CLISSOLD INDUSTRIES OPTIONS
1. Since the Black-Scholes model uses the standard deviation of the underlying asset, and there is only
one underlying asset no matter how many strike prices are available, we would only expect to see
one implied standard deviation.
2. To find the implied volatility for an option, you can set up a spreadsheet to calculate the option price.
The Solver function in Excel will allow you to input the desired price and will solve for the desired
unknown variable. We did this (the spreadsheet is available), and the implied standard deviation for
each of the options is:
Strike Price Option Price Implied Standard Deviation
$30 $27.65 144.80%
40 19.45 109.42%
50 11.95 83.16%
55 9.55 78.82%
3. There are two possible explanations. The first is model misspecification. Although the Black-
Scholes option pricing model is widely acclaimed, it is possible that the model specifications are
incorrect. One potential variable that is incorrectly specified is the assumption of constant volatility.
In fact, the volatility of the underlying stock is itself volatile, and will increase or decrease over time.
The Black-Scholes model may also ignore important variables. For example, Fisher Black describes
trades he, Myron Scholes, Robert Merton, and others made when the model was first developed
(Black, Fisher, 1989, “How we can up with the option pricing formula,” The Journal of Portfolio
Management, Winter, 4-8.) As in any potential arbitrage opportunity, they purchased underpriced
assets, in this case warrants on National General stock. Unfortunately, soon after they took this
position, American Financial announced a tender offer for National General, which sharply reduced
the value of the warrants. The market had already priced the potential tender offer in the warrant
price, while this variable was not accounted for in the Black-Scholes model.
A second possible explanation is liquidity. At- or near-the-money options tend...