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Working Paper

Exercise Price Bias Test and Firm Size Effect in the Black and Scholes Model

페이스북
커버이미지
  • 저자 금정연(琴正淵)
  • 발행일 1989/03/01
  • 시리즈 번호 8908
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요약 In the Black and Scholes model, the standard deviation
(ISD) is constant; there in no bias. But empirical studies find
exercise price bias. We use the empirical finding of the inverse
relationship between the stock price volatility and the stock
prices, and explain the exercise price bias. Also we examine
possible other factors that affect the bias : If the extent of
responsiveness of the change of the stock price volatility to the
change of stock price is different according to the money
position, we can expect the exercise price bias. Also, the
probability of early exercise is examined to examine the exercise
price bias.

If the quoted prices do not reflect the simultaneous traded
prices, the relationship between the exercise price and the ISD
will be more irregular.

From the examination of the firm-size effect on stock
volatility we can find the inverse relationship between WISD and
firm size. Also, the short time to maturity series has a higher
sample average WISD than the long time series.

Contrary to the existing findings, but anticipated from the
explanation on the exercise price bias, the relationship between
the ISD and exercise price is not consistently observed
throughout the sample period. The U-shaped relationship is
observed more often than the inverse relationship or positive
relationship. This finding is most conspicuous for the large
firms. Consistent with the findings in Rubinstein's study, the
early-exercise group shows no significant difference from the
no-early-exercise group.
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