Binary options - PowerPoint PPT Presentation


Title: Binary options


1
Binary options
  • Giampaolo Gabbi

2
Definition
  • In finance, a binary option is a type of option
    where the payoff is either some fixed amount of
    some asset or nothing at all. The two main types
    of binary options are the cash-or-nothing binary
    option and the asset-or-nothing binary option.
    The cash-or-nothing binary option pays some fixed
    amount of cash if the option expires in-the-money
    while the asset-or-nothing pays the value of the
    underlying security.
  • Thus, the options are binary in nature because
    there are only two possible outcomes. They are
    also called all-or-nothing options, digital
    options (more common in forex/interest rate
    markets), and Fixed Return Options (FROs) (on the
    American Stock Exchange). Binary options are
    usually European-style options.
  • For example, a purchase is made of a binary
    cash-or-nothing call option on XYZ Corp's stock
    struck at 100 with a binary payoff of 1000.
    Then, if at the future maturity date, the stock
    is trading at or above 100, 1000 is received.
    If its stock is trading below 100, nothing is
    received.

3
Definition
  • Cash-or-nothing call
  • This pays out one unit of cash if the spot is
    above the strike at maturity
  • Cash-or-nothing put
  • This pays out one unit of cash if the spot is
    below the strike at maturity
  • Asset-or-nothing call
  • This pays out one unit of asset if the spot is
    above the strike at maturity
  • Asset-or-nothing put
  • This pays out one unit of asset if the spot is
    below the strike at maturity

4
Definition
  • A key difference compared to vanilla options for
    the option writer is that the maximum possible
    downside is known in advance.
  • This makes selling binary options a much more
    risk controlled and less negatively skewed
    strategy than the typical short volatility
    position.

5
Definition
6
Expressing a Range Trading View
  • A binary option spread, such as one set up by
    purchasing a binary call at a given strike versus
    selling a binary call at a higher strike, is the
    cleanest way of implementing the view that the
    underlying remains with a defined range.
  • Since a binary option is similar to a call
    spread, a binary call spread offers a risk reward
    similar to a condor.

7
Expressing a Range Trading View
  • For instance, with the SPX Aug12 1250 binary
    trading at 0.5 and the Aug12 1300 binary at 0.3,
    the 1250-1300 binary call spread costs 0.2 and
    pays out 1 if the index ends between 1250 and
    1300 as of the August expiration.
  • In comparison, the condor wins in a similar range
    but the boundaries are not as clearly defined

8
Definition
9
Market
  • Options are generally traded either OTC or on a
    national securities exchange registered with the
    Securities and Exchange Commission ("SEC") or on
    a contract market designated by the Commodity
    Futures Trading Commission ("CFTC"). A registered
    national securities exchange or designated
    contract market are hereinafter referred to
    collectively as "organized exchange. An
    instrument is described as trading OTC if it
    trades in some context other than on or through
    an organized exchange. OTC derivatives are
    understood to be specifically tailored to the
    needs and requirements of the end-user, and
    therefore, lack the standardization and
    transparency found on organized exchanges.
  • The majority of derivative products are traded
    OTC. In such a market, large financial
    institutions serve as derivatives dealers,
    customizing products for the needs of particular
    clients. Contract terms are negotiated between
    the parties, and typically each party has only
    their contra-party to look to for performance of
    the contract.

10
Market
  • Binary options have been traded for some time in
    an OTC environment between institutional traders
    but not on a national securities exchange.
    Contract markets have offered "binary options
    based on catastrophic events as well as on
    certain economic indexes such as the Consumer
    Price Index (CPI). In France, Germany and
    Austria, binary options have been traded OTC in a
    one-sided market between investors and an
    institution. The institution in these cases is
    the issuer of the contract and establishes, if
    applicable, the market for the binary option.
  • OTC binary options have several drawbacks and
    disadvantages. One disadvantage is that OTC
    binary options are typically offered by an
    institution on a non-fungible basis so that a
    customer can purchase the option only from the
    institution, and cannot easily resell to a third
    party because they are not standardized or traded
    on an exchange. As a result, OTC binary options,
    as compared to standardized exchange- traded
    options, lack important attributes of a trading
    market such as transparency and liquidity.

11
Non exchange-traded binary options
  • Binary option contracts have long been available
    Over-the-counter (OTC), i.e. sold directly by the
    issuer to the buyer. They were generally
    considered "exotic" instruments and there was no
    liquid market for trading these instruments
    between their issuance and expiration. They were
    often seen embedded in more complex option
    contracts.
  • Since mid-2008 binary options web-sites called
    binary option trading platforms have been
    offering a simplified version of exchange-traded
    binary options. It is estimated that around 30
    such platforms (including white label products)
    have been in operation as of January 2011

12
Exchange-traded binary options
  • In 2007, the Options Clearing Corporation
    proposed a rule change to allow binary options,
    and the Securities and Exchange Commission
    approved listing cash-or-nothing binary options
    in 2008.
  • In May 2008, the American Stock Exchange (Amex)
    launched exchange-traded European cash-or-nothing
    binary options, and the Chicago Board Options
    Exchange (CBOE) followed in June 2008. The
    standardization of binary options allows them to
    be exchange-traded with continuous quotations.
  • Amex offers binary options on some ETFs and a few
    highly liquid equities such as Citigroup and
    Google.
  • Amex calls binary options "Fixed Return Options"
    calls are named "Finish High" and puts are named
    "Finish Low". To reduce the threat of market
    manipulation of single stocks, Amex FROs use a
    "settlement index" defined as a volume-weighted
    average of trades on the expiration day.
  • CBOE offers binary options on the SP 500 (SPX)
    and the CBOE Volatility Index (VIX).
  • The tickers for these are BSZ and BVZ,
    respectively. CBOE only offers calls, as binary
    put options are trivial to create synthetically
    from binary call options. BSZ strikes are at
    5-point intervals and BVZ strikes are at 1-point
    intervals. The actual underlying to BSZ and BVZ
    are based on the opening prices of index basket
    members.
  • Both Amex and CBOE listed options have values
    between 0 and 1, with a multiplier of 100, and
    tick size of 0.01, and are cash settled

13
Example of a Binary Options Trade
  • A trader who thinks that the EUR/USD strike price
    will close at or above 1.2500 at 300 p.m. can
    buy a call option on that outcome. A trader who
    thinks that the EUR/USD strike price will close
    at or below 1.2500 at 300 p.m. can buy a put
    option or sell the contract.
  • At 200 p.m. the EUR/USD spot price is 1.2490.
    the trader believes this will increase, so he
    buys 10 call options for EUR/USD at or above
    1.2500 at 300 p.m. at a cost of 40 each.

14
Example of a Binary Options Trade
  • The risk involved in this trade is known. The
    traders gross profit/loss follows the all or
    nothing principle. He can lose all the money he
    invested, which in this case is 40 x 10 400,
    or make a gross profit of 100 x 10 1000. If
    the EUR/USD strike price will close at or above
    1.2500 at 300 p.m. the trader's net profit will
    be the payoff at expiry minus the cost of the
    option 1000 - 400 600.
  • The trader can also choose to liquidate (buy or
    sell to close) his position prior to expiration,
    at which point the option value is not guaranteed
    to be 100. The larger the gap between the spot
    price and the strike price, the value of the
    option decreases, as the option is less likely to
    expire in the money.
  • In this example, at 300 p.m. the spot has risen
    to 1.2505. The option has expired in the money
    and the gross payoff is 1000. The trader's net
    profit is 600

15
CBOE to list binary options on SP 500, VIX
16
CBOE Binary Options
  • CBOE Binary Options are contracts that have an
    "all-or-nothing" payout depending on the
    settlement price of the underlying broad-based
    index relative to the strike price of the binary
    option.
  • Binary Call Options pay either 1) a fixed cash
    settlement amount, if the underlying index
    settles at or above the strike price at
    expiration or 2) nothing at all, if the
    underlying index settles below the strike price
    at expiration.
  • Binary Put Options pay either 1) a fixed cash
    settlement amount, if the underlying index
    settles below the strike price at expiration or
    2) nothing at all, if the underlying index
    settles at or above the strike price at
    expiration.

17
CBOE Binary Options
18
CBOE Binary Options
19
CBOE Binary Options
20
CBOE Binary Options
21
Creating Contingent Premium Options
  • Contingent premium options are those in which the
    buyer pays a premium only if the option finishes
    in the money, and are commonly used as a
    cheapening mechanism.
  • A plain vanilla option in combination with a
    binary option whose payoff at expiration would
    equal the premium of the vanilla creates a
    structure similar to a contingent premium option.
  • Such a structure loses close to the strike in
    compensation for the lower premium but does not
    involve a premium payment if ones directional
    view happens to be incorrect.

22
Creating Contingent Premium Options
23
Binary Option value
  • For binary options with European exercise,
    pricing is relatively straightforward as an
    analytical expression is available in the Black
    Scholes world.
  • For the European binary call that pays off 1 at
    expiration T if the underlying S is over the
    strike K, the expiration payoff can be summarized
    as

24
Relationship to vanilla options' Greeks
  • Since a binary call is a mathematical derivative
    of a vanilla call with respect to strike, the
    price of a binary call has the same shape as the
    delta of a vanilla call,
  • The delta of a binary call has the same shape as
    the gamma of a vanilla call.

25
Interpretation of prices
  • In a prediction market, binary options are used
    to find out a population's best estimate of an
    event occurring - for example, a price of 0.65 on
    a binary option triggered by the Democratic
    candidate winning the next US Presidential
    election can be interpreted as an estimate of 65
    likelihood of him winning.
  • In financial markets, expected returns on a stock
    or other instrument are already priced into the
    stock. However, a binary options market provides
    other information. Just as the regular options
    market reveals the market's estimate of variance
    (volatility), i.e. the second moment, a binary
    options market reveals the market's estimate of
    skew, i.e. the third moment.
  • A portfolio of binary options can also be used to
    synthetically recreate (or valuate) any other
    option (analogous to integration).

26
Interpretation of prices (Intrade)
27
Interpretation of prices
28
Replication with Option Spreads
  • The simplest listed instrument available that
    reasonably mimics the payoff of a binary call
    option is a call spread. The ideal hedge would be
    a spread of infinitesimal width, but even with
    the strike intervals available in listed options,
    replication of a binary is reasonably accurate
    except very close to expiration.
  • The imperfectness of such a hedge is a
    consequence of the non-zero probability of the
    underlying finishing between the two strikes.
    Since the 5-point interval between strikes for
    near term SPX options is much tighter than the
    1-point interval between VIX option strikes, this
    theoretical hedge implies a narrower range for
    the bid-offer spread on SPX binaries.

29
Replication with Option Spreads
  • To illustrate the construction of a replicating
    call spread, we consider the 1300 strike binary
    call option on the SPX expiring in Aug11. A
    potential hedge for this is the 1295-1300 call
    spread on SPX with the same expiration.
  • Since the binary pays off 1 (corresponding to a
    payoff of 100 per contract) if SPX closes at or
    above 1300 at expiration, compared to a 5 payoff
    for the spread, we need 0.2 units of the call
    spread for each binary option.

30
Replication with Option Spreads
  • Next figure illustrates how the price of a binary
    option varies as a function of the underlying as
    expiration approaches.
  • With several months to go in the life of the
    option, the mark to market of the option is not
    unlike that of the underlying itself.
  • With about a week to expiration, it resembles a
    call spread with a similar time to expiration.
  • However, very close to expiration, the binary
    becomes very convex just below the strike and is
    highly negatively convex at levels slightly above
    the strike.

31
Replication with Option Spreads
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Binary options

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Title: Binary options


1
Binary options
  • Giampaolo Gabbi

2
Definition
  • In finance, a binary option is a type of option
    where the payoff is either some fixed amount of
    some asset or nothing at all. The two main types
    of binary options are the cash-or-nothing binary
    option and the asset-or-nothing binary option.
    The cash-or-nothing binary option pays some fixed
    amount of cash if the option expires in-the-money
    while the asset-or-nothing pays the value of the
    underlying security.
  • Thus, the options are binary in nature because
    there are only two possible outcomes. They are
    also called all-or-nothing options, digital
    options (more common in forex/interest rate
    markets), and Fixed Return Options (FROs) (on the
    American Stock Exchange). Binary options are
    usually European-style options.
  • For example, a purchase is made of a binary
    cash-or-nothing call option on XYZ Corp's stock
    struck at 100 with a binary payoff of 1000.
    Then, if at the future maturity date, the stock
    is trading at or above 100, 1000 is received.
    If its stock is trading below 100, nothing is
    received.

3
Definition
  • Cash-or-nothing call
  • This pays out one unit of cash if the spot is
    above the strike at maturity
  • Cash-or-nothing put
  • This pays out one unit of cash if the spot is
    below the strike at maturity
  • Asset-or-nothing call
  • This pays out one unit of asset if the spot is
    above the strike at maturity
  • Asset-or-nothing put
  • This pays out one unit of asset if the spot is
    below the strike at maturity

4
Definition
  • A key difference compared to vanilla options for
    the option writer is that the maximum possible
    downside is known in advance.
  • This makes selling binary options a much more
    risk controlled and less negatively skewed
    strategy than the typical short volatility
    position.

5
Definition
6
Expressing a Range Trading View
  • A binary option spread, such as one set up by
    purchasing a binary call at a given strike versus
    selling a binary call at a higher strike, is the
    cleanest way of implementing the view that the
    underlying remains with a defined range.
  • Since a binary option is similar to a call
    spread, a binary call spread offers a risk reward
    similar to a condor.

7
Expressing a Range Trading View
  • For instance, with the SPX Aug12 1250 binary
    trading at 0.5 and the Aug12 1300 binary at 0.3,
    the 1250-1300 binary call spread costs 0.2 and
    pays out 1 if the index ends between 1250 and
    1300 as of the August expiration.
  • In comparison, the condor wins in a similar range
    but the boundaries are not as clearly defined

8
Definition
9
Market
  • Options are generally traded either OTC or on a
    national securities exchange registered with the
    Securities and Exchange Commission ("SEC") or on
    a contract market designated by the Commodity
    Futures Trading Commission ("CFTC"). A registered
    national securities exchange or designated
    contract market are hereinafter referred to
    collectively as "organized exchange. An
    instrument is described as trading OTC if it
    trades in some context other than on or through
    an organized exchange. OTC derivatives are
    understood to be specifically tailored to the
    needs and requirements of the end-user, and
    therefore, lack the standardization and
    transparency found on organized exchanges.
  • The majority of derivative products are traded
    OTC. In such a market, large financial
    institutions serve as derivatives dealers,
    customizing products for the needs of particular
    clients. Contract terms are negotiated between
    the parties, and typically each party has only
    their contra-party to look to for performance of
    the contract.

10
Market
  • Binary options have been traded for some time in
    an OTC environment between institutional traders
    but not on a national securities exchange.
    Contract markets have offered "binary options
    based on catastrophic events as well as on
    certain economic indexes such as the Consumer
    Price Index (CPI). In France, Germany and
    Austria, binary options have been traded OTC in a
    one-sided market between investors and an
    institution. The institution in these cases is
    the issuer of the contract and establishes, if
    applicable, the market for the binary option.
  • OTC binary options have several drawbacks and
    disadvantages. One disadvantage is that OTC
    binary options are typically offered by an
    institution on a non-fungible basis so that a
    customer can purchase the option only from the
    institution, and cannot easily resell to a third
    party because they are not standardized or traded
    on an exchange. As a result, OTC binary options,
    as compared to standardized exchange- traded
    options, lack important attributes of a trading
    market such as transparency and liquidity.

11
Non exchange-traded binary options
  • Binary option contracts have long been available
    Over-the-counter (OTC), i.e. sold directly by the
    issuer to the buyer. They were generally
    considered "exotic" instruments and there was no
    liquid market for trading these instruments
    between their issuance and expiration. They were
    often seen embedded in more complex option
    contracts.
  • Since mid-2008 binary options web-sites called
    binary option trading platforms have been
    offering a simplified version of exchange-traded
    binary options. It is estimated that around 30
    such platforms (including white label products)
    have been in operation as of January 2011

12
Exchange-traded binary options
  • In 2007, the Options Clearing Corporation
    proposed a rule change to allow binary options,
    and the Securities and Exchange Commission
    approved listing cash-or-nothing binary options
    in 2008.
  • In May 2008, the American Stock Exchange (Amex)
    launched exchange-traded European cash-or-nothing
    binary options, and the Chicago Board Options
    Exchange (CBOE) followed in June 2008. The
    standardization of binary options allows them to
    be exchange-traded with continuous quotations.
  • Amex offers binary options on some ETFs and a few
    highly liquid equities such as Citigroup and
    Google.
  • Amex calls binary options "Fixed Return Options"
    calls are named "Finish High" and puts are named
    "Finish Low". To reduce the threat of market
    manipulation of single stocks, Amex FROs use a
    "settlement index" defined as a volume-weighted
    average of trades on the expiration day.
  • CBOE offers binary options on the SP 500 (SPX)
    and the CBOE Volatility Index (VIX).
  • The tickers for these are BSZ and BVZ,
    respectively. CBOE only offers calls, as binary
    put options are trivial to create synthetically
    from binary call options. BSZ strikes are at
    5-point intervals and BVZ strikes are at 1-point
    intervals. The actual underlying to BSZ and BVZ
    are based on the opening prices of index basket
    members.
  • Both Amex and CBOE listed options have values
    between 0 and 1, with a multiplier of 100, and
    tick size of 0.01, and are cash settled

13
Example of a Binary Options Trade
  • A trader who thinks that the EUR/USD strike price
    will close at or above 1.2500 at 300 p.m. can
    buy a call option on that outcome. A trader who
    thinks that the EUR/USD strike price will close
    at or below 1.2500 at 300 p.m. can buy a put
    option or sell the contract.
  • At 200 p.m. the EUR/USD spot price is 1.2490.
    the trader believes this will increase, so he
    buys 10 call options for EUR/USD at or above
    1.2500 at 300 p.m. at a cost of 40 each.

14
Example of a Binary Options Trade
  • The risk involved in this trade is known. The
    traders gross profit/loss follows the all or
    nothing principle. He can lose all the money he
    invested, which in this case is 40 x 10 400,
    or make a gross profit of 100 x 10 1000. If
    the EUR/USD strike price will close at or above
    1.2500 at 300 p.m. the trader's net profit will
    be the payoff at expiry minus the cost of the
    option 1000 - 400 600.
  • The trader can also choose to liquidate (buy or
    sell to close) his position prior to expiration,
    at which point the option value is not guaranteed
    to be 100. The larger the gap between the spot
    price and the strike price, the value of the
    option decreases, as the option is less likely to
    expire in the money.
  • In this example, at 300 p.m. the spot has risen
    to 1.2505. The option has expired in the money
    and the gross payoff is 1000. The trader's net
    profit is 600

15
CBOE to list binary options on SP 500, VIX
16
CBOE Binary Options
  • CBOE Binary Options are contracts that have an
    "all-or-nothing" payout depending on the
    settlement price of the underlying broad-based
    index relative to the strike price of the binary
    option.
  • Binary Call Options pay either 1) a fixed cash
    settlement amount, if the underlying index
    settles at or above the strike price at
    expiration or 2) nothing at all, if the
    underlying index settles below the strike price
    at expiration.
  • Binary Put Options pay either 1) a fixed cash
    settlement amount, if the underlying index
    settles below the strike price at expiration or
    2) nothing at all, if the underlying index
    settles at or above the strike price at
    expiration.

17
CBOE Binary Options
18
CBOE Binary Options
19
CBOE Binary Options
20
CBOE Binary Options
21
Creating Contingent Premium Options
  • Contingent premium options are those in which the
    buyer pays a premium only if the option finishes
    in the money, and are commonly used as a
    cheapening mechanism.
  • A plain vanilla option in combination with a
    binary option whose payoff at expiration would
    equal the premium of the vanilla creates a
    structure similar to a contingent premium option.
  • Such a structure loses close to the strike in
    compensation for the lower premium but does not
    involve a premium payment if ones directional
    view happens to be incorrect.

22
Creating Contingent Premium Options
23
Binary Option value
  • For binary options with European exercise,
    pricing is relatively straightforward as an
    analytical expression is available in the Black
    Scholes world.
  • For the European binary call that pays off 1 at
    expiration T if the underlying S is over the
    strike K, the expiration payoff can be summarized
    as

24
Relationship to vanilla options' Greeks
  • Since a binary call is a mathematical derivative
    of a vanilla call with respect to strike, the
    price of a binary call has the same shape as the
    delta of a vanilla call,
  • The delta of a binary call has the same shape as
    the gamma of a vanilla call.

25
Interpretation of prices
  • In a prediction market, binary options are used
    to find out a population's best estimate of an
    event occurring - for example, a price of 0.65 on
    a binary option triggered by the Democratic
    candidate winning the next US Presidential
    election can be interpreted as an estimate of 65
    likelihood of him winning.
  • In financial markets, expected returns on a stock
    or other instrument are already priced into the
    stock. However, a binary options market provides
    other information. Just as the regular options
    market reveals the market's estimate of variance
    (volatility), i.e. the second moment, a binary
    options market reveals the market's estimate of
    skew, i.e. the third moment.
  • A portfolio of binary options can also be used to
    synthetically recreate (or valuate) any other
    option (analogous to integration).

26
Interpretation of prices (Intrade)
27
Interpretation of prices
28
Replication with Option Spreads
  • The simplest listed instrument available that
    reasonably mimics the payoff of a binary call
    option is a call spread. The ideal hedge would be
    a spread of infinitesimal width, but even with
    the strike intervals available in listed options,
    replication of a binary is reasonably accurate
    except very close to expiration.
  • The imperfectness of such a hedge is a
    consequence of the non-zero probability of the
    underlying finishing between the two strikes.
    Since the 5-point interval between strikes for
    near term SPX options is much tighter than the
    1-point interval between VIX option strikes, this
    theoretical hedge implies a narrower range for
    the bid-offer spread on SPX binaries.

29
Replication with Option Spreads
  • To illustrate the construction of a replicating
    call spread, we consider the 1300 strike binary
    call option on the SPX expiring in Aug11. A
    potential hedge for this is the 1295-1300 call
    spread on SPX with the same expiration.
  • Since the binary pays off 1 (corresponding to a
    payoff of 100 per contract) if SPX closes at or
    above 1300 at expiration, compared to a 5 payoff
    for the spread, we need 0.2 units of the call
    spread for each binary option.

30
Replication with Option Spreads
  • Next figure illustrates how the price of a binary
    option varies as a function of the underlying as
    expiration approaches.
  • With several months to go in the life of the
    option, the mark to market of the option is not
    unlike that of the underlying itself.
  • With about a week to expiration, it resembles a
    call spread with a similar time to expiration.
  • However, very close to expiration, the binary
    becomes very convex just below the strike and is
    highly negatively convex at levels slightly above
    the strike.

31
Replication with Option Spreads
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