Options Pricing: Profit and Loss Diagrams

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It's very helpful to be able to chart the payoffs an option can return. This page discusses the four basic option charts and how to set them up. The first chart we'll make shows what happens when you Long a Call buy a call option.

When you buy a call option, you must pay a premium the price of the option. You can make a profit if the value of the underlying asset sufficiently increases. The x-axis represents the price of the underlying asset or "S" like the stock. To draw the lines we will be placing on the chart, it is best to set up the following helpful table. The next row shows the value of the call option for each scenario. If the asset's value is less than or equal to the strike price, then the call option is worthless; however, if the asset's value is greater than the strike price, then the call option can be used to make a profit of S-X.

The next line shows the cost of the premium at each scenario--since we are long on the option, the premium is some negative number whatever was payed to purchase the option. The last row is simply a total of the two rows above it.

To make the chart, we first must plot the strike price on the x-axis. This is represented with an "X". The blue line represents the payoff of the call option. If S is less than X, the payoff of the option is 0, so it will follow the x-axis. After reaching the strike price, the payoff of the option is S-X, so the line will increase at a 45 degree angle if the numbers are spaced the same on both axes.

The green line represents the profit from excersizing the call option. It runs parallel to the payoff line but since it takes into account the price that was payed for the premium the cost of the call option it will be that far below the payoff line. Perhaps an example would be helpful: Let's say you are purchasing a call option for ABC stock X strike price: Now that we've got the first chart out of the way, we can move a bit quicker and show a few other charts.

Now we'll see what happens when you Short a Call sell a call option. Since you are writing the option, you get to collect the premium.

You'll only end up losing money if the value of the underlying asset increases too much since you'll be forced to sell the asset at a strike price lower than market value. Here's our nifty table: The chart doesn't really need a payoff curve since you're not the one holding the call option.

The profit will hold steady at the premium until it reaches the strike price, at which point every dollar the asset gains is a dollar you will lose. Buying a put option gives you the right to sell the underlying asset at the strike price. When you long a put buy a putyou will profit only if the price of the underlying asset decreases. Let's start by setting up the table; this time we'll use "p" as the price of the premium: This makes sense--the option will only give a payoff if the asset is below the strike price.

The payoff less the premium will be your profit. The chart looks just like the "Long a Call" chart except it's flipped vertically at the strike price. Our last simple but helpful option chart shows what happens when you short a put sell a put. Since you are the writer of the put in this case, you are happiest when the asset's value doesn't fall below the strike price.

Again, since you don't hold the option we've only included a "Profit" line and not a "Payoff" line. Now that you have seen the four basic types of options charts, we can do some stuff that's a lot more fancy and understand option-trading strategies that are a bit more tricky. Other sites in the eonor.

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Let's say you want to by a TV on sale at Wal-Mart. You drive there only to find out that it's "sold out". So you go to the clerk and ask for a "rain check". This "rain check" is a guarantee that you will get the TV for the sale price when they are back in stock. There may be an expiration date on the "rain check" for 1 month from the out of stock date.

This rain check qualifies as an Call option. You have the right to purchase the TV for the sale price up to 1 month regardless of how much the TV goes up or down in price during that period. You are the buying this call option and Wal Mart is the seller.

The only difference of this rain check versus a real option is that there is NO value on this option and it is probably non-transferable.

Now, let's use this same concept for a stock. On the other side of this deal, there is someone who is willing to sell you this right for you to buy Microsoft from him for Rain check for TV Expiration Date.

Profit loss VS Price graphs are by far the simplest and most powerful way to communicate the risk and reward assoicated with any option or option spread two or more options. Back to the Microsoft stock option example from above. The contract size is shares. Profit loss Price - microsoft stock Your profits are same as if you had bought Microsoft stock less the option price. The PL vs Price graph consists of: Profit or loss of the position plotted on the Y-axis.

Underlying price plotted on the X-axis. The current price of the underlying is located in the center of the X-axis underlying price range.

These two graphs represent just buying or selling the instrument stock, future, index. They are simply 45 degree lines which intersect at the current underlying price. For every dollar the underlying price moves up or down, there is an incremental profit loss movement. Selling the Underlying also is known for stocks is known as shorting the stock selling the stock without first owning it.

Buying a call option: The above graph is shows the profit or loss of buying a call option for a range of projected underlying prices at expiration day for the call option.

Notice below that the loss is limited to the price of the call option if the underlying price at options expiration is LOWER than the current underlying price. Buying a put option: The above graph is shows the profit or loss of buying a put option for a range of projected underlying prices at expiration day for the call option. Notice below that the loss is limited to the price of the put option if the underlying price at options expiration is HIGHER than the current underlying price.

Profit and Loss moves incrementally 45 degree angle if the underlying price at options expiration day is LESS than the underlying price today.

The above graphs show the profit and loss at options expiration for selling a call or put. But the profit is limited to the price of the option. For example, if you combine buying a call and buying a put together, this forms a spread known as a straddle:. The straddle spread is a strategy which would profit if the underlying moved considerably up or down.

Remaining the same would cause a loss limited to the combined prices of the call and put options. This position could be reversed to selling a put and selling a call known as a Short Straddle spread.

The above Short Straddle position is a neutral strategy profitable if the underlying price remains the same. Maximum profit is the combined prices of the call and put options and maxiumum loss is unlimited. Another common spread position is known as a covered call. This is formed by buying the underlying and sell a call. Your maximum profit is the price of the call. Your maximum loss is the value of the underlying less the call you sold.

You would make money so long as the underlying stayed the same or moved up. Strike price is the price of the underlying that you have the "option" to buy or sell for. For example, a 50 call would mean that you have a right to buy the underlying for 50 before a certain date. All call and put options have a series of strike prices. This series has a center as the current price of the underlying. For example, if a stock is trading at This strike is also known as the "at the money" option.

The 50 call would be the "at the money" call since it is closest to the underlying current price of An "in the money" call would be any call with a strike price LESS than the at the money call.

An "Out of the money" Put strike would be an "In the money" Call strike. When we view the PL chart for varying CALLS, we see that the in the money calls have higher maximum losses, but a lower break even price.

This spread consists of buying one call option of a particular strike price and selling another call option of a different strike price. You can also do the same for puts.

The main difference between the credit versus debit spread is that in a credit spread, your sell option price will be greater than your buy option price giving you a net credit when you open the position.

The debit spread buy price is greater than the sell price giving you a net debit when you open the position. The PL graph would look like the following:. Notice how the call debit spread has a limited loss as the net option cost of buying and selling the calls. It has a maximum profit as the net difference in the strikes of both calls.

For example, assume we buy a 50 call for 2 and sell a 60 call for 1. The maximum loss would be -1, and the maximum gain would be The spread initially gives you a net credit of the sell option price less the buy price. This is a bearish position which is profitable only as the price of the underlying goes down. The maximum gain is the net credit of the option prices, the maximum loss is the difference in the option strike prices. Put credit and debit spreads work the opposite way of Calls For a Put debit spread we would: The spread would give us an initial cost of the difference between the buy option and sell option which would also be the maximum loss.

The maximum gain is the difference in the strike prices. It would give you an initial credit of the net cost of the two options with a maximum gain of the difference of the option strike prices. It is a bullish strategy profitable if the underlying price increases. Here is an easier way to summarize option components when combining them to construct spreads.

The ratio spread is usually a three option spread strategy with 1 at the money option combined with 2 out of the money options. As we can see from the above graphs, backspreads have a lower maximum risk but smaller profit range.

Most 4 option spreads form high probability of profit neutral strategies. This high probability of profit comes from the statistical fact that the the underlying price will most likely remain nearly the same given a time limitation.

There two main types of four option spreads: The butterfly and the iron condor. The main difference is that the iron condor combines both call and put options whereas the butterfly is call or put exclusive. Notice how the butterfly spread is a neutral strategy being most profitable when if the underlying price stays the same.

Notice also how the loss is limited to the net option price. You can visualize how both credit spreads are overlayed together to form the iron condor. Notice how the flat iron condor has range of maxiumum profit versus the butterfly having one point. For any PL vs Price chart, you usually see two plots: Here is what the PL vs price today graph would look like as compared to the PL at expiration for a the basic options:. Observe how the PL vs Price Today would obviously have a zero profit if you closed the position today and the underlying price stayed the same.