189:. Note that before the knock-in/out event, both options have positive value, and hence both are strictly valued below the corresponding vanilla option. After the knock-in/out event, the knock-out option is worthless and the knock-in option's value coincides with that of the corresponding vanilla option. At maturity, exactly one of the two will pay off identically to the corresponding vanilla option, which of the two that depends on whether the knock-in/out event has occurred before maturity.
1294:
287:), chosen so as to mimic the value of the barrier at expiry and at selected discrete points in time along the barrier. This approach was pioneered by Peter Carr and gives closed form prices and replication strategies for all types of barrier options, but usually only by assuming that the Black-Scholes model is correct. This method is therefore inappropriate when there is a
130:
For example, a
European call option may be written on an underlying with spot price of $ 100 and a knockout barrier of $ 120. This option behaves in every way like a vanilla European call, except if the spot price ever moves above $ 120, the option "knocks out" and the contract is null and void. Note
201:
occurs when the underlying crosses the barrier level. While it seems straightforward to define a barrier event as "underlying trades at or above a given level," in reality it's not so simple. What if the underlying only trades at the level for a single trade? How big would that trade have to be?
202:
Would it have to be on an exchange or could it be between private parties? When barrier options were first introduced to options markets, many banks had legal trouble resulting from a mismatched understanding with their counterparties regarding exactly what constituted a barrier event.
266:
The valuation of barrier options can be tricky, because unlike other simpler options they are path-dependent – that is, the value of the option at any time depends not just on the underlying at that point, but also on the
233:
is a barrier option where the barrier condition applies only once the price of the underlying instrument has spent at least a given period of time on the wrong side of the barrier.
134:
By in-out parity, we mean that the combination of one "in" and one "out" barrier option with the same strikes and expirations yields the price of the corresponding vanilla option:
187:
333:
the PDE backwards from the boundary condition (which is the terminal payoff at expiry, plus the condition that the value along the barrier is always 0 at any time). Both
837:
412:
326:
296:
Another approach is to study the law of the maximum (or minimum) of the underlying. This approach gives explicit (closed form) prices to barrier options.
1177:
867:
214:, which is a payoff to the option holder in case of a barrier event. Rebates can either be paid at the time of the event or at expiration.
98:
Some variants of "Out" options compensate the owner for the knock-out by paying a cash fraction of the premium at the time of the breach.
999:
77:
If the barrier price is close to being breached, the knock-in option will be worth slightly less than the corresponding vanilla option.
735:
80:
If the barrier price has been breached, the knock-in option will trade at the exact same value as the corresponding vanilla option.
31:
is an option whose payoff is conditional upon the underlying asset's price breaching a barrier level during the option's lifetime.
88:
If the barrier price is far from being breached, the knock-out option will be slightly less than the corresponding vanilla option.
1237:
405:
84:"Out" options start their lives active and become null and void in the event that a certain knock-out barrier price is breached:
67:
exercise style. But they become activated (or extinguished) only if the underlying breaches a predetermined level (the barrier).
242:
is a barrier option namely a knock out call that is initially in the money and with the barrier at the same level as the strike.
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taken by the underlying (since, if it has crossed the barrier, a barrier event has occurred). Although the classical
831:
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924:
291:. For a more general but similar approach that uses numerical methods, see Derman's "Static Options Replication."
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barrier options is the same one satisfied by a vanilla option under Black and
Scholes assumptions, with extra
1182:
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If the barrier price is close to being breached, the knock-out option will be worth slightly more than zero.
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If the barrier price is far from being breached, the knock-in option will be worth slightly more than zero.
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114:: spot price starts above the barrier level and has to move down for the option to become null and void.
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70:"In" options only become active in the event that a predetermined knock-in barrier price is breached:
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126:: spot price starts above the barrier level and has to move down for the option to become activated.
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If the barrier price has been breached, the knock-out option will trade at the exact value of zero.
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120:: spot price starts below the barrier level and has to move up for the option to become activated.
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108:: spot price starts below the barrier level and has to move up for the option to be knocked out.
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1004:
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is one for which the barrier event is considered at discrete times, rather than the normal
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When an exact formula is difficult to obtain, barrier options can be priced with the
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demanding that the option become worthless when the underlying touches the barrier.
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that the option does not reactivate if the spot price falls below $ 120 again.
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approach does not directly apply, several more complex methods can be used:
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A simple approach of binomial tree option pricing also applies.
279:
The simplest way to value barrier options is to use a static
322:(sensitivities) using this approach is numerically unstable.
361:
Derman, Emanuel; Ergener, Deniz; Kani, Iraj (31 May 1995).
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210:Barrier options are sometimes accompanied by a
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283:of vanilla options (which can be valued with
8:
327:Finite difference methods for option pricing
101:The four main types of barrier options are:
443:
413:
399:
391:
43:that are similar in some ways to ordinary
167:
151:
139:
303:(PDE) approach. The PDE satisfied by an
1238:Power reverse dual-currency note (PRDC)
1178:Constant proportion portfolio insurance
353:
7:
1173:Collateralized debt obligation (CDO)
335:explicit finite-differencing methods
39:Barrier options are path-dependent
25:
1292:
246:Barrier options can have either
182:{\displaystyle C=C_{in}+C_{out}}
1000:Year-on-year inflation-indexed
1:
1010:Zero-coupon inflation-indexed
341:scheme have their advantages.
301:partial differential equation
363:"Static Options Replication"
325:A faster approach is to use
1213:Foreign exchange derivative
605:Callable bull/bear contract
1336:
370:The Journal of Derivatives
299:Yet another method is the
1287:
1114:Stock market index future
428:
318:. However, computing the
1233:Mortgage-backed security
1228:Interest rate derivative
1203:Equity-linked note (ELN)
1188:Credit-linked note (CLN)
316:Monte Carlo option model
1183:Contract for difference
484:Risk-free interest rate
382:10.3905/jod.1995.407927
965:Forward Rate Agreement
183:
1193:Credit default option
537:Employee stock option
281:replicating portfolio
184:
1147:Inflation derivative
1132:Commodity derivative
1104:Single-stock futures
1094:Normal backwardation
1084:Interest rate future
925:Conditional variance
431:Derivative (finance)
339:Crank–Nicolson
138:
1299:Business portal
1152:Property derivative
309:boundary conditions
1157:Weather derivative
1142:Freight derivative
1124:Exotic derivatives
1044:Commodities future
731:Intermarket spread
494:Synthetic position
422:Derivatives market
224:continuous barrier
179:
1320:Options (finance)
1307:
1306:
1208:Equity derivative
1198:Credit derivative
1166:Other derivatives
1137:Energy derivative
1099:Perpetual futures
980:Overnight indexed
930:Constant maturity
891:
890:
838:Finite difference
771:Protective option
16:(Redirected from
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1069:Forwards pricing
843:Garman–Kohlhagen
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289:volatility smile
258:exercise style.
220:discrete barrier
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1269:Great Recession
1264:Government debt
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1218:Fund derivative
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1079:Futures pricing
1054:Dividend future
1049:Currency future
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863:Put–call parity
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786:Vertical spread
721:Diagonal spread
691:Calendar spread
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18:Barrier options
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644:Mountain range
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29:barrier option
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1254:Consumer debt
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1247:Market issues
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1064:Forward price
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975:Interest rate
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868:MC Simulation
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828:Black–Scholes
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781:Risk reversal
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711:Credit spread
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635:Interest rate
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630:Forward start
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557:Option styles
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474:Open interest
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454:Delta neutral
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285:Black–Scholes
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273:Black–Scholes
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239:turbo warrant
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199:barrier event
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50:
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42:
34:
32:
30:
19:
1074:Forward rate
985:Total return
873:Real options
776:Ratio spread
756:Naked option
716:Debit spread
589:
547:Fixed income
489:Strike price
376:(4): 78–95.
373:
369:
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304:
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112:Down-and-out
111:
105:
100:
97:
83:
69:
38:
28:
26:
1005:Zero Coupon
935:Correlation
883:Vanna–Volga
741:Iron condor
527:Bond option
124:Down-and-in
1279:Tax policy
995:Volatility
905:Amortising
746:Jelly roll
681:Box spread
676:Backspread
668:Strategies
504:Volatility
499:the Greeks
464:Expiration
349:References
206:Variations
106:Up-and-out
47:. You can
970:Inflation
920:Commodity
878:Trinomial
813:Bachelier
805:Valuation
686:Butterfly
620:Commodore
469:Moneyness
262:Valuation
118:Up-and-in
1314:Category
1109:Slippage
1039:Contango
1023:Forwards
990:Variance
950:Dividend
945:Currency
858:Margrabe
853:Lattices
832:equation
818:Binomial
766:Strangle
761:Straddle
658:Swaption
640:Lookback
625:Compound
567:Warrants
542:European
522:American
514:Vanillas
479:Pin risk
459:Exercise
337:and the
256:European
252:Bermudan
248:American
65:European
61:Bermudan
57:American
1028:Futures
648:Rainbow
615:Cliquet
610:Chooser
590:Barrier
577:Exotics
439:Options
331:diffuse
45:options
41:exotics
1089:Margin
955:Equity
848:Heston
751:Ladder
701:Condor
696:Collar
653:Spread
600:Binary
595:Basket
320:Greeks
212:rebate
960:Forex
915:Basis
910:Asset
897:Swaps
823:Black
726:Fence
585:Asian
447:Terms
366:(PDF)
226:case.
63:, or
35:Types
794:Bull
790:Bear
532:Call
269:path
49:call
562:Put
378:doi
329:to
305:out
254:or
55:in
53:put
51:or
1316::
792:,
552:FX
372:.
368:.
250:,
236:A
229:A
218:A
197:A
59:,
27:A
834:)
830:(
796:)
788:(
414:e
407:t
400:v
384:.
380::
374:2
175:t
172:u
169:o
165:C
161:+
156:n
153:i
149:C
145:=
142:C
20:)
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