(2.) As firms usually grant at-the-money options
, the grant value is based on at-the-money option
Table 1 lists estimation results selecting at-the-money option
price data and out-of-the-money option price data within the sample.
The strikes of the call-on-call options are set equal to 0.5, 1.0, 1.5, 2.0, and 2.5 times the one-month at-the-money option
(21) They determined that 18.9% of unscheduled at-the-money option
grants to top executives between 1996 and 2005 were backdated or otherwise manipulated.
Next, assuming that the volatility smile can be approximated by a piecewise linear function (see Dumas et al., 1994), we compute the implied volatility for an at-the-money option
by linearly interpolating between the implied volatilities of the in-the-money and out-of-money options.
exercise price of an at-the-money option
should presumably be based on
Because of accounting treatment differences between in-the-money and at-the-money option
grants, backdating resulted in materially understated employee compensation expenses and overstated operating income and company performance.
Suppose an at-the-money option
grant in our sample has been backdated by twenty business days.
Instead, Bates (1996) approximates the relation between the BS IV and expected variance until expiry with a Taylor series expansion of the BS price for an at-the-money option
. That is, for at-the-money options
, the BS formula for futures reduces to
By making grants before the release of good news, the manager effectively awards himself an in-the-money option, which is more valuable than the at-the-money option
that he appears to grant himself.
Lassek explained terms such as margin call, at-the-money option
and strike price during the seminar.
Louis' monthly Monetary Trends, said, "Using the trading prices of options on the S&P 100, the CBOE estimates the implied volatility corresponding to a hypothetical at-the-money option
with one month to expiration.