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					Exotic Options and
 Structured Notes
    Types of Exotics
• Package               •   Binary options
• Nonstandard American •    Lookback options
  options               •   Shout options
• Forward start options •   Asian options
• Compound options      •   Options to exchange
• Chooser options           one asset for another
• Barrier options       •   Options involving
                            several assets
        Packages (page 529)

• Portfolios of standard options
• Examples from Chapter 10: bull
  spreads, bear spreads, straddles, etc
• Often structured to have zero cost
• One popular package is a range forward
      Non-Standard American
          Options (page 530)
• Exercisable only on specific dates
• Early exercise allowed during only
  part of life (initial “lock out” period)
• Strike price changes over the life
  (warrants, convertibles)
• Perpetual American options
Forward Start Options (page 531)

• Option starts at a future time, T1
• Most common in employee stock option
• Often structured so that strike price
  equals asset price at time T1
    Compound Option (page 531)
• Option to buy or sell an option
  – Call on call
  – Put on call
  – Call on put
  – Put on put
• Can be valued analytically
• Price is quite low compared with a
  regular option
    Chooser Option “As You Like It”
                     (page 532)

• Option starts at time 0, matures at T2
• At T1 (0 < T1 < T2) buyer chooses whether it
  is a put or call
• This is a package!
Chooser Option as a Package

At time T1 the value is max(c, p )
From put - call parity
               r (T2 T1 )              q (T2 T1 )
p ce                        K  S1e
The value at time T1 is therefore
       q (T2 T1 )                  ( r  q )(T2 T1 )
ce                   max(0, Ke                             S1 )
This is a call maturing at time T2 plus
a put maturing at time T1
        Barrier Options (page 535)
• Option comes into existence only if stock
  price hits barrier before option maturity
  – ‘In’ options
• Option dies if stock price hits barrier
  before option maturity
  – ‘Out’ options
      Barrier Options (continued)
• Stock price must hit barrier from below
  – ‘Up’ options
• Stock price must hit barrier from above
  – ‘Down’ options
• Option may be a put or a call
• Eight possible combinations
      Barrier Options (continued)
  Depending on the stock price observation
frequencies, there are two types of barrier
• Continuous monitoring barrier options
• Discrete monitoring barrier options
  For knock-out (knock-in) options, discrete
monitoring barrier options are more
expensive (cheaper) than continuous
monitoring barrier options.
      In-Out Parity Relations
c = cui + cuo
c = cdi + cdo
p = pui + puo
p = pdi + pdo
       Binary Options          (page 535)

• Cash-or-nothing: pays Q if ST > K,
  otherwise pays nothing.
  – Value = e–rT Q N(d2)
• Asset-or-nothing: pays ST if ST > K,
  otherwise pays nothing.
  – Value = S0 N(d1)
項 目         台指選擇權       二元台指選擇權    S&P 500指數選擇 二元S&P 500指數
                                         權        選擇權
交易標 臺灣證券交易所發行量加權       同TXO       S&P 500指數    同SPX
的   股價指數
中文簡 臺指選擇權              二元臺指選擇權    S&P 500指數選擇   二元S&P 500指數
稱   (臺指買權、臺指賣權)        (二元臺指買權、   權             選擇權(買權、賣
                       二元臺指賣權)    (買權、賣權)       權)

英文代 TXO            TXB            SPX           BSZ
履約型 歐式(僅能於到期日行使權利) 同TXO           歐式(僅能於到期      同SPX
態                                 日行使權利)
契約乘 指數每點新臺幣50元         同TXO       指數每點美金100     同SPX
數                                 元
到期月 自交易當月起連續三個月份, 同TXO            自交易當月起連續 同SPX
份   另加上三月、六月、九月、                  三個月份,另加上
    十二月中二個接續的季月,                  三月、六月、九月、
    總共有五個月份的契約在市                  十二月中三個接續
    場交易                           的季月,總共有六
履約價      履約價格未達3000點: 同TXO         近月份契約5點,所有契約皆為5點
格間距       近月契約為50點,季月               遠月份契約25
          契約為100點                   點
         履約價格3000點以上,
         履約價格8000點以上,
         履約價格12000點以上:
        Decomposition of a Call
Long Asset-or-Nothing option
Short Cash-or-Nothing option where payoff
  is K

Value = S0 N(d1) – e–rT KN(d2)
     Lookback Options (page 536)
• Lookback call pays ST – Smin at time T
• Allows buyer to buy stock at lowest
  observed price in some interval of time
• Lookback put pays Smax– ST at time T
• Allows buyer to sell stock at highest
  observed price in some interval of time
• Analytic solution
     Shout Options (page 537)

• Buyer can ‘shout’ once during option life
• Final payoff is either
  – Usual option payoff, max(ST – K, 0), or
  – Intrinsic value at time of shout, St – K
• Payoff: max(ST – St , 0) + St – K
• Similar to lookback option but cheaper
• How can a binomial tree be used to
  value a shout option?
         Asian Options (page 538)
• Payoff related to average stock price
• Average Price options pay:
  – Call: max(Save – K, 0)
  – Put: max(K – Save , 0)
• Average Strike options pay:
  – Call: max(ST – Save , 0)
  – Put: max(Save – ST , 0)
              Asian Options
• No analytic solution
• Can be valued by assuming (as an
  approximation) that the average stock price is
  lognormally distributed
• Asian options are usually (not always?) cheaper
  than the plain vanilla European options
• Asian options are good instruments for hedging
  average price risk
     Exchange Options (page 540)
• Option to exchange one asset for
• For example, an option to exchange
  one unit of U for one unit of V
• Payoff is max(VT – UT, 0)
• Widely used in mutual fund industry for
  the design of management fee (especially
  for hedge fund)
       Basket Options (page 541)
• A basket option is an option to buy or sell
  a portfolio of assets
• This can be valued by calculating the first
  two moments of the value of the basket
  and then assuming it is lognormal
Options on Foreign Asset
Option valuation under domestic risk reutral measure
Option valuation under domestic risk reutral measure
         Self Test: Are you able to
       answer the following question?
   Compare the expensiveness of the following options and explain
your answer.
Self Test
     Structured Notes (結構債)
• Structured notes are one of the most
  complicated financial products in the
  market. They are so complicated that only
  the expert can understand their risk-return
  characteristics. Therefore they are suitable
  for trading by individual investors!!
    What are structured notes?
• Unlike straight derivatives whose entire value is
  dependent on some underlying security, index or
  rate, structured securities are hybrids, having
  components of straight debt instruments and
  derivatives embedded.
• Rather than paying a straight fixed or floating
  coupon, these instruments’ interest payments
  are tailored to a myriad of possible indices or
    What are structured notes?
• In addition to the interest payments, the
  securities’ redemption value and final maturity
  can also be affected by the derivatives
  embedded in structured notes.
• Most structures contain embedded options,
  generally sold by the investor to the issuer.
  These options are primarily in the form of caps,
  floors, or call features.
• The identification, pricing and analysis of these
  options give structured notes their complexity.
     Why have structured notes
         become popular?
• Structured notes, whose cash flows and market
  values are linked to one or more benchmarks,
  offer the potential for greater returns than
  prevailing market rates.
• The fact that most structured notes are issued
  by Government Sponsored Enterprises (GSEs)
  means that credit risk - the risk that the issuer
  will default - is minimal.
      Why have structured notes
          become popular?
• Another attractive feature of such securities is
  that they can serve to hedge unique risks faced
  by the investor.
• For example, a company which is long (owns)
  Japanese yen is exposed to the risk of yen
  depreciation. The FHLB issued a one-year
  structured range note which accrued interest
  daily at 7% if the JPY/US$ > 108.50 or at 0% if
  the JPY/US$≦108.50. If the yen depreciates, the
  note accrues interest at an above-market rate.
     Why have structured notes
         become popular?
• A third reason for purchasing structured
  notes is to take a market view.
• The expected rate of return of structured
  notes seems “attractive” when the market
  interest rate (deposit rate) is low.
    Some Common Structures And
          Attendant Risks
•   Step-Ups/Multi-Steps
•   Index-Amortizing Notes
•   Dual Index Notes
•   De-Leveraged and Leveraged Floaters
•   Range Notes
•   Target Redemption Notes
•   Inverse Floaters
•   Index Floaters
• Step-up notes/bonds are generally callable by
  the issuer, pay an initial yield higher than a
  comparable maturity Treasury security, and
  have coupons which rise — or “step up” —at
  predetermined points in time if the issue is called.
• If the coupon has more than one adjustment
  period, it is referred to as a multi-step.
• An example is an FHLB 5-year note issued in
  May of 1994. The issue is callable in 2 years and
  the coupons increase according to the following
        6.25% for year 1 (May 1994)
        6.50% for year 2 (May 1995)
        7.00% for year 3 (May 1996)
        8.20% for year 4 (May 1997)
        9.25% for year 5 (May 1998)
• Since the first call date is May 1996 (and every
  coupon date thereafter), only the first two
  coupon levels are guaranteed.
       Index-Amortizing Notes
• An index-amortizing note (IAN) is a form of
  structured note for which the outstanding
  principal - or note - amortizes according to a
  predetermined schedule.
• The predetermined amortization schedule is
  linked to the level of a designated index (LIBOR,
  CMT, the prepayment rate of a specified
  passthrough pool, etc.).
       Index-Amortizing Notes
• Thus, the timing of future cashflows, and hence
  the average life and yield to maturity of the note,
  become uncertain.
• The IAN does have a stated maximum maturity
  date, however, at which time all remaining
  principal balance is retired.
       Index-Amortizing Notes:
• To illustrate, consider an IAN issued by the
  FHLB on September 15, 1994 and with a
  maturity date of September 15, 1999.
• The coupon resets quarterly at [3-month LIBOR
  + 42 basis points].
• However, the coupon can never reset higher
  than 50 basis points above the previous coupon,
  and has a lifetime cap of 9.5%.
         Index-Amortizing Notes:
• Additionally, there is an initial “lock out” period of
  one year, during which time the entire principal
  remains outstanding and the amortization
  schedule is irrelevant.
• Beginning September 15, 1995, the outstanding
  principal is redeemed in whole or in part subject
  to the schedule, and paydown of principal may
  continue quarterly thereafter.
  Index-Amortizing Notes:
 9% or greater        100.00%
   8.75%               96.25%
   8.50%               92.50%
   8.00%               85.00%
   7.75%               80.00%
   7.50%               75.00%
   7.00%               65.00%
   6.50%               32.50%
   6.25%               16.25%
  6% or less            0.00%
            Dual Index Notes
• A dual index note is a security whose coupon is
  tied to the spread between two market indices.
• Typical indices used to structure payoffs to these
  notes are: the prime rate, LIBOR, and CMT
  yields of different maturities.
• A purchaser of this type of security is typically
  making an assumption about the future shape of
  the yield curve.
• These notes can be structured to reward the
  investors in either steepening or flattening yield
  curve environments.
            Dual Index Notes
• This feature explains an alternative designation
  for dual index notes: yield curve anticipation
  notes (YCAN).
• However, these notes can also be tied to
  indices other than interest rates such as foreign
  exchange rates, stock indices or commodity
            Dual Index Notes
• An example of a note which would appeal to
  investors with expectations of a flattening yield
  curve would be one with a coupon that floats at:
  [the 5 year CMT-the 10 year CMT+ a designated

• Based on this formula, the coupon will increase
  if the yield curve flattens between the 5 year and
  the 10 year maturities.
            Dual Index Notes
• Alternatively, a yield curve steepening play
  would be an issue that floats at:
  [the 10 year CMT-the 5 year CMT+ a designated

• In this case, coupons would increase as the
  spread between the long and medium term
  indices widens.
    De-Leveraged and Leveraged
• De-leveraged and leveraged floating rate notes
  give investors the opportunity to receive an
  above-market initial yield and tie subsequent
  coupon adjustments to a specific point on the
  yield curve.
• A leveraged note’ s coupon will adjust by a
  multiple of a change in the relevant interest rate,
  eg, [1.25 x LIBOR + 100 basis points].
• Conversely, a de-leveraged security’ s coupon
  adjusts by a fraction of the change in rates, eg,
  [.50 x 10-year CMT + 100 basis points].
 De-Leveraged and Leveraged
 One reported source of BankAmerica’s troubles
with their Pacific Horizon Money Funds in 1994
(BankAmerica injected about $68 million to
protect the fund’s net asset value) was their
holding of $40 million of a 5-year SLMA note,
issued in March 1993.
    De-Leveraged and Leveraged
• The first year’ s coupon was 4.50% after which
  the coupon reset quarterly according to the
  the greater of 4.125% or
   [50% x 10-year Treasury rate + 125 basis points].
               Range Notes
• Range notes (also called accrual notes) accrue
  interest daily at a set coupon which is tied to an
• Most range notes have two coupon levels; the
  higher accrual rate is for the period that the
  index remains within a designated range, the
  lower rate is used during periods that the index
  falls outside the range.
• This lower level may be zero.
               Range Notes
• Most range notes reference the index daily such
  that interest may accrue at 7% on one day and
  at 2% on the following day, if the underlying
  index crosses in and out of the range.
• However, they can also reference the index
  monthly, quarterly or only once over the note’s
• If the note only references quarterly, then the
  index’s relationship to the range matters only on
  the quarterly reset date.
               Range Notes
• With the purchase of one of these notes, the
  investor has sold a series of digital (or binary)
  options; a call struck at the high end of the range
  and a put struck at the low end of the range.
• This means that the accrual rate is strictly
  defined and the magnitude of movement outside
  the range is inconsequential.
• The narrower the range, the greater the coupon
  enhancement over a like instrument.
• In some cases, the range varies each year that
  the security is outstanding.
                Range Notes
• An example of a range note is depicted bellow

  Coupon   5%

                                    6-month LIBOR
                   3.125%   3.75%
               Range Notes
• For ease of calculation, we will illustrate a note
  which only references the index quarterly, rather
  than daily.
• In this case, the coupon remains fixed
  throughout the entire quarter based on the level
  of the index on the reset date.
• This note was offered on April 28, 1993 and
  matures on April 28, 1995.
• The coupon for the first six months was 3.51%
  and coupons reset semi-annually.
                Range Notes
• Further coupon levels are tied to 6-month LIBOR
  with the following range:

If (3.125%≦ 6 month LIBOR ≦ 3.75%)
  then Coupon rate= 5%
If (3.125%> 6 month LIBOR or
    6 month LIBOR > 3.75%)
   then Coupon rate= 2%
      Target Redemption Notes
• The time to maturity of a target redemption
  depends on when the target rate of return (e.g.
  25%) is met.
• A target redemption note was offered on July 19,
  2003 and matures on July 18, 2013.
• The coupon for the first six months was 5% and
  coupons reset semi-annually.
       Target Redemption Notes
• Further daily coupon levels are tied to 6-month
   LIBOR with the following range:
If (6 month LIBOR ≦ 3.75%)
  then Coupon rate= 5%
Otherwise Coupon rate= 0%

• The note will mature early when the aggregate
  coupon equals 10% of the face value.
 Min maturity=1 year, max maturity=10 years
            Inverse Floaters
• An inverse floater is a note structured so that its
  coupon varies inversely with a designated index.
• Simply stated, as the index (eg, LIBOR, COFI)
  falls, the coupon on the note rises, and vice
• Inverse floaters can be structured using any
  index, and are present not only in the agency
  structured note arena but also in mortgage
  backed securities.
            Inverse Floaters
• FNMA issued an inverse floater in 1992 which is
  tied to the level of COFI. The coupon floats at
  [11.95% - COFI], resetting monthly and paying
• It matures 11/16/95. Based on the formula, the
  note’s coupon will rise as COFI falls, and fall as
  COFI rises.
• The most recent coupon level was 8.09%, set
  on 9/16/94 when COFI was 3.86%.
             Index Floaters
• An index floater usually has a very simple
  structure, eg, [prime - fixed spread] or [3 month
  LIBOR + fixed spread].
• Investors in such securities make assumptions
  about expected movements in the index relative
  to other like-maturity instruments.
             Index Floaters
•   For example, a coupon of [prime - 263 basis
    points] with quarterly reset dates would
    outperform a 3 month Treasury only for as long
    as the prime rate remained at least 263 basis
    points higher than the 3 month rate.
    (As of October 1994, the spread was roughly
    275 basis points.)
              Index Floaters
• For investors who believed that short rates might
  begin to trend downward before the prime rate
  or that rates would remain pretty stable for a
  while, this structure would offer a slightly better
  return than a simple 3 month T-bill.
• 連結標的:MSCI台灣指數(TWY Index)、
  韓國KOSPI 200指數(KOSPI2 Index)、
  MSCI新加坡指數(SGY Index)
• 計價幣別:台幣
• 產品天期:2年
• 保本比率:到期65%保本產品


• 變動配息:每日比價,每月配息
      7%(台幣/年化)x n/N
• 提前到期事件:自進場後第4個月開始,
•   下限價格:期初價格的65%
•   到期日返還金額:若未發生提前到期事件,則
    1. 所有連結標的每日收盤價均不曾觸及下限價格,則到
    2. 任一連結標的每日收盤價曾經觸及其相對應之下限價


• 連結標的:挪威再生能源、德國Q-cells、丹麥
• 保本比率:到期70%保本產品
• 首季固定配息:首季實領固定配息6%(年化
• 評價頻率:自第四個月第一天起,日日比
• 提前出場條件:自第四個月第一天起,只要任


• 變動配息:自第四個月第一天起,只要任
• 下限價格:期初價格的60%


•   到期日領回:到期前未達提前出場條件,本金
    1. 若任一連結標的之日收盤價格從未曾小於或等於其期
    2. 若任一連結標的之日收盤價格曾經小於或等於其期初

• 投資幣別:美元計價
• 保 本 率:到期100%保本
• 連結標的:30Y CMS-10Y CMS
• 提前買回:產品發行半年(含)後,發行


• 配息頻率:每季配息
• 配息公式:
Y1-2 9.00%
Y3-4 Max{0,30*〔30y CMS-10y CMS〕}
Y5-6 Max{0,35*〔30y CMS-10y CMS〕}
Y7-8 Max{0,40*〔30y CMS-10y CMS〕}
Y9-10 Max{0,45*〔30y CMS-10y CMS〕}
Y11-12 Max{0,50*〔30y CMS-10y CMS〕}

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