178:. 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.
1283:
276:), 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
119:
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
190:
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?
191:
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.
255:
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
222:
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.
123:
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:
176:
322:
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
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315:
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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.
1166:
856:
203:, 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.
87:
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.
988:
66:
If the barrier price is close to being breached, the knock-in option will be worth slightly less than the corresponding vanilla option.
724:
69:
If the barrier price has been breached, the knock-in option will trade at the exact same value as the corresponding vanilla option.
20:
is an option whose payoff is conditional upon the underlying asset's price breaching a barrier level during the option's lifetime.
77:
If the barrier price is far from being breached, the knock-out option will be slightly less than the corresponding vanilla option.
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73:"Out" options start their lives active and become null and void in the event that a certain knock-out barrier price is breached:
56:
exercise style. But they become activated (or extinguished) only if the underlying breaches a predetermined level (the barrier).
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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
820:
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998:
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913:
280:. 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
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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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103:: spot price starts above the barrier level and has to move down for the option to become null and void.
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59:"In" options only become active in the event that a predetermined knock-in barrier price is breached:
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115:: 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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109:: spot price starts below the barrier level and has to move up for the option to become activated.
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97:: spot price starts below the barrier level and has to move up for the option to be knocked out.
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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.
268:
The simplest way to value barrier options is to use a static
311:(sensitivities) using this approach is numerically unstable.
350:
Derman, Emanuel; Ergener, Deniz; Kani, Iraj (31 May 1995).
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199:Barrier options are sometimes accompanied by a
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272:of vanilla options (which can be valued with
8:
316:Finite difference methods for option pricing
90:The four main types of barrier options are:
432:
402:
388:
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32:that are similar in some ways to ordinary
156:
140:
128:
292:(PDE) approach. The PDE satisfied by an
1227:Power reverse dual-currency note (PRDC)
1167:Constant proportion portfolio insurance
342:
7:
1162:Collateralized debt obligation (CDO)
324:explicit finite-differencing methods
28:Barrier options are path-dependent
14:
1281:
235:Barrier options can have either
171:{\displaystyle C=C_{in}+C_{out}}
989:Year-on-year inflation-indexed
1:
999:Zero-coupon inflation-indexed
330:scheme have their advantages.
290:partial differential equation
352:"Static Options Replication"
314:A faster approach is to use
1202:Foreign exchange derivative
594:Callable bull/bear contract
1325:
359:The Journal of Derivatives
288:Yet another method is the
1276:
1103:Stock market index future
417:
307:. However, computing the
1222:Mortgage-backed security
1217:Interest rate derivative
1192:Equity-linked note (ELN)
1177:Credit-linked note (CLN)
305:Monte Carlo option model
1172:Contract for difference
473:Risk-free interest rate
371:10.3905/jod.1995.407927
954:Forward Rate Agreement
172:
1182:Credit default option
526:Employee stock option
270:replicating portfolio
173:
1136:Inflation derivative
1121:Commodity derivative
1093:Single-stock futures
1083:Normal backwardation
1073:Interest rate future
914:Conditional variance
420:Derivative (finance)
328:Crank–Nicolson
127:
1288:Business portal
1141:Property derivative
298:boundary conditions
1146:Weather derivative
1131:Freight derivative
1113:Exotic derivatives
1033:Commodities future
720:Intermarket spread
483:Synthetic position
411:Derivatives market
213:continuous barrier
168:
1309:Options (finance)
1296:
1295:
1197:Equity derivative
1187:Credit derivative
1155:Other derivatives
1126:Energy derivative
1088:Perpetual futures
969:Overnight indexed
919:Constant maturity
880:
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827:Finite difference
760:Protective option
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1058:Forwards pricing
832:Garman–Kohlhagen
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278:volatility smile
247:exercise style.
209:discrete barrier
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1258:Great Recession
1253:Government debt
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1207:Fund derivative
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1068:Futures pricing
1043:Dividend future
1038:Currency future
1021:
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852:Put–call parity
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775:Vertical spread
710:Diagonal spread
680:Calendar spread
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633:Mountain range
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182:Barrier events
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18:barrier option
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1053:Forward price
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964:Interest rate
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857:MC Simulation
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817:Black–Scholes
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770:Risk reversal
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700:Credit spread
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619:Forward start
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546:Option styles
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463:Open interest
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443:Delta neutral
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274:Black–Scholes
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262:Black–Scholes
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228:turbo warrant
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188:barrier event
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23:
21:
19:
1063:Forward rate
974:Total return
862:Real options
765:Ratio spread
745:Naked option
705:Debit spread
578:
536:Fixed income
478:Strike price
365:(4): 78–95.
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358:
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101:Down-and-out
100:
94:
89:
86:
72:
58:
27:
17:
15:
994:Zero Coupon
924:Correlation
872:Vanna–Volga
730:Iron condor
516:Bond option
113:Down-and-in
1268:Tax policy
984:Volatility
894:Amortising
735:Jelly roll
670:Box spread
665:Backspread
657:Strategies
493:Volatility
488:the Greeks
453:Expiration
338:References
195:Variations
95:Up-and-out
36:. You can
959:Inflation
909:Commodity
867:Trinomial
802:Bachelier
794:Valuation
675:Butterfly
609:Commodore
458:Moneyness
251:Valuation
107:Up-and-in
1303:Category
1098:Slippage
1028:Contango
1012:Forwards
979:Variance
939:Dividend
934:Currency
847:Margrabe
842:Lattices
821:equation
807:Binomial
755:Strangle
750:Straddle
647:Swaption
629:Lookback
614:Compound
556:Warrants
531:European
511:American
503:Vanillas
468:Pin risk
448:Exercise
326:and the
245:European
241:Bermudan
237:American
54:European
50:Bermudan
46:American
1017:Futures
637:Rainbow
604:Cliquet
599:Chooser
579:Barrier
566:Exotics
428:Options
320:diffuse
34:options
30:exotics
1078:Margin
944:Equity
837:Heston
740:Ladder
690:Condor
685:Collar
642:Spread
589:Binary
584:Basket
309:Greeks
201:rebate
949:Forex
904:Basis
899:Asset
886:Swaps
812:Black
715:Fence
574:Asian
436:Terms
355:(PDF)
215:case.
52:, or
24:Types
783:Bull
779:Bear
521:Call
258:path
38:call
551:Put
367:doi
318:to
294:out
243:or
44:in
42:put
40:or
1305::
781:,
541:FX
361:.
357:.
239:,
225:A
218:A
207:A
186:A
48:,
16:A
823:)
819:(
785:)
777:(
403:e
396:t
389:v
373:.
369::
363:2
164:t
161:u
158:o
154:C
150:+
145:n
142:i
138:C
134:=
131:C
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