### INPUTS

Q: What should I input for volatility?

A: Many online brokerages and options-related sites publish information about historical and implied volatility.

Q: What volatility should I use with this calculator - implied or historical?

A: It's common to use the current implied volatility, since that reflects the market's current opinion. But you might choose different values based on historical volatility or your own opinion of the stock's true volatility.

Q: How does volatility affect the results?

A: In two ways:

• Volatility affects the theoretical value of an option: options with higher volatility demand higher premiums.
• In projecting possible price paths for the underlying stock, the volatility is used to determine how far the stock is likely to wander from its current price.

For both uses, this risk calculator assumes (like most others) that the volatility is constant over the life of the trade. This is not a particularly good assumption, but avoids the hopeless task of trying to forecast future volatility changes.

Q: How does the calculator compute implied volatility? Why do I have to choose which option to use? Why is the result sometimes 0?

A: Implied volatility is computed by applying the Black-Scholes option pricing model backwards: given a stock price, option premium, risk-free and dividend rates, and option premium, what value of volatility would result in this premium? The answer is the "implied volatility" - the market's opinion (as expressed through option price) of the stock's volatility.

Because implied volatility works from data about an option position, you need to choose an option position on which to base the calculation. Different positions will have different implied volatilities - there's no single right answer. When choosing a position for this calculation, it's best to choose one that is reasonably close to the money, and not too close to expiration. If the bid-ask spread is large, it's a good idea to set a premium value that averages the two: this best represents the market's consensus about the option's value.

The calculation of implied volatility might fail - there may be no volatility value that could possibly result (in the pricing model) in the given option premium. In that case, the calculation will compute an implied volatility of 0. This is especially likely if the premium is toward the low end of a large bid/ask spread. A better-chosen premium value (say, averaging bid and ask) should solve that problem.

Q: How does dividend rate affect the results?

A: The Black-Scholes options pricing model discounts the value of a stock by the present value of future dividends, based on the assumption that dividend payments lower a stock's value by the amount of the dividend. Naturally, this affects the theoretical pricing of options on dividend stocks, decreasing call premiums and increasing put premiums.

Q: What's the purpose of the "Projected Stock Growth Rate" input?

A: Every investment decision, including options, depends on some assumption about where the price is headed: Up? Down? Unchanged? The purpose of this input is to supply an expected compounded annual growth rate for the underlying stock, which is then used to forecast the distribution of possible future prices.

Q: Why don't other option price calculators ask for this input?

A: Many option price calculators use the risk-free interest rate as the growth rate. This is double-duty, since the risk-free rate is also used for theoretical option pricing. This tool lets you specify the growth rate separately. You can choose to leave that field empty, in which case it will also use the risk-free interest rate.

### CAPABILITIES

Q: Why does the risk chart only project as far as the first option expiration? How do I evaluate a horizontal spread all the way to the end?

A: All risk charts do that. Once you reach the first expiration, the composition of the trade changes. What happened at the first expiration? Did the option(s) expire worthless? Did you exercise? Were you assigned? Did you close the trade? Put money into the trade? Take money out of the trade? Roll the expired option? More to the point - how do you even represent the outcomes of a previously closed position in a risk chart?

That is why the Option Risk Calculator offers the Outcome Probability Chart - it lets you evaluate a trade beyond the initial option expiration.

### OUTCOME PROBABILITY CHART

Q: What is the purpose of the "Reject Outliers" choice when setting up a run of the Outcome Probability or Full Trade charts?

A: During the simulation, the calculator will simulate random-walk stock price trajectories using the geometric Brownian motion discussed on the theory page. As is the nature with such random distributions, a small number of the outcomes may include a large stock price change - which might (for non-spread trades) lead to a large gain or loss. This small number of extreme outcomes does not contribute much to understanding the trade, but can make the results difficult to view: the chart may scale its Y-axis to fit in the extreme value(s), compressing the more common outcomes into a small, difficult-to-read area. The default behavior for these charts is to reject the roughly 0.3% of price movements that fall more than 3 standard deviations from the average projected price movement.

### DATA

Q: What is the data source used for the option chain lookup?

A: Options chain and stock price information is looked up through the Yahoo Query Language service, from Yahoo Community Tables. The lookup takes place directly from your browser (it does not involve the OptionRisk server), and the returned data is intended only for your personal use.

Q: Why doesn't the option chain lookup find a particular stock, or particular option positions, that I know are available? Why does the lookup sometimes stall or fail entirely?

A: The Yahoo Community Tables, and Yahoo, make no representation that the data is complete or accurate, or that the lookup capability is even available. All information from this lookup is for personal use, at your own risk.

Q: Why doesn't the OptionRisk tool use a better data source?

A: Market data is not free. While sites like Yahoo and MarketWatch allow you to look up market data for your personal use, they do not provide free data feeds. If there is enough interest, I will consider providing a professional (paid) version of the OptionRisk tool that uses a good data feed.

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DISCLAIMER: This risk calculator is for educational purposes only, and is not intended as a basis for trading decisions. Use at your own risk.