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Transcript of CBOE Risk Management Conference March 2013 Volatility · PDF fileCBOE Risk Management...

  • CBOE Risk Management Conference March 2013

    Volatility Trading

    Sheldon Natenberg Chicago Trading Co.

    440 South LaSalle St. Chicago, IL 60605 (312) 863-8004

    sheldon.natenberg@chicagotrading.com

  • Volatility the degree to which the price of a contract tends to fluctuate over time

    Annualized standard deviation

    of percent (logarithmic) price changes.

    The price changes are assumed to be normally distributed and

    continuously compounded.

  • The volatility of the underlying contract over some period of time

    realized volatility:

    derived from the prices of options in the marketplace

    implied volatility: The marketplaces consensus forecast of future volatility;

    (historical volatility, future volatility)

  • pricing model

    theoretical value

    5.50

    6.75

    exercise price

    time to expiration

    underlying price

    interest rate

    volatility 27% volatility

    ??? 31%

    implied volatility

  • today

    realized volatility

    backward looking

    (what has occurred)

    implied volatility

    forward looking

    (what the marketplace thinks will occur)

    implied volatility = price

    realized volatility = value

  • Strategies which attempt to capture the value of realized volatility

    Volatility Trading

    Strategies which attempt to capture changes in implied volatility

    How can we capture volatility value?

    implied volatility = 20%

    future volatility = 25%

    (gamma strategies)

    (vega strategies)

  • buy a call option

    theo

    reti

    cal v

    alu

    e

    underlying price

    exercise price

    value at expiration?

    value prior to expiration?

  • theo

    reti

    cal v

    alu

    e

    underlying price

    current underlying

    price

    determine the options delta

    (C)

    C

    take an opposing delta position in the underlying contract

    (-C)

    -C

    Delta Neutral

  • theo

    reti

    cal v

    alu

    e

    underlying price

    C -C

    Due to the options curvature, as market conditions change the position will become unhedged.

    current underlying

    price

    { unhedged

    amount

  • theo

    reti

    cal v

    alu

    e

    underlying price

    Determine the new delta of the option.

    Rehedge the position to return to delta neutral

    current underlying

    price

    new C

    new -C

  • theo

    reti

    cal v

    alu

    e

    underlying price

    current underlying

    price

    } unhedged

    amount

    new C

    new -C

  • theo

    reti

    cal v

    alu

    e

    underlying price

    current underlying

    price

    new C

    new -C

    Dynamic Hedging Continue the rehedging process throughout the life of the option.

  • Suppose we add up all the profit opportunities over the life of the option which result from the rehedging process.

    the options theoretical value

    The rehedging process is a type of statistical arbitrage.

    What should this equal?

    Each time the position becomes unhedged there is a potential profit opportunity. We can capture this profit by rehedging the position.

  • Volatility Trading

    1. Compare implied volatility to an expected future realized volatility

    2. If implied is lower, buy options; if implied is higher, sell options

    3. Hedge the position, delta neutral, against the underlying contract

    4. As the underlying price moves rehedge the position in order to remain delta neutral (dynamic hedging)

    5. At expiration close out the entire position

  • It sounds good in theory, but ..

    2. It may not always be possible to dynamically hedge an option position.

    3. The volatility sensitivity of an option is not constant. As time passes, or as the underlying price changes in relation to the options exercise price, the option may become either more or less sensitive to changes in volatility.

    4. Percent price changes in the real world may not be normally distributed.

    1. The transaction costs of dynamically hedging a position may affect the expected results.

  • diffusion process

  • Dynamic hedging is not possible if the market gaps

    jump diffusion process

  • 25 January 2013 S&P 500 = 1502.96

    June Futures = 1489.00

    1450 call

    1500 call

    1550 call

    increase implied

    13.92%

    11.24%

    9.45%

    8.48

    10.91

    8.12

    March

    March Futures = 1495.70 7 weeks

    21 weeks

    price 10% 15%

    58.15

    22.50

    4.15

    51.63

    19.80

    4.89

    60.11

    30.71

    13.01

    1450 call

    1500 call

    1550 call

    increase implied

    14.77%

    13.23%

    11.86%

    17.41

    18.78

    16.79

    June price 15% 20%

    76.45

    44.65

    21.40

    59.78

    32.52

    15.38

    77.28

    51.30

    32.17

  • 90

    95

    100

    105

    110

    Whats the value of the 100 call?

    time

  • 90

    95

    100

    105

    110

    Whats the value of the 100 call?

    time

  • Time to expiration = 107 days Volatility = 32.00% Forward price = 100.00

    100 C/P

    constant volatility

    rising volatility

    falling volatility

    6.90

    4.93

    8.10

    80 P

    .72

    1.03

    .43

    120 C

    1.43

    1.89

    .99

  • nu

    mb

    er o

    f o

    ccu

    rren

    ces

    daily price change (nearest 1/4 percent)

    S&P 500 Daily Price Changes: January 2003 through December 2012

    number of days: 2535 biggest up move: +11.58% (13 October 2008) biggest down move: -9.03% (15 October 2008) mean: +.0296% standard deviation: 1.31% volatility: 20.81% skewness: -.0536 kurtosis: +10.4150

    0

    25

    50

    75

    100

    125

    150

    175

    200

    225

    250

    275

    300

    325

    350

    375

    -10% -8% -6% -4% -2% 0% 2% 4% 6% 8% 10% 12%

  • Volatility Products

    implied volatility futures a contract which at expiration settles into the implied volatility of options on an underlying contract

    realized volatility futures a contract which at expiration settles into the realized volatility of an index

    Is it possible to trade volatility without all the problems associated with dynamic hedging?

    (VIX)

  • Volatility Futures Applications

    Speculation

    Hedging a volatility position

    Hedging a market position (inverse correlation between market direction and volatility)

    Hedging an indirect volatility position

    Trading volume

    Liquidity

    A volatility-sensitive strategy

  • Daily VIX Change vs. SPX Change: January 2006 December 2012

    Correlation = - .7539

    -40%

    -20%

    0%

    20%

    40%

    60%

    80%

    -10% -5% 0% 5% 10% 15%

    Percent Change in SPX

    Perc

    en

    t C

    han

    ge i

    n V

    IX

  • Volatility may affect the total returns to an investment or portfolio management strategy.

    year 1 returns

    year 2 returns

    year 3 returns

    average return

    +25%

    total return

    -20% +10% +25%

    +29% -34% +13% +44%

    +25%

    +22.6%

    +16% -6% +9% +17% +27.6%

    +8.5% +8.5% +8.5% +8.5% +27.7%