Options Pricing: Profit And Loss Diagrams
A profit and loss diagram, or risk graph, is a visual representation of the possible profit and loss of an option strategy at a given point in time. Option traders use profit and loss diagrams to evaluate how a strategy may perform over a range of prices, thereby gaining an understanding of potential outcomes. Because of the visual nature of a diagram, traders can evaluate the potential profit and loss, and the risk and reward of the position, at a glance.
To create a profit and loss diagram, values are plotted along X and Y axes. The horizontal axis (the x-axis) shows the underlying prices, labeled in order with lower prices on the left and rising prices towards the right. The current underlying price is usually centered along this axis. The vertical axis (the y-axis) represents the potential profit and loss values for the position. The breakeven point (that indicates no profit and no loss) is usually centered on the y-axis, with profits shown above this point (higher along the y-axis) and losses below this point (lower on the axis). Figure 8 shows the basic structure of a profit and loss diagram.
|Figure 8: The basic structure of a profit and loss diagram. Any value plotted above the x-axis would represent a gain; any value plotted below would indicate a loss.|
The graph line represents the potential profit and loss across the range of underlying prices. For simplicity, we'll begin by taking a look at a long stock position of 100 shares. Assume an investor has bought 100 shares of stock for $25 each, or a total cost of $2,500. The diagram in Figure 9 shows the potential profit and loss for this position. When the graph line is on $25 (the cost per share), note that the profit and loss value is $0.00 (breakeven). As the stock price moves higher, so does the profit; conversely, as the price moves lower, the losses increase. The figure shows the position breaks even at $25 (our purchase price) and as the stock's price increases (moving right along the x-axis) the profits correspondingly increase. Since there is, in theory, no upper limit to the stock's price, the graph line shows an arrow on one end.
|Figure 9: A profit and loss diagram for a hypothetical stock (this does not factor in any commissions or brokerage fees).|
With options, the diagram will look a bit different since our downside risk is limited to the premium that was paid for option. In this example, shown in Figure 10, a call option has a strike price of $50 and a $200 cost (for the contract). The downside risk is $200 - the premium paid. If the option expires worthless (for example, the stock price was $50 at expiration), the loss would be $200, as shown by the graph line interested the y-axis at a value of negative 200. The breakeven point would be a stock price of $52 at expiration; here, the investor has "lost" $200 by paying the premium and the stock's rising price is equal to a $200 gain, canceling out the premium. In this example, every $1 increase in the stock's price at expiration is equal to a $1 gain. For example, if the stock price rises to $54, it would represent a $200 profit.
|Figure 10: A profit and loss diagram for a long option position.|
It should be noted that the above example shows a typical graph line for a long call; each option strategy - such as long call butterflies and short straddles - has a "signature" profit and loss diagram that characterized the profit and loss potential for that particular strategy. Figure 11, taken from the Options Industry Council's Web site, shows various options strategies and the corresponding profit and loss diagrams.
|Figure 11: Various profit and loss diagrams for different options strategies. Image is from the Options Industry Council Web site.|
Most options trading platforms and analysis software allow traders to create profit and loss diagrams for specified options. In addition, the charts can be created by hand, by using spreadsheet software such as Microsoft Excel, or by purchasing commercially available analysis tools. Options Pricing: The Greeks
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