# Long Directions

1) Introduction:

OptionPosition+ is a financial analysis App that estimates the value of a set of shares and put and call options for a particular stock. It allows the investor to explore various option hedging positions and create a portfolio that is sensitive to price and volatility fluctuations or that provides protection for various concerns. OptionPosition+ graphically illustrates the value of put protection, covered calls, call spreads, time spreads, delta neutral skew trades, iron condors, etc..

The OptionPosition+ App goes out to the web to retrieve information on available put and call strike dates and strike prices and all stock and option prices. It uses the Black-Scholes equation to determine an implied volatility associated with each put or call option. Those implied volatilities can be displayed at each expiration date (a volatility 'smile') or strike price. Using the calculated implied volatility, OptionPosition+ estimates the value of the option as the price of the stock changes, as time progresses or as volatility increases or decreases. OptionPosition+ then graphs the value or Greek function (i.e. derivatives with respect to price, time or volatility) versus the price of the stock. It also plots the value and Greek functions at any time between now and the first strike date and under the assumption of increased or decreased volatility. Graph scales can be easily moved, expanded or contracted with one or two finger touch moves.

OptionPosition+ comes with a one month free trial subscription. After that one month, and without a subscription, OptionPortfolio+ is limited to the stock AAPL. With an auto-renewable monthly subscription, or during the one month free trial subscription period, OptionPosition can access all NYSE and NASDAQ stocks. OptionPosition+ has the capacity to remember 30 different portfolios at any one time. Each portfolio relates to a particular stock trading on the NYSE or NASDAQ. Each portfolio can have 6 different asset lines selected from a quantity of long or short shares, and a quantity of long or short puts or calls with various strike dates and strike prices.

These Directions contain the following sections:

1) Introduction (this section)

2) Portfolios

3) Graphs

4) Subscriptions

5) Technical details (Calculation related, Quotes/Price related, Dividend related, Volatility timing for Theta and Expiration, Risk free interest rate, and Stock quote delay).

2) Portfolios:

To enter a portfolio, tap the ‘Portfolio’ tab. Get information on the Portfolios by tapping the 'info' button at the top of the Portfolio page. Your portfolio ticker and asset selections are stored on iCloud when you exit the app. Portfolios are synchronized with all devices that share a purchased subscription using your App Store ID. If you have not purchased a subscription then your portfolios are synchronized with all devices that use your Apple ID.

OptionPosition+ has the capacity to remember 30 different portfolios at any one time. Each portfolio relates to a particular stock trading on the NYSE or NASDAQ. (Read 'Subscriptions' below regarding stocks other than AAPL.) Each portfolio can have 6 different asset lines selected from a quantity of long or short shares, or a quantity of long or short puts or calls with various strike dates and strike prices. One or more of the 6 assets in a portfolio can also be any quantity of a different portfolio containing shares, puts and calls of another, or the same, stock.

3) Graphs:

Once one or more portfolios have been populated with items, tap the ‘Graph’ or 'Volatility Smile' tab bar. (If a graph does not appear tap ‘Rescale’ – graph scaling is discussed below.) The black line indicates the gain/loss value of the portfolio of assets as a function of the stock price as of today. As time moves on and we approach the strike date, the value will change. To see the value at some point in the future, tap the ‘Date’ segment on the ‘Red Line’ and move the slider to the right. To see the value were the volatility to increase or decrease, tap ‘Vol.’ on the ‘Green Line’ and move the slider to the right or the left. A portfolio ('parent' portfolio) can contain one or more different 'child' portfolios as items. The price of the underlying stock in a child portfolio is assumed fully correlated with the price of the underlying stock of the 'parent' portfolio and related by a Price Change Multiplier. The value of all of the Price Change Multipliers can be further adjusted by tapping 'PCM' on one of the sliders.

To move the graph, touch anywhere within the graph area and move the graph with one finger. To increase or decrease the scale along the X or Y direction, touch anywhere within the graph area with two fingers and spread or pinch the two fingers along the X or Y direction or both. To return the scales to their preselected values tap Rescale.

To determine the value at any point on a curve, tap near that point and the values at an indicated point will appear along with a verticle white line. Then move the curves so that the point for which you want the value becomes the indicated point. Also displayed is the value at the point that the various curves cross the white line. To erase the white line tap to the left of, or below the graph.

To view any of the Greek functions, tap the 'Greeks' segmented control at the bottom. Delta is the derivative of the gain/loss value with respect to stock price, normalized to a $1 change in stock price. A share of stock has a Delta of 1. Delta is expressed in terms of shares. An at-the-money option has a delta of 0.50. Vega is the derivative of the gain/loss value with respect to volatility, normalized to a change in volatility of 1% (i.e. 9% goes to 10%). Vega is expressed in terms of portfolio $’s per 1% change. Theta is the derivative of the gain/loss value with respect to time, normalized to one day. Theta is expressed in terms of $’s per day. Gamma is the second derivative of the gain/loss value with respect to stock price, normalized to a $1 change in stock price. It is the change in delta with respect to price. Gamma is expressed in terms of shares per $.

To view the future Price and Gain/Loss probabilities, tap the 'Probabilities' segmented control at the bottom. Tap the right 'info' button for an explanation of those graphs.

To eliminate some of the screen clutter, tap the ‘Hide’ button. To restore those functions, tap the ‘Show’ button."

4) Subscriptions:

OptionPosition+ comes with an initial one month subscription period. A subscription is necessary to access stock and option information for all stocks except AAPL (Apple Inc.). After the initial one month subscription period, ongoing auto-renewable subscriptions are available for 1 month, 2 months and 3 months at the App Store through an In-App Purchase. To purchase an auto-renewable subscription, tap the button labeled ‘Tap here for subscription information or to restore a subscription'. Shortly before the subscription period expires the auto-renewable subscription will automatically renew unless you turn off the auto-renewing function through your Settings App.

If your subscription period terminates, you will retain your portfolio positions and the data that is stored in your device (i.e. stock and option prices that were downloaded while their subscription was active). However, with the exception of the stock AAPL, those stock and option prices will not be updated.

5) Technical details:

Calculation related: OptionPosition+ uses the Black-Scholes equation to calculate an implied volatility for each option. The assumption that the price of an option is determined by the Black-Scholes equation is, therefore, inherent in all valuations within OptionPosition+. Because it uses Black-Scholes, the app assumes all options are European options that can only be exercised at expiration leading to a small error for Amercian options. If the implied volatility (annualized standard deviation) is calculated to be less than 0% or more than 1000% the item is excluded from calculations and listed as having 0% or 1000% volatility. Derivatives are calculated by finite differences rather than closed forms. For Delta, a $0.10 difference is normalized to $1.00. For Vega, a 1% difference is used. For Theta a full day's difference is used. For Gamma, a $0.01 difference is normalized to $1.00.

Quotes/Price related: The price of an option is assumed to be 1/2 of the current bid price plus ask price. If there is no bid then the price is assumed to be 1/2 the ask price and is indicted as defective with a \" * \". If there is no bid or ask then the last trade price is used and is indicated as defective with a \" * \". Option quotes are all delayed by approximately 15 minutes with variations in that delay based on the particular market reporting the quotes; the corresponding delayed Stock price is determined at the precise time of the option quotes by using put-call parity on near term, at-the-money put/call options.

Dividend related: When a stock declares a dividend payment to shareholders of record on a specific ex-dividend date, OptionPosition+ assumes that, ceteris paribus, the stock price will fall by the amount of that dividend on the date that the stock will go ex-dividend. Most importantly, OptionPosition+ assumes that dividends will continue to be declared in the future as they have been declared in the past – both in terms of dividend amounts and scheduled ex-dividend dates. As dividend increases are announced or ex-dividend dates altered, these facts are reflected in the calculations when such information has been correctly transcribed by our proprietary data sources. (We make no guarantees of accuracy with respect to dividend information or any other data.) The portfolio value of a stock assumes that dividends will be reinvested risk free rather than used to purchase additional shares. Because the value of the dividend is retained in the portfolio, the value of a portfolio that includes shares does not change when the stock goes ex-dividend. However, because the break-even price of the stock is assumed to decrease when the stock goes ex-dividend, the price axis scale must be shifted by the dividend amount for all graphs that are shown for a future date. This new scale is displayed in the color of the future-date slider (i.e. red or green). Because OptionPosition+ is assuming a scheduled payment of fixed dividends and not a ‘dividend rate’, dividends do not change as the underling price of the stock changes. Therefore, OptionPosition+ calculates a Delta value that differs from the closed form and other Black-Sholes formulas that assume that dividend rates are fixed and therefore that dividends change with stock price (i.e. [d/dP] of [S*exp(-rate*T)] differs from [d/dP] of [S – sum(Di)]). We believe our approach is more correct. Please send us your comments on this matter.

Volatility timing for Theta and Expiration: OptionPosition+ assumes that stock volatility occurs during 6.5 hours of active trading for 5 trading days each week and, while the markets are closed, for the equivalent of 5 additional hours realized just before each market open. (This 6.5/5 hour split in market open/market closed volatility is based on a statistical analysis of the 9:30am-4pm volatility compared to the 4pm-9:30am volatility.) Because Theta is based on the change in a full day (i.e. 1/5 of a week or 1/261 of a year) OptionPosition+'s theta may be 7/5 larger than other thetas. Option expiration is assumed to occur after one period of market closed volatility following the close of the market on the exercise date. On the last one or two days of trading inefficient trading costs dominate assumptions underlying Black-Scholes and the calculations may be unreliable.

Risk free interest rate: OptionPosition+ uses the 3 month US dollar LIBOR.

Stock quote delay: All quotes are delayed by approximately 20 minutes although we reserve the right to increase or decrease that delay without notice.