VEGA OR OMEGA (Ω)
3. The implied volatility levels between months do not always correlate with each other because the further months are part of a vega play and
the closer expirations are more of a theta vs. gamma play.
Exhibits 3-16 to 3-19 show some interesting characteristics of vega. At-the-money options have the greatest price sensitivity to the changes in implied volatility (Exhibit 3-16). Far-term options are more sensitive than near-term ones (Exhibit 3-17).
E X H I B I T 3 – 1 6
100*100 Strike Vega Over Time – From 91 Days to Expiration, 10% Volatility, .01% Interest and Using Black-Scholes Futures Style Margin
0
93.00 94.75 96.50 98.25 100.00 102.00 104.00 106.00
Underlying Price
©1996-2006 Charles M. Cottle [email protected]
E X H I B I T 3 – 1 7
100*100 Strike Vega as Time Passes – 91 Days, 10% Volatility, .01% Interest and Using Black-Scholes Futures Style Margin
9 21 33 45 60 75 90
E X H I B I T 3 – 1 8
100*100 Strike Vega as Implied Volatility Changes – 91 Days, Starting at 10% Volatility, .01% Interest and Using Black-Scholes Futures Style Margin
281
-5.00 -3.00 -1.00 1.00 2.00 3.00 4.00 5.00
-5.00 -2.00
©1996-2006 Charles M. Cottle [email protected]
E X H I B I T 3 – 1 9
100*100 Strike Vega as Implied Volatility Changes – 91 Days, Starting at 10% Volatility, .01% Interest and Using Black-Scholes Futures Style Margin
93.00
93.00 94.75 96.50 98.25 100.00 102.00 104.00 106.00
Vega
Exhibits 3-18 and 3-19 display what happens to vega as implied volatility changes. The most important lesson here is that at-the-money (ATM) vegas are not affected (that is, vega remains constant) in the way that in-the-money (ITM) and out of-in-the-money (OTM) vegas are. Go back and see the vega values in Exhibit 3-6 that show that it does not matter what the implied volatility is for that ATM 100 strike option. It means that each option should change by .199 (on that point in time) for every 1 percentage point change in implied volatility, i.e. from 5% to 6%
represents the same .199 vega as from 14% to 15%. This is graphically indicated by the straight line for the ATM options at the top of Exhibit 3-18. This is also shown in the top center of Exhibit 3-19 where all the lines converge. Furthermore, the fact that this relationship does not hold for away-from-the-money options is of profound significance. When the option, in this example, is either 7 points ITM or OTM, as seen in the extremes (93.00 and 107.00) of all the graphs, the vega amount varies by about .00281 for every 1% change. This may not seem like a lot, but think again because it grows exponentially with each 1 percentage point increase. Consider the effect that it would have on a ratio spread where the OTMs, in greater quantity, increase exponentially while the ATMs increase linearly. Implied volatility, in the bond options, screamed to 36% in seconds during the Rocket to Quality coinciding with the Stock Market Crash of ’87 and stayed there long enough to drag the victims out of the pits forever.
RHO (P)
Rho is to interest rates what vega is to implied volatility. Most of the time it is of little concern, and is usually a trader’s lowest priority.
However, in periods when interest rates are volatile, rho can affect the market maker’s profit and loss considerably. This is especially true in places like Brazil, where greater attention was placed on rho risk than delta risk because of the huge swings in interest rates that occurred in the mid 90’s. The sensitivity is greater for the instruments with more time until expiration, as it is in the case of vega. The more time there is, the more borrowing or lending is impacted by a change in interest rates.
DIVIDENDS
When a stock has a dividend, there are a myriad of considerations for traders who have, or anticipate having, a position in that particular stock.
Dividends have an unusual impact on the valuations of not only the everyday strategies but also on the locks. A change in the amount of the proposed dividend, the sudden declaration of a dividend, or a change in
©1996-2006 Charles M. Cottle [email protected]
the ex-dividend date can create either unanticipated profit or loss for anyone having an existing position. An important lesson to be learned for anyone considering initiating a trade based on a deviation from a fair valuation is to check first to see whether something is wrong, whether a variable has not been considered, or whether any of the variables have changed. On the other hand, hesitating could result in a missed opportunity if nothing was wrong in the first place. This is a luxury that no trader can afford. Because of these unknown factors, there is a huge gap between the practical and theoretical approach to using options.
Besides the list of variables that affect the valuations of every options strategy, the biggest and the most obvious unknown is: Where will the stock be when it is time to exercise? This unknown means that there is an opportunity for a rent-a-put early exercise play.
Dividend-paying corporations make an announcement of the dividend’s particulars on a quarterly basis in the United States. In many countries, however, dividends are paid only once or twice a year. The announcement states the amount declared and the pertinent dates, important for both shareholders and market players, to consider. Along with the variables of time until expiration and the interest rate, these dates are required for valuation purposes. They are record date, payable date, ex-date or ex-dividend date, and the settlement dates for both the stock and the options. The latter two subject the trader not only to the dividend but also to the cost of carry.
Record Date
The record date is the date set by the corporation paying the dividend and the stockholder must own “settled5” stock in order to be considered the
“owner of record” so that he or she can receive the payment.
Payable Date
The payable date, also set by the paying corporation, is the day when the cash payment will be paid to the owners of record. It is announced when the dividend amount and record date are declared.
Ex-Date or Ex-Dividend Date
On or before the ex-dividend date or ex-date (this date is set by the paying corporation) the stock has to have been bought, sold, or shorted for it to be subject to the dividend. Keep in mind that dividends must be paid if the trader is short stock because the transaction needs time to settle, and that happens on the settlement date.
5 Settlement
Settlement refers to the actual payment and transfer of ownership for the shares.
Settlement Date for Stock
This is the date that the buyer becomes the owner of record. Stock settles in three business days in the United States6 (e.g. a stock traded on Tuesday settles on Friday). Settlement is postponed a day for each holiday in between. For stock to be subject to the dividend it must be settled by the record date. On Friday, in this example, the buyer becomes the owner of record for dividend purposes.
Agreements at the time of transaction can be negotiated between the buyer and seller to alter the date. Stock traded for cash “same day settlement”7 causes the buyer to become the owner of record by the same day’s close.8 Similarly “next day settlement” causes the buyer to become the owner of record by the next day’s close.
The settlement of stock as a result of an option exercise also settles in three business days.
Settlement Date for Options
Options settlement is the next day after the transaction. If an option is exercised on the same day that it is transacted, it follows that the option settlement will take place the next day and the stock settlement will take place in three days.
Keep in mind that if a stock is purchased, or an option is exercised, prior to the weekend, two extra (sometimes more if there is a holiday) days without carry should be factored into, or rather out of, the valuation.
Countries other than the United States have other variables to consider. First, in many countries9 there is a different tax rate for
6 Settlement Procedures
Settlement procedures vary from country to country.
7 Cash Settlement
Based upon an agreement between buyer and seller at the point of sale, the stock will be settled by the end of the business day that it was transacted.
8 Settlement by Agreement
Based upon an agreement between buyer and seller at the point of sale, the stock will be settled by the end of the business day that it was transacted.
9 International Dividends
Germany, for example, factors other variables into the valuation. These include the following:
Doppelbesteuerungsabkommen, an agreement between countries to avoid double taxation on dividends for foreign shareholders.
Kapitalertragssteuer, a tax reduction for foreign investors.
Bruttodividende, the gross dividend received by a German resident.
Bardividende, the net dividend paid by the company to the shareholder.
Courtage, a transaction fee paid to a broker (Amtliche Makler or Freimakler).
Körperschaftssteuer, or Steuerguthaben, the amount of tax credit for shareholders who are German residents.
©1996-2006 Charles M. Cottle [email protected]
dividend income (or expense) than there is for interest income (or expense). There may also be different tax rates for foreign and domestic investors. Long-term and short-term capital gains may be treated differently. There may also be different levels of taxation for corporations relative to individuals.