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11
When are real options exercised? An empirical study of mine closings
, 1999
"... In this paper, we study a wellknown real option: the opening and closing of mines. Using a new database that tracks the annual opening and closing decisions of 285 developed North American gold mines in the period 19881997, we confirm many of the predictions from real options models. As predicted, ..."
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In this paper, we study a wellknown real option: the opening and closing of mines. Using a new database that tracks the annual opening and closing decisions of 285 developed North American gold mines in the period 19881997, we confirm many of the predictions from real options models. As predicted, the empirical results demonstrate that the probability that a mine is open is related to marketwide factors (including the level and volatility of the gold price and the interest rate) as well as to minespecific factors (including the mine's fixed costs, variable costs, and reserves.) These results are both statistically significant and economically material. There is strong evidence of hysteresis, which would result from nonzero opening and closing costs. Together, the data provide strong support for the real options model as a useful model to describe and predict a mine's opening and shutting decisions. In addition, we find that the decision whether to shut a mine is related to firmspecific managerial factors not normally considered within a strict real options model, most notably the profitability of other mines in the firm's portfolio and of the firm's other businesses. These relationships do not seem to be based on geographic synergies and we suspect they are an indication of capital allocation processes within these firms.
Professor Bronzin’s Option Pricing Models: Contents, Contribution and Background”, chapter 11 in Geoffrey Poitras (ed.) (2006), Pioneers of Financial Economics (vol.1). NOTES Alternative terminology is also used, e.g., Poitras (2000) refers to ‘pure deriv
, 2006
"... This paper originates in an email sent by the second author wondering whether the first author knew about Bronzin’s booklet on option pricing, dating back almost a century and containing formulas which appear rather similar to those developed by BlackScholes. The scepticism of the first author qui ..."
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This paper originates in an email sent by the second author wondering whether the first author knew about Bronzin’s booklet on option pricing, dating back almost a century and containing formulas which appear rather similar to those developed by BlackScholes. The scepticism of the first author quickly disappeared after reading Bronzin’s manuscript. While the second author continued to work on the history and social use of derivatives, we also had the plan to make the content of Bronzin’s booklet accessible to a wider audience. The purpose of this paper is to discuss the major elements of Bronzin’s theory and to put it in perspective with modern option pricing models. The content of this paper was first presented in an lecture de
Black, Merton and Scholes: Their work and its consequences
, 1997
"... this article, we take stock of markets for financial derivatives, and the work of Black, Merton and Scholes. ..."
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this article, we take stock of markets for financial derivatives, and the work of Black, Merton and Scholes.
Performativity in Financial Economics
"... ABSTRACT This paper describes and analyses the history of the fundamental equation of modern financial economics: the BlackScholes (or BlackScholesMerton) option pricing equation. In that history, several themes of potentially general importance are revealed. First, the key mathematical work was ..."
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ABSTRACT This paper describes and analyses the history of the fundamental equation of modern financial economics: the BlackScholes (or BlackScholesMerton) option pricing equation. In that history, several themes of potentially general importance are revealed. First, the key mathematical work was not rulefollowing but bricolage, creative tinkering. Second, it was, however, bricolage guided by the goal of finding a solution to the problem of option pricing analogous to existing exemplary solutions, notably the Capital Asset Pricing Model, which had successfully been applied to stock prices. Third, the central strands of work on option pricing, although all recognizably ‘orthodox ’ economics, were not unitary. There was significant theoretical disagreement amongst the pioneers of option pricing theory; this disagreement, paradoxically, turns out to be a strength of the theory. Fourth, option pricing theory has been performative. Rather than simply describing a preexisting empirical state of affairs, it altered the world, in general in a way that made itself more true.
Mergers and acquisitions, Black–Scholes formula, success probability, fallback
, 2009
"... When a cash merger is announced but not completed, there are two main sources of uncertainty related to the target company: the probability of success and the price conditional on the deal failing. We propose an arbitragefree option pricing formula that focuses on these sources of uncertainty. We t ..."
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When a cash merger is announced but not completed, there are two main sources of uncertainty related to the target company: the probability of success and the price conditional on the deal failing. We propose an arbitragefree option pricing formula that focuses on these sources of uncertainty. We test our formula in a study of all cash mergers between 1996 and 2008 which have sufficiently liquid options traded on the target company. The estimated success probability is a good predictor of the deal outcome. Our option formula for cash mergers does significantly better than the Black– Scholes formula and produces a volatility smile close to the one observed in practice. In particular, we provide an explanation for the kink in the volatility smile and show that the kink increases with the probability of deal success.
VALUATION OF WARRANTS WITH IMPLICATIONS TO THE VALUATION OF EMPLOYEE STOCK OPTIONS
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OPTIONS: PRICING FORMULAE FOR FIRMS WITH MULTIPLE WARRANTS/EXECUTIVE OPTIONS
, 2002
"... The textbook treatment for the valuation of warrants takes as a state variable the value of the firm and shows that the value of a warrant is equal to the value of a call option on the equity of the firm multiplied by a dilution factor. This approach however applies only for the not so realistic cas ..."
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The textbook treatment for the valuation of warrants takes as a state variable the value of the firm and shows that the value of a warrant is equal to the value of a call option on the equity of the firm multiplied by a dilution factor. This approach however applies only for the not so realistic case where the firm issues only a single warrant. By a single warrant we mean n warrants with a single exercise price and time to maturity. What happens however in the “real world ” where corporations issue multiple warrants and executive stock options? What happens for example when firms issue warrants of different exercise prices, different maturities and different dilution factors? Valuing each type of warrants independently of the others is clearly inappropriate and will result in mispricing. In this paper we derive distributionfree (and distributionspecific) formulae for firms that issue warrants with different maturities, different strike prices, and different dilution factors and for firms that issue warrants of the same maturity but different strike prices (and different dilution factors). The distinction we make between warrants and executive stock options is simply a matter of whether the contract is traded or not. We use the term warrant to cover both cases.