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To: Lizzie Tudor who wrote (64152)6/1/2003 2:14:06 PM
From: GVTucker  Read Replies (1) | Respond to of 77400
 
"Risk premium" is not part of the Black Scholes equation.

Volatility in this case means just that--volatility. Most people that use Black Scholes make the assumption that the recent volatility will be roughly equal to future volatility. Sometimes that is valid, sometimes it isn't.

But that has nothing to do with risk premium, which is related to expected return.



To: Lizzie Tudor who wrote (64152)6/6/2003 8:17:20 AM
From: rkral  Read Replies (1) | Respond to of 77400
 
OT .. re "That means that I equate risk premium to be almost entirely volitility."
Gee Lizzie, that's why I asked "Are you maybe referring to volatility?" .. in my opening post to you. Why did you first provide irrelevant links?

When the employee "buys" an ATM call option valued with Black-Scholes option valuation model ("Model"), the employee is accepting three risks ...
1) Probability Risk -- The stock price may remain at, or below, the exercise price,
2) Volatility Risk -- The price volatility may be less that assumed for the Model. If so, the employee paid too much for the option,
3) Interest-rate Risk -- The risk-free interest rate may be less than assumed for the Model. If so, the employee overpaid.

Now to call the impact of either volatility or interest-rate risk on the option value "risk premium" .. is a misuse of the term IMHO. Traditionally, *risk premium* is the additional return a rational investor expects for assuming additional risk. IOW, the expected future value is discounted by the risk. The greater the perceived risk, the greater the discount, and *the lesser the price*.

On the other hand, a greater stock price *volatility* increases the probability a call option will be exercised. This increased risk is incurred by the call writer, who demands a greater option premium. Hence, the greater the perceived risk, *the greater the price*.

See the difference?

But being quite sure what you meant, I didn't really care what you called it, until you wrote "well the real issue as far as expenses on a new IPO imo isn't really the amt of the grant but the *risk premium*, which is probably an infinite number". (#reply-18990151) Then I wasn't sure any more. You see, stock prices don't become infinite, which means volatility doesn't become infinite, which means option values don't become infinite. Hmmm. "Lizzie must be talking about something else", I thought.

So I asked what you meant, but you weren't talking about something else .. apparently.

Now assume a company grants an NQSO at an exercise price of $15 (when the stock price is also $15). How great would the Black-Scholes option value be .. if the volatility actually *was* infinity? Could it exceed $15?

Regards, Ron