Understanding Volatility

Transcription

1 Options Trading Forum October 2 nd, 2002 Understanding Volatility Sheldon Natenberg Chicago Trading Co. 440 S. LaSalle St. Chicago, IL (312) [email protected]

2 exercise price time to expiration -1- underlying price interest rate pricing model theoretical value volatility (dividends)

3 % 10% 20% 20% 40% 20% 10% 20% long an underlying contract -2-10%* %*110 long a 100 call = %*5 + 10%*10 = 2.00 Expected Return

4 The theoretical value is the price you would be willing to pay today in order to just break even. If the expected return of the 100 call -3- is 2.00, what is its theoretical value? interest rates = 12% 2 months to expiration (2.00 x 2%) = 1.96

5 underlying prices probabilities -4- normal distribution

6 Standard deviation how fast the curve spreads out. Mean where the peak of the curve is located -5- All normal distributions are defined by their mean and their standard deviation.

7 each day value = each day value = put each day value = days to expiration 120 call option value

8 +1 S.D. 34% -1 S.D. 34% +2 S.D. 47.5% -2 S.D. 47.5% mean ±1 S.D. 68% (2/3) ±2 S.D. 95% (19/20) S.D. +1 S.D. -2 S.D. +2 S.D.

9 Mean the break even price at expiration for a trade made at today s price (forward price) -8- Standard deviation volatility Volatility: one standard deviation, in percent, over a one year period.

10 1-year forward price = volatility = 20% One year from now: -9-2/3 chance the contract will be between 80 and 120 (100 ± 20%) 19/20 chance the contract will be between 60 to 140 (100 ± 2 x 20%) 1/20 chance the contract will be less than 60 or more than 140

11 What does an annual volatility tell us about movement over some other time period? monthly price movement? -10- weeky price movement? daily price movement? volatility t = volatility annual x v t

12 Daily volatility (standard deviation) Trading days in a year? Assume 256 trading days t = 1/256 v t = v1/256 = 1/16 volatility daily volatility annual / 16

13 volatility daily = 20% / 16 = 1¼% One trading day from now: 2/3 chance the contract will be between and (100 ± 1¼%) 19/20 chance the contract will be between and (100 ± 2 x 1¼%)

14 Weekly volatility: t = 1/52 v t = v1/52 1/7.2 volatility weekly = volatility annual / Monthly volatility: t = 1/12 v t = v1/12 1/3.5 volatility monthly = volatility annual / 3.5

15 stock = 68.50; volatility = 42.0% daily standard deviation? x 42% / = x 2.625% 1.80 weekly standard deviation? x 42% / 7.2 = x 5.83% 4.00

16 stock = 68.50; volatility = 42.0% daily standard deviation = Is 42% a reasonable volatility estimate? How often do you expect to see an occurrence greater than one standard deviation?

17 8 8 normal distribution lognormal distribution 0-16-

18 underlying price = call normal distribution 3.00 lognormal distribution put call = put = 3.00 Are the options mispriced? Could there is something wrong with the model?

19 future volatility: The volatility of the underlying contract over some period in the future historical volatility: The volatility -18- of the underlying contract over some period in the past forecast volatility: Someone s estimate of future volatility

20 implied volatility: derived from the prices of options -19- in the marketplace the marketplace s forecast of future volatility

21 -20- exercise price time to expiration underlying price interest rate 31%??? volatility 27% implied volatility pricing model 3.25 theoretical value 2.50

22 Option trading decisions often begin by comparing implied volatility = price -21- to future volatility = value historical volatility forecast volatility

23 Volatility Trading Initially buy underpriced options or strategies, or sell overpriced options or strategies Offset the option position by taking an opposing market position, delta neutral, in the underlying contract -22- Periodically buy or sell an appropriate amount of the underlying contract to remain delta neutral over the life of the strategy (dynamic hedging) At expiration liquidate the entire position In theory, when the position is closed out the total profit (or loss) should be approximately equal to the amount by which the options were originally mispriced.

24 Volatility Trading Risks You may have incorrectly -23- estimated the future volatility The model may be wrong

25 SPX Historical Volatility January August % 50-day volatility 250-day volatility 30% 25% % 15% 10% 5% Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02

26 Volatility characteristics -25- serial correlation in the absence of other data, the best volatility guess over the next time period is the volatility which occurred over the previous time period. mean reversion volatility tends to return to its historical average momentum a trend in volatility is likely to continue

27 40 Volatility Cones implied volatility (%) time to expiration (months)

28 Volatility Forecasting Methods (G)ARCH (generalized) autoregressive conditional -27- heteroscedasticity (V)ARIMA (vector) autoregressive integrated moving average

29 SPX Daily Price Changes: January August number of days: 3186 biggest up move: +5.73% (24 July 2002) biggest down move: -6.87% (27 October 1997) mean: % standard deviation: % volatility: 16.24% skewness: kurtosis: number of occurrences % -6% -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% daily price change (nearest 1/8 percent)

30 Volatility Skew: The tendency of options at different exercise prices to trade at different implied volatilities -29- A consequence of how people use options weaknesses in the pricing model

31 38 SPX June Implied Volatilities - 22 February