Complex Swaps Page


Vanilla options

Key Concepts
An option is a contract, traded over-the-counter or on an exchange, that grants the buyer the right to buy (call option) or sell (put option) a pre-agreed amount (the notional principal) of a specified asset or index (the underlying) at a pre-determined price or rate (the strike price) and time specified in the contract.
The option holder is said to exercise the option if he exercises his right to buy or sell the underlying.
If exercise is allowed only at the option's maturity then the option is said to be European-style.
If exercise is allowed at any point during the life of the option it is said to be American-style.
If it can be exercised on a number of pre-determined dates it is said to be a Bermudan or Atlantic option.
The seller of the option is also known as the option writer.
The underlying asset can be a foreign exchange rate, an interest rate or swap rate, a commodity or commodity index, an individual equity or an equity index, baskets of any of these assets or spreads between them.
In exchange for this right, the buyer of most types of option makes an upfront payment, the premium.
The level of this premium is not straightforward to calculate but depends on, among other things, the option's payoff structure and maturity, the level of interest rates and the volatility of the underlying.
What distinguishes options from other financial instruments is the asymmetric payments they generate.
Options allow their holders to profit when the price of the underlying moves in their favour while limiting downside to the premium paid.
This is unlike the symmetrical payoffs associated with forwards and futures.
These are options whose payoffs are continuous, whose strike prices are fixed, which exist in the same form throughout their maturity and for which a standard upfront premium is payable.
It also includes a number of combinations of standard options (known as spreads) which are commonly used to create more complex payoff profiles tailored to more specific views on the part of the buyers and sellers.

Back {forward} spread
(i) Any option spread where more options are purchased {sold} than sold {purchased}. (ii) An option spread whose value will rise {fall} given a sharp movement up or down in the price of the underlying.

Box [spread]
Generally the term box position refers to any offsetting spread positions; for example, the combination of bull and bear spreads.
Another example is the combination of a horizontal or calendar call spread and a calendar put spread with both spreads having the same expiration dates on their long and short positions.
These types of spread positions are used to capture the value in mispriced options while hedging against market risk or, alternatively, are used to tie up or free up cash.

Butterfly [spread]
A combination of four options.
Used to describe either the combination of a bull with a bearspread, or of an at-the-money straddle with an out-of-the-money strangle.
A long butterfly might be long an option (put or call) at 40, short two at 60 and long one at 80.
For a limited premium upfront the strategy will achieve a maximum payoff of 20 if spot at expiry is 60.
A short butterfly is short two options and long two options.
The characteristic shared by all the combinations is that the holder benefits from stable prices in the underlying while remaining protected against large movements in prices.

Call {put} option
An option that grants the holder the right but not the obligation to buy a pre-agreed amount of a specified underlying at a pre-determined price or rate.
The buyer of a call is expressing a bullish view on the underlying and also implicitly, since he is long an option, believes either that volatility will rise or at least that it will not fall.
The right to sell the underlying and so express a bearish view is called a put option.
In a foreign exchange option, since the option is to exchange one currency for another, all options are call options on one currency and, by definition, put options on the other currency.
For example, in EUR/USD, a EUR call is a USD put and vice versa.
See put-call parity.

Call {put} spread
An option spread involving the simultaneous purchase and sale of call {put} options on the same underlying either with different strike prices or maturities.
These positions can be bullish or bearish depending on the strike prices of the options.
So a bull {bear} call spread is the purchase of a call option with one exercise price and the sale of a call with a higher {lower} exercise price both generally with the same expiration.
This reduces the cost of the position at the expense of limiting participation in the appreciation of the underlying.
And a bull {bear} put spread is the purchase of a put option with one exercise price and the sale of a put with a higher {lower} exercise price, both generally with the same expiration.
These two combinations produce identical payoff profiles.

Cap {floor}
A call {put} option on an interest rate index. Above {below} the strike the holder of a cap {floor} with a notional principal equal to an underlying liability is hedged against rises {falls} in interest rates.
Caps are therefore used as hedges against rate rise by borrowers and floors as hedges against rate falls by lenders or investors.
In practice, caps and floors are medium-term agreements under which, in exchange for a one-time upfront premium payment, the seller agrees to pay the buyer the difference (if positive) between the strike rate and the current rate at preset times over the life of the cap {floor} thus establishing a maximum {minimum} interest rate for the holder. The buyer selects the maturity, interest rate strike level, reference floating rate, reset period and notional principal amount. The maturity of standard caps {floors} means that they are actually made up of a series of caplets/single period caps {floorlets/single period floors}. A caplet {floorlet} can be viewed either as a call {put} on an interest rate index or a put {call} on an interest futures contract or zero coupon bond. Vanilla caps and floors are not a continuous rate guarantee; claims can only be made on specified settlement dates.
This makes them best suited to hedging the interest rate on floating-rate instruments that are reset periodically.
Caps and floors are priced off the implied forward curve the relevant implied forwards being either the swap rate for the period of the cap/floor or the FRA rate for a caplet/floorlet. The simplest approach to pricing caps/floors assumes that these forward interest rates are lognormally distributed. Caps are sometimes also known as ceiling rate agreements.
Interest rate caps can be quantized (see chapter on 'Multi-factor options').
A quanto cap is one option or a series of options whose payout is based upon a reference (foreign) Libor exceeding (cap) or falling below (floor) an absolute strike rate or spread with respect to the base (domestic) Libor. The payout is in arrears on a money market basis, as in a normal cap/floor, but is denominated in the base (domestic) currency. The ability to cap or floor the differential between two currencies' Libors in one currency can be more efficient and economical than doing vanilla caps and floors in each currency individually. Variants include: The rate differential option is a quanto cap or floor on the foreign interest rate or domestic currency payment stream in a differential swap. For example, a borrower of Swiss francs paying three-month dollar Libor plus a spread in exchange for three-month Swiss franc Libor under a differential swap could cap his absolute rate payment. The spread differential option is a quanto cap whose buyer receives the spread between two interest rates in different currencies minus a strike spread, with the payment denominated in his required currency. Payments are made in the domestic currency when the spread exceeds the strike level. It can be viewed as a strip of options on forward spread agreements. The floor version is used to ensure that coupons in leveraged currency protected notes do not become negative. Capped call {floored put}
An option with both a strike price and an in-the-money cap {floor} strike.
If the underlying hits the cap {floor} strike then the option is automatically exercised for its intrinsic value.
It is different from a call {put} spread in that the cap {floor} is locked in if ever the trigger is hit regardless of subsequent movements in the underlying. Payment can either be immediate or made on the original expiry date of the option. These instruments can be used as one element of a collar or risk reversal strategy in which, as soon as the underlying trades through the cap strike, the short option explodes (expires) and the long option pays out. Because the automatic exercise locks in the intrinsic value of the option, these options have a similar risk profile to vanilla options. Also known as cliquet options ('cliqueter' is French for 'to knock'; the automatic exercise became known as the cliquet clause),exploding options, lock-in options, trigger options (not to be confused with true barrier options also sometimes called trigger options). See knock-out trigger option, switchback option. Condor [spread] An options (or futures) spread position similar to the butterfly.
The holder is long and short two spread positions strangles on the same market.
A long condor can be constructed by, for example, buying a call struck at 40, selling a call struck at 60, selling another call struck at 70, and buying a call struck at 80. The maximum payoff on this strategy occurs when the underlying trades between 60 and 70 a wider range than the butterfly but with the compromise of a smaller maximum potential profit.
The position is limited on both the up- and downside and is directionally neutral.
The short condor sells the lowest strike call, buys the two higher strike price calls and sells the highest strike price call.

Conversion [arbitrage]
An arbitrage trade so called because it can be used by the holder of a put to alter his position to a call or vice versa.
A conversion, also known as a long option box, is the purchase of the underlying or future, purchase of a put and sale of a call with the same exercise price and expiration date.
This converts a put to a call and creates a short synthetic futures position hedged by a position in the underlying or future.
The opposite is known as a reversal or short option box or reverse conversion and is the purchase of a call, sale of a put with the same exercise price and expiration and sale of the underlying or future.
This is the reverse of a conversion as it converts a call position into a put.
The position is a synthetic long futures position hedged by the sale of the futures contract.
These arbitrages maintain and rely on put-call parity.
If a put is overvalued (or if the put is fairly valued but the call is undervalued), a riskless profit can be made by executing the reversal.
If the call is overvalued (or the call is fairly valued but the put is undervalued), the riskless profit is generated by selling the call, buying the put and buying the underlying or a future.
The actual arbitrage return depends on the additional borrowing costs {investment returns} from the money market transactions which fund (result from} these trades.

A call spread constructed from the purchase of an interest rate cap at one level and sale of another at a higher level.
The holder of the corridor is protected against rate rises between the strikes of the two calls.
Unlike the holder of a collar though, the holder benefits fully from any downward movement in rates.
Also sometimes applied to a collar on a swap created by using two swaptions.

Diagonal spread
An option spread in which the holder is short the same type (call or put) of options of one maturity and strike price and long options of a different maturity and different strike price.
A diagonal bull spread is the sale of a shorter maturity option and purchase of a longer maturity, lower strike price option.
A diagonal bear spread is the purchase of a longer maturity option and sale of a shorter maturity, lower strike price option.
'Diagonal' because it is a cross between a horizontal and vertical spread.

An option on an FRA giving the holder the right but not the obligation to purchase an FRA at a predetermined strike.
A cap can be thought of as being constructed from a string of interest rate guarantees.
Also known as an interest rate guarantee.
Participating option
An option which changes the rate of participation in a price or rate movement once the strike price has been reached.
A participating call option on the FTSE-100 stock index might give 100% participation from a strike at-the-money up to the point at which the index has moved up 10%.
Then further participation is limited to 50%.
Effectively the option holder has sold a call at that level on half the notional principal of the original call.
Because of this, the participating option is cheaper than the standard variety.
The cap version is known as a partial cap.
It reduces exposure to an upward move in the price of the underlying rather than eliminating it completely.
Either the hedger simply buys a cap with a smaller notional principal than the underlying exposure, giving both counterparties participation on an average basis.
Or, if a zero premium structure is required, the hedger simultaneously buys an out-of-the-money cap and sells an in-the-money floor with a lower notional amount.
Since the floor is in the money, it needs to be struck on less notional principal to create a zero premium.
The structure limits participation in downward rates to the portion of the underlying exposure not covered by the floor sale.

Horizontal spread
A generic name for the simultaneous purchase of one type of option (call or put) and sale of the same type of option with the same strike price but a different maturity.
Usually used specifically of the simultaneous sale of an option with a nearby expiry date and the purchase of an option with a later expiry date, both with the same strike price.
This trade will profit if the time decay on the short position is faster than that of the long.
Also known as a calendar spread, money spread. See vertical spread.

Ratio/variable spread
Any option spread in which the number or notional amount of options purchased is not the same as the number or notional amount sold.
For example, a ratio bull spread is the simultaneous purchase of in- or at-the-money options and sale of a larger quantity of out-of-the-money options.
And a call ratio forward spread is the simultaneous purchase of at- or in-the-money calls and sale of a larger number of out-of-the-money calls.
The position will make money from the long calls as long as the underlying rises.
If however it rises beyond the strike of the short calls so far that the intrinsic value from the long position is overwhelmed, the position can lose value, The potential losses on the position are unlimited.
The strategy is cheaper to purchase than the plain bull spread and is suitable when spot is expected to be stable or if it moves is more likely to rise.
The position then benefits from the time decay of the options sold.

Risk reversal
The simultaneous purchase of an out-of-the-money call {put} and sale of an out-of-the-money put {call} usually with zero upfront premium.
To a trader, the term means more specifically the purchase of a less than 50% delta (³) call {put} financed by the sale of a similar delta put {call} for zero upfront cost.
The options being bought and sold will typically have the same notional size and pre-specified maturity and the deltas will typically be set to 25%.
According to Black-Scholes the purchase and sale of options with similar deltas (and so out-of-the-money forward to the same extent) should be zero cost.
In practice the market favours one side versus the other in the simplest case the implied volatilities of out-of-the-money puts and calls of the same strike and maturity are different and the extra cost of the favoured side is commonly known as the risk reversal spread.
This reflects the market's perception that the relevant probability distribution is not symmetrical around the forward but skewed in the direction of the favoured side.
Another way of interpreting this is to say that implied volatility is correlated with spot, an impossibility in a Black-Scholes world.
The one-month 25³ risk-reversal is the market's benchmark indicator of skew in a particular asset class and is commonly used to trade the skew.
When positive, it indicates that calls are more favoured by the market than puts and that the market is more likely to rally significantly than fall (and vice versa when it is negative).
The 15³ risk-reversal is also gaining in popularity as a benchmark trade as it is used to hedge the second order volatility risk (švega/šspot) in some barrier options.
See strangle.
When combined with a short {long} forward position, a risk reversal becomes a cylinder or range forward.
Confusingly, because this latter position is known as a collar in interest rate markets, the naked risk reversal is also sometimes referred to as a collar.
A short EUR cash position could be hedged with the purchase of a EUR call/USD put struck at 1.0477 and the sale of a EUR put/USD call struck at 1.0290.
Assuming a forward rate of 1.0377 this three month collar would be zero premium.
At expiry if the spot is above 1.0477 then further losses on the underlying position are hedged by the purchased option.
If spot is between the two strikes the underlying is exchanged at the prevailing spot rate as with a normal forward.
If it is below 1.0290 then the profits on the underlying are capped by the sold option.

A ratio spread comprising the purchase of a call spread and the sale of a put with a strike below that of the calls, or vice versa.
This produces a schematic payoff profile that resembles a tilted and elongated 'M' - like a schematic representation of a bird or seagull.

A long straddle is the purchase of a put option and a call option on the same underlying with the same strike price and the same time to expiry.
The position is usually initially delta neutral since it is typically struck at the forward rate.
The position (which can also be constructed from two long puts and a long position in the underlying or two long calls and a short position in the underlying)
will make money if volatility is high.
A short straddle is the sale of a put option and a call option on the same underlying with the same strike price and the same maturity.
It exposes the holder to unlimited downside but will make money if volatility is low.
Since the strategy, when struck at-the-money-forward, has a large vega position and zero delta, it is the commonest way to trade volatility used by interbank and other sophisticated players.

Similar to a straddle except that the strike of the call lies above the strike of the put.
A long {short} strangle is the purchase {sale} of a put option and a call option on the same underlying with the same expiry date but with different strike prices.
The short strangle generates less premium than the straddle because options sold are out-of-the-money and so cheaper.
This is compensated for by the wider break-even range of the position.
Straddles and strangles involve combinations of two options, which differentiates them from, say, butterflies, which involve combinations of four options, and can in fact be constructed by combining a strangle and short straddle and vice versa.
The one month 25³ strangle is the standard strangle trade and a common market indicator of the amount of leptokurtosis or "extreme event probability" in that asset class and is sometimes used to hedge second-order vega risk in some barrier options.
See risk reversal.

The option to enter into a swap contract.
The simplest swaption is an option to pay or receive fixed rate in an interest rate swap.
This can be considered an option to buy or sell a fixed-rate bond versus selling or buying a Libor flat floating-rate note.
A payer('s) swaption is an option that gives the buyer the right but not the obligation to enter into an interest rate swap paying fixed and receiving floating.
It is also called a put swaption as it is analogous to a put on a fixed-rate instrument (that is, an option to issue a bond).
The buyer benefits if rates rise as the option will become more valuable.
If rates rise above the fixed rate payable under the swaption, then the holder can exercise it and swap an existing floating rate liability into an advantageous fixed rate.
The payer swaption is similar to a cap in that it provides an interest rate ceiling, but it has to be exercised to provide the fixed rate, and once exercised, the holder is locked into paying a fixed rate, unlike the cap holder who can still benefit if rates fall.
Also, while caps tend to reference the short end of the yield curve, the payer swaption tends to reference the two- to 10-year part of the curve.
A receiver('s) swaption is an option giving the holder the right to receive fixed rate under an interest rate swap.
As it is analogous to having a call option on a fixed-rate bond, it is also known as a call swaption.
A receiver swaption behaves like a floor.
Typically, the option period is for a year or less on swap maturities of between three and ten years.
So a typical transaction might be to buy a three-month payer swaption with a strike price of 7.50% for cash settlement on a notional principal of $50 million.
If swap rates rise to 8.00%, the option would be exercised and a cash payment made to the swaption buyer. (Most swaptions are cash-settled)
Swaptions are usually European style, although American-style swaptions, allowing the buyer of the option to enter into a swap at any time after the exercise date, typically on a payment date, are available.
Swaptions are available on most vanilla and exotic swaps on most underlying assets.
Swaptions can be combined with swap positions to create extendible or cancellable swaps.
See callable swap, extendible swap, reversible swap.
They are also used, like forward start swaps, to monetize call and put options embedded in callable and puttable bonds. See monetization.
A swaption on a cross-currency swap is sometimes known as a cross-currency swaption.
Here one counterparty sells/buys the right to enter into a currency swap with another counterparty on a pre-determined date under which the first counterparty pays a pre-set fixed or floating rate in one currency in exchange for a pre-set fixed or floating rate in another currency.
The principal amount for final exchange is set for both currencies.
Initial exchange of principal amounts is not necessary.
A borrower who wished to reduce his funding costs by issuing a note denominated in one currency but convertible into one denominated in another could use this instrument to hedge against investor exercise.
An investor seeks the better performing of a EUR fixed-rate asset and a USD fixed-rate asset.
Both currency and interest rate exposure are sought.
For the option the investor pays the premium in the form of reduced yield.
A EUR 100 million 5% five-year note convertible once in one year into a $103.10 million 6.75% note with the same maturity is issued by a European agency.
This borrower buys a fixed EUR/fixed USD cross-currency swaption to hedge potential investor exercise.
This gives him the right, once at the end of one year, to enter into the following currency swap: USD notional: $103.10 million payable at maturity by the swaption writer; EUR notional: EUR 100 million payable at maturity by the borrower; Maturity: four years from exercise; Payer of 6.75% semi-annual USD: writer; Payer of fixed 5% annual EUR: agency; Initial currency exchange: none; Premium: 2.53%, EUR 2.53 million paid by the agency.
The borrower gets cheaper funding regardless of option exercise, the investor gains the required exposure.
The swaption is more economical than the purchase of an FX option and two interest rate options, unless the implied correlation between them is zero.

A ratio spread in which the purchase of an option is paid for by sales of the same option at two different strike prices.
So called because of the representation of its payoff profile.
For example, the purchase of one call option with a strike of 40 and the sale of one call struck at 60 and another struck at 80.

Vertical spread
A generic term used to describe the simultaneous sale of one type of option (call or put) and purchase of the same type of option with the same maturity but a different strike price. Contrast with horizontal spread.

An option in the form of a listed security rather than an over-the-counter contract. Warrants are available on all the asset classes used as the underlying in option contracts. Warrants are also available on a variety of government debt instruments and both debt and equity warrants can be attached to public bond issues by corporations and financial institutions. See cover.