Vega, Greek The IV

以下文章摘自：http://www.thehindubusinessline.com/iw/2003/08/10/stories/2003081001121200.htm Vega, Greek The IV by C. Raja Rajeshwari HAVE you wondered why these option premiums keep changing but never in the same proportion of the change in the underlying stock? The knowledge of the Greeks will help in explaining why the option premium changes the way they do. Recap: The Greeks introduced in this column so far are delta, gamma and theta. * Delta tells you how much the option premium increases/decreases with increase/decrease in the underlying stock price. # Calls have positive delta. Every increase in stock premium will lead to increase in the option price. # Puts have negative delta. Every increase in stock price leads to decrease in the option premium. * Gamma, tells you the pace at which the option premium increases or decreases - effectively the rate at which delta would change. # Unlike the delta, gamma is dependent on the position and not on the option type whether it is a call or put. # If you have bought an option (long position) then the Gamma is positive. Your long position in calls will increase at an increasing pace, if stock price increases. # If you have sold or written an option, then the Gamma is negative. Your short position in calls would decrease at an increasing rate, if stock price moves up. # Delta and gamma would largely explain the changes in option premium with respect to the underlying option price. * Theta tells you the rate at which the time value component in the option premium will decrease. # European options, which can be exercised only on expiry, have negative or positive theta deepening on the moneyness of the option. # For an option buyer (long position), theta tells the daily cost of holding the option. # For an option writer (short position), theta is the daily profit that accrues from selling the option contract. The volatility factor Volatility can be a very important factor in deciding what kind of options to buy or sell. Volatility tells you the range that the underlying stock price has fluctuated in a certain period. The more volatile an underlying stock is, the more costly is an option on this stock. When dealing in options, you have to consider two kinds of volatility - historical volatility and implied volatility. Historical Volatility: This reflects the past price movements of the underlying stock. Historical volatility is a key input to find the fair value of an option. The theoretical price of an option can be computed by using the current price of the underlying security, strike price of the option, dividends to be paid by stock, current risk-free interest rate and historical volatility. However, there is always a difference between the fair value as computed by the model and the market price of the option. Implied volatility: The reason for this difference is that the market is assuming a different volatility from the historical volatility that can be computed for a security. To calculate this volatility, all other data except for the volatility is input into the model along with the market price of the option. The model then throws up the volatility, based on the current market price. This is `implied volatility'. Implied volatility (IV) is the market's perception of the stock's future volatility. Vega for Volatility This will tell you how much your option premium will increase or decrease with increase/ decrease in the level of its volatility (IV). For example, a Vega of 0.93 means that your option premium would increase by 0.93 if IV increases by one per percentage point. Therefore, if the volatility jumps by 5 per cent then your option premium would change more or less by Rs 4.65. Why is Vega important? Vega is important because it will tell you how your position is exposed to changes in volatility. If the Vega is high then your option will rapidly gain or lose value. If you are wrong on the direction of the underlying, then the position can lose value. For instance, you have bought a call thinking that the underlying stock price will increase rapidly, driven by volatility levels that are expected to be higher than what prevails at the time of entering the contract. Then the premium will increase with your Vega and you can square your position at higher premiums. However, the opposite has happened leaving your call worthless. You will sustain losses, which would be the initial payout for buying the option. Long or short: Vega is always positive, but depending upon your position (long or short), it will help you make or lose money. # An option buyer benefits from rising IV, which means that the option premium will go up. Falling IV will make him lose money because the option premium will fall. # An option seller or a writer of an option will suffer from rising IV - option premium will go up. On the other hand, falling IV will make him lose money because the option premium will fall. How to calculate: To know the theta of an option, a Black-Scholes spreadsheet/calculator that is available in many financial Web sites is needed. Such a calculator is available in http://www.bseindia.com/ too. On input of strike price, spot price, premium/volatility, time-period, dividend yield, risk free rate into the calculator it gives the values of the Greeks. Trading with Vega: Trading based on Vega is buying cheap options or selling expensive options and holding the position until it return to fair valuation levels. We call it volatility-based trading because of the way we measure option cheapness or dearness, using implied volatility. The IV levels of the options will help in determining what strategies to be used. When IV is very high, market price of options will be greater than theoretical price. Such options are considered `expensive'. Many traders favour premium-selling strategies. Periods of high volatility are followed by periods of normal to low volatility and vice-versa. Therefore, if one is selling volatility, the Vega should be higher. This means that selling longer-term options would be a better idea when selling volatility. Why so? Longer-term options (with a sizable period to expiry of the contract) tend to have higher Vega. In case you have sold option contracts with higher Vega, you have sold an expensive option. The period available for the volatility levels to move closer to the normal level is large. So you can wait for it to return to normal levels, by when the option price would have reduced. Squaring your position at a lower price would leave you with a profit. The profit is the difference between the price you sold the option and the price of buying the option back. Note: Option prices are very sensitive to volatility; trading options on this basis can be attractive. However there is substantial risk of loss in trading if you get the direction wrong. IV can increase or decrease even without price changes in the underlying security. This is because implied volatility is the level of expected volatility (this means it is also based not on actual prices of the security, but expected price trends). IV also declines as the option gets closer to expiration, as changes in volatility become less significant with fewer trading days.