# Picturing Option Profits – Volatility

In the last three articles, which you can read here, here and here, I discussed using option payoff diagrams to visualize profits. I talked about how Delta and Gamma are portrayed on the graphs. Today we’ll look how changes in implied volatility can be expected to affect things, as measured by Vega.

A quick review – people are willing (with good reason) to pay more for options on stocks whose prices change rapidly. An option buyer is making a bet that the price will move. Stocks that have moved fast in the past will likely do so in the future – their movement is a surer bet, based on experience.

The option pricing “models,” or formulas, which make the option market possible, describe the mathematical relationship between a stock’s volatility, on one hand, and the theoretical value of each of its options on the other. That is given the past price movement, which is called Historical Volatility (HV); and also taking into account the option’s strike price, the stock price, and how much time is left in the option’s life, a theoretically correct price of every option can be calculated. If an option is actually trading near that theoretical price, then option buyers are showing they are willing to pay it, and option market makers and/or other sellers are willing to accept it. The option traders are indicating that they expect the past rate of change to continue into the future.

If the options are trading at significantly different prices from the theoretical, however, that implies something different. In that case, the option traders are saying that they believe that the future movement in the stock price will be at a different rate than in the past. Using the actual prices at which any option is changing hands, in fact, the formula can calculate the exact rate of change that is being anticipated. That anticipated rate of change is called Implied Volatility, or IV. It can be the same as, or it can be different from, historical volatility.

IV might be lower than historical volatility, for example if a one-time event has recently caused a significant move in price. Say that it was announced that oil had been discovered under the parking lot at a company’s property. The stock doubles overnight. A couple of weeks later, it turns out to be a false alarm, and the company’s stock returns to its former price. This would be an example of very high historical volatility. No one would expect that rate of price change to happen again, so option prices would not price in an expected doubling in price, even though that has in fact happened in the past. Implied volatility now would be much lower than historical volatility.

An opposite situation might be where a drug company’s FDA approval, or not, of a new product was due. Either way it went, the stock would move. The announcement has been expected for weeks, and the stock has barely moved. The options will be very expensive, since a much greater rate of change is almost certain.

There is an option metric that measures how sensitive an option’s price is to a change in IV – that is, to a change in *expectations* about the stock’s price. This measure is called Vega. It measures how many *dollars and cents per share* an *option’s price* will change, in response to *a one percentage point change* in expected volatility (IV).

For example, say an option’s IV is 25%, indicating that this is the expected rate of change in the stock price. Assume that that option’s *Vega* is .18. Now an unexpected event occurs. Before the stock’s price actually changes at all, the expected rate of change increases from 25% to 30%, a 5-percentage-point increase. That option’s price should change by the Vega of .18, multiplied by the 5-point change in expected price, or 5 * .18 = $.90. Whatever the option’s price was before, it should now be 90 cents higher. This is true whether the option was a put or a call. Increased *expectations* of stock price movement make all options more expensive, whether any actual stock price movement has yet occurred or not.

OK. How is sensitivity to IV changes illustrated by an option payoff diagram?

Once again, here are the price and option payoff diagrams for our example trade. GLD was in a downtrend, which we expected to continue. At a time when GLD was trading at around $124, we expected it to stay under $130 until the November expiration. We sold the October $130 call option for $ 1.36 per share, and simultaneously bought the November $135 call options as protection, for $.555 per share. Our net credit was $1.36 – $.555 = $.805 per share, or $80.50 for the 100-share contract.

Figure 1 – GLD price chart

Figure 2 – GLD November 130/135 Bear Call Spread Payoff Diagram

- Implied volatility affects only time value; it has no effect on intrinsic value. When they expire, all options have zero time value, so
*at expiration time*implied volatility is meaningless. There is then no more time for expectations to be borne out, so future expectations then will no longer matter at all. This is shown by the straight black line above, which is the position’s P/L at expiration. That line is horizontal at a value of exactly $80.50, at any GLD price below $130. If at expiration GLD is below the $130 strike, then both the calls expire worthless and the profit is the original $80.50 credit, period. If at expiration GLD is*above*$130, then the $130 call which we are short will have value, which we will have to pay to liquidate it. It will have one cent worth of value for every penny GLD is above $130. If GLD is above $135, however, then our long $135 call will also have value. It then makes a penny for us for every additional penny that our short $130 call costs us as GLD rises further. Our loss will then have topped out at its maximum of $135 – $130 – $.805 = $4.195, or $419.50 for the contract. *Before*expiration, expectations do matter. When there is time, and if there is any realistic chance that in that time an option could finish in the money, then that option will have time value. Its P/L curve will not be dictated by stock price alone – its P/L curve vs price*will not be a straight line.*Notice the blue, green and purple curved lines above. Each of them represents what the position’s P/L would be at a different selected future date – October 10 (blue line), October 22 (green line), or November 3 (purple line). Look at where those lines cross the vertical red line, where GLD’s price is $123.18. The black line at that point is at its maximum, which is + $80.50.All the other curves, however, are lower.

How those P/L lines curve tells us a great deal about how the position will react to changes in expectations. Next week we’ll continue talking about what they tell us.

For comments questions in this article, contact me at rallen@tradingacademy.com