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This paper provides an in-depth analysis of the properties of popular tests for the existence and the sign of the market price of volatility risk. These tests are frequently based on the fact that for some option pricing models under continuous hedging the sign of the market price of volatility risk coincides with the sign of the mean hedging error. Empirically, however, these tests suffer from both discretization error and model mis-specification. We show that these two problems may cause the test to be either no longer able to detect additional priced risk factors or to be unable to identify the sign of their market prices of risk correctly. Our analysis is performed for the model of Black and Scholes (1973) (BS) and the stochastic volatility (SV) model of Heston (1993). In the model of BS, the expected hedging error for a discrete hedge is positive, leading to the wrong conclusion that the stock is not the only priced risk factor. In the model of Heston, the expected hedging error for a hedge in discrete time is positive when the true market price of volatility risk is zero, leading to the wrong conclusion that the market price of volatility risk is positive. If we further introduce model mis-specification by using the BS delta in a Heston world we find that the mean hedging error also depends on the slope of the implied volatility curve and on the equity risk premium. Under parameter scenarios which are similar to those reported in many empirical studies the test statistics tend to be biased upwards. The test often does not detect negative volatility risk premia, or it signals a positive risk premium when it is truly zero. The properties of this test furthermore strongly depend on the location of current volatility relative to its long-term mean, and on the degree of moneyness of the option. As a consequence tests reported in the literature may suffer from the problem that in a time-series framework the researcher cannot draw the hedging errors from the same distribution repeatedly. This implies that there is no guarantee that the empirically computed t-statistic has the assumed distribution. JEL: G12, G13 Keywords: Stochastic Volatility, Volatility Risk Premium, Discretization Error, Model Error
Real options theory applies techniques known from finance theory to the valuation of capital investments. The present paper investigates further into this analogy, considering the case of a portfolio of real options. An implementation of real option models in practice will mostly be concerned with a portfolio of real options, so the analysis of portfolio aspects is of both academic and practical interest. Is a portfolio of real options special? In order to shed some light on this question, the present paper will outline the relevant features of a portfolio of real options. It will show that the analogy to financial options remains great if compound option models are applied. As a result, a portfolio of real options, and therefore the firm as such, generally is to be understood as one single compound, real option.
Over-allotment arrangements are nowadays part of almost any initial public offering. The underwriting banks borrow stocks from the previous shareholders to issue more than the initially announced number of shares. This is combined with the option to cover this short position at the issue price. We present empirical evidence on the value of these arrangements to the underwriters of initial public offerings on the Neuer Markt. The over-allotment arrangement is regarded as a portfolio of a long call option and a short position in a forward contract on the stock, which is different from other approaches presented in the literature.
Given the economically substantial values for these option- like claims we try to identify benefits to previous shareholders or new investors when the company is using this instrument in the process of going public. Although we carefully control for potential endogeneity problems, we find virtually no evidence for a reduction in underpricing for firms using over-allotment arrangements. Furthermore, we do not find evidence for more pronounced price stabilization activities or better aftermarket performance for firms granting an over-allotment arrangement to the underwriting banks.
EFM Classification: 230, 410
Over-allotment arrangements are nowadays part of almost any initial public offering. The underwriting banks borrow stocks from the previous shareholders to issue more than the initially announced number of shares. This is combined with the option to cover this short position at the issue price. We present empirical evidence on the value of these arrangements to the underwriters of initial public offerings on the Neuer Markt. The over-allotment arrangement is regarded as a portfolio of a long call option and a short position in a forward contract on the stock, which is different from other approaches presented in the literature.
Given the economically substantial values for these option-like claims we try to identify benefits to previous shareholders or new investors when the company is using this instrument in the process of going public. Although we carefully control for potential endogeneity problems, we find virtually no evidence for a reduction in underpricing for firms using over-allotment arrangements. Furthermore, we do not find evidence for more pronounced price stabilization activities or better aftermarket performance for firms granting an over-allotment arrangement to the underwriting banks.
Over-allotment arrangements are nowadays part of almost any initial public offering. The underwriting banks borrow stocks from the previous shareholders to issue more than the initially announced number of shares. This is combined with the option to cover this short position at the issue price. We present empirical evidence on the value of these arrangements to the underwriters of initial public offerings on the Neuer Markt. The over-allotment arrangement is regarded as a portfolio of a long call option and a short position in a forward contract on the stock, which is different from other approaches presented in the literature. Given the economically substantial values for these option-like claims we try to identify benefits to previous shareholders or new investors when the company is using this instrument in the process of going public. Although we carefully control for potential endogeneity problems, we find virtually no evidence for a reduction in underpricing for firms using over-allotment arrangements. Furthermore, we do not find evidence for more pronounced price stabilization activities or better aftermarket performance for firms granting an over-allotment arrangement to the underwriting banks.
In der heutigen Theorie der Optionsbewertung wird davon ausgegangen, daß die Markterwartungen genau berechenbar sind. Die Unsicherheit besteht lediglich darin, welcher Aktienkurs sich letztlich realisiert, die Eintrittswahrscheinlichkeiten sind bekannt. Dabei treten jedoch erhebliche Probleme auf, denn theoretisch erwartete Preise entsprechen oft nicht den am Markt beobachteten. Ziel dieser Arbeit ist es, zu untersuchen, ob auch dann eine Optionsbewertung möglich ist, wenn die Unsicherheit nicht nur auf die Stochastik reduziert wird, sondern wenn zusätzlich angenommen wird, daß Marktteilnehmer nur unscharfes Wissen über künftige Preisentwicklungen haben. Hierbei dient die Fuzzy Set Theorie zur Modellierung der nur größenordnungsmäßig bekannten künftigen Aktienkurse. Es wird in dieser Arbeit zwischen der Optionspreistheorie und der Fuzzy Set Theorie eine Verbindung geschaffen, die es zukünftig erlauben wird, die Unsicherheit im Markt besser zu modellieren, als dies mit heute dominierenden Methoden der Optionsbewertung möglich ist.
This study contributes to the valuation of employee stock options (ESO) in two ways: First, a new pricing model is presented, admitting a major part of calculations to be solved in closed form. Designed with a focus on good replication of empirics, the model fits with publicly observable exercise characteristics better than earlier models. In particular, it is able to account for the correlation of the time of exercise and the stock price at exercise, suspected of being crucial for the option value. The impact of correlation is weak, however, whereas cancellations play a central role. The second contribution of this paper is an examination to what extent the ESO pricing method of SFAS 123 is subject to discretion of the accountant. Given my model were true, the SFAS price would be a good proxy. Yet, outside shareholders usually cannot observe one of the SFAS input parameters. On behalf of an example I show that there is wide latitude left to the accountant.
This study contributes to the valuation of employee stock options (ESO) in two ways: First, a new pricing model is presented, admitting a major part of calculations to be solved in closed form. Designed with a focus on good replication of empirics, the model fits with publicly observable exercise characteristics better than earlier models. In particular, it is able to account for the correlation of the time of exercise and the stock price at exercise, suspected of being crucial for the option value. The impact of correlation is weak, however, whereas cancellations play a central role. The second contribution of this paper is an examination to what extent the ESO pricing method of SFAS 123 is subject to discretion of the accountant. Given my model were true, the SFAS price would be a good proxy. Yet, outside shareholders usually cannot observe one of the SFAS input parameters. On behalf of an example I show that there is wide latitude left to the accountant.