FX Derivatives
trader school
CH 28
Accrual and Target
Redemption Options
Accrual and Target Redemption Options
⚫ Popular
⚫ Typically added to a forward contract or a strip of forward contracts
Improve the transaction rate for the client
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Accrual Options
Key characteristic
⚫ The notional, rather than being static, builds up (accrues) over time
⚫ Have a fixing schedule
⚫ The rate of accrual
Depends on where spot fixes compared to the accrual barriers
◼ European
If spot goes through the barrier, accrual stops with what has been accrued retained,
but if spot later comes back inside the barrier, accrual restarts
◼ American Keep
If spot ever goes through the barrier, accrual stops, but what
has been accrued prior to that point is retained.
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Range Accrual Option
⚫ Pays out an accrued notional at expiry
⚫ Range accrual prices are quoted in payout currency % terms
Split between the fixings equally
→ USD1m/250 = USD 4000 per fixing.
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European Accrual Barriers
⚫ If spot goes outside the range
and then later fixes within the
range again
Notional continues to accrue
⚫ Cash payout at expiry
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If there is just one fixing at expiry
European digital range
(pays out the full notional if spot is within the range at expiry)
European range accruals
can be perfectly replicated by a strip of European digital ranges
(expiring at each fixing within the range accrual)
(The Vega profile from a long European digital range also applies to European range accruals)
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European range accrual vega profile
loss
gain
long vega
short vega
loss
long vega
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American Keep Range Accrual
⚫ If spot ever goes through the American keep accrual barrier, accrual will stops
what has been accrued prior to that point is retained
The vega profile of a long american keep range accrual
Vega=0
short vega
Vega=0
Similar to a long double-no-touch option,
with no vega beyond the barriers
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Accrual Forward
⚫ Contain a forward payout at maturity
⚫ The notional determined by how spot moves
⚫ Many variations, most popular is : double accrual forward
◼ 1× (notional/number of fixings)
for each spot fix in an area where the payoff is positive for the client at maturity
◼ 2× (notional/number of fixings)
for each spot fix in an area where the payoff is negative for the client at maturity
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American Keep Double Accrual Forward
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American Keep Double Accrual Forward Vega
peak around the strike
similar to
American knock-out option
Almost always long vega
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Target Redemption Options
⚫ The option payoff depends in some way on a quantity that
counts up to a target over time
⚫ Standard target redemption forward (TARF)
◼ The client’s gains count up and the whole structured expired
Customers : Limited gain, unlimited loss
◼ The client’s losses do not count toward the target
◼ Target
Accumulation gain
Accumulation counts(gain)
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Example: EUR/USD 1yr TARF with monthly fixings
Strike
$ 1.229
Loss x 2
Spot
Forward
$ 1.277
1.28
Gain x 1
Target : USD 30000
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Vega Risk
Close to
Strike
Spot
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The vega chart of the TARF
compared to the equivalent leveraged forward structure
Equivalent Vanilla
Vega
TARF Vega
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Target redemption vega profiles
for different targets
High target
Low target
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Target Redemption Fixing Risk
Risk : Gamma, vega risk and Fixing Risk
Example : EUR/USD (Target: USD 30000/ strike: 1.229)
⚫ If spot = 1.329
Paying to client = (1.329-1.229)*300k USD = 30k USD
Knock out at first fixing
⚫ If spot = 1.279
Paying to client = (1.279-1.229)*300k USD = 15k USD
The deal will knock out at the second fixing if spot fixes at or above 1.2790 again
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Target Redemption Fixing Risk
⚫ The more frequently fixings occur within a structure
The more digital risks must be risk managed
⚫ If the termination level is close to the strike
Digital risks will be particularly large
⚫ Strike changes within the contract details of the trade
generate large digital risk
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