS No. 69. The set of information items currently required are more disaggregated than the set that was required prior to SFAS No. 69. The study results offer new insights and provide the first evidence that gross profits from production are positively associated with returns. In addition, the findings suggest that discoveries and purchases of reserves are negatively associated with returns during the test period. Although this appears to be counterintuitive, it is consistent with analyses of the oil and gas industry by McConnell and Muscarella (1985), Picchi (1985), and Jensen (1986a, 1986b) that the market reacted negatively to oil firms investing in exploration and development (E & D) during this time period. They describe the period as one in which oil prices were declining, and firms were spending too much on E & D, and had excessive levels of reserves. Thus, additions to reserves as measured by CSM components such as discoveries need not be positively associated with returns. In addition, there is some evidence that the tax change component reflects a tax adjustment to the values of the other components. The analysis of the CSM components is replicated using abnormal returns estimated from a market model that includes industry and market indexes. The results show that net income is positively related to abnormal returns, which indicates that earnings do provide information about firmspecific events for producers. The results also indicate that the six CSM components described above are associated with the dual-index returns.]

A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

Review of Financial Studies 1993 6(2), 327-343
I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the Black-Scholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original Black-Scholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants

The Changing View of the Standard-of-Living Question in the United States

American Economic Review 1993
The standard-of-living question was initially framed by the long-running debate over the effects of the industrial revolution on the living conditions of ordinary people. Karl Marx and Friedrich Engels posed the question most dramatically arguing that industrialization reduced both the absolute and relative standard of living for workers. This formulation of the question made both the average income and the distribution of income matter in treatments of the standard-of-living question. In principle, a rise in average per capita income could be accompanied by an increase in inequality so that the living standards of workers and their families did not necessarily improve with growth in per capita income. The debate over the trend in the standard of living, especially that of workers, was fierce and ongoing. By the 1920's, the weight of evidence had