Diff (erential) swap

is an interest rate swap of floating for fixed or floating, where one of the floating legs is a foreign interest rate. The exchange of payments are defined in terms of a domestic notional. Thus there is a quanto aspect to this instrument. One must model interest rates and the exchange rate, and as with quantos generally, the correlation is important.

Digital option

is the same as a binary option.

Exponential Collateralized Debt Obligation (ECDO)

You've heard of CDOs. You've heard of CDO squared. So why not CDO cubed? Hell, why not eCDO? That's an ECDO. Or what about LCDO? The logarithm of a CDO, after all CDOs can only go to zero ... now minus infinity is attainable! No, these contracts don't exist, I made them up. I made up the ECDO while listening, many years pre-global financial crisis, to what I thought were the stupidest models in the hope that a bit of satire might make people realize how dangerous these products could be. You've read the news, the message did not get across!

Extendible option/swap

is a contract that can have its expiration date extended. The decision to extend may be at the control of the writer, the holder or both. If the holder has the right to extend the expiration then it may add value to the contract, but if the writer can extend the expiry it may decrease the value. There may or may not be an additional premium to pay when the expiration is extended. These contracts are best valued by finite-difference means because the contract contains a decision feature.

Floating Rate Note (FRN)

is a bond with coupons linked to a variable interest rate issued by a company. The coupon will typically have a spread in excess of a government interest rate, and this spread allows for credit risk. The coupons may also have a cap and/or a floor. The most common measure of a floating interest rate is the London Interbank Offer Rate or LIBOR. LIBOR comes in various maturities, one-month, three-month, six-month, etc., and is the rate of interest offered between Eurocurrency banks for fixed-term deposits.


is a fixed-income option in which the holder receives a payment when the underlying interest rate falls below a specified level, the strike. This payment is the strike less the interest rate. These payments happen regularly, monthly, or quarterly, etc., as specified in the contract, and the underlying interest rate will usually be of the same tenor as this interval. The life of the floor will be several years. They are bought for protection against falling interest rates. Market practice is to quote prices for floors using the Black '76 model. A contract with a single payment as above is called a floor let.


is an agreement to buy or sell an underlying, typically a commodity, at some specified time in the future.

The holder is obliged to trade at the future date. This is in contrast to an option where the holder has the right but not the obligation. Forwards are OTC contracts. They are linear in the underlying and so convexity is zero, meaning that the volatility of the commodity does not matter and a dynamic model is not required. The forward price comes from a simple, static, no-arbitrage argument.

Forward Rate Agreement (FRA)

is an agreement between two parties that a specified interest rate will apply to a specified principal over some specified period in the future. The value of this exchange at the time the contract is entered into is generally not zero and so there will be a transfer of cash from one party to the other at the start date.

Forward-start option

is an option that starts some time in the future. The strike of the option is then usually set to be the value of the underlying on the start date, so that it starts life as an at-the-money option. It is also possible to have contracts that begin in or out of the money by a specified amount. Although the option comes into being at a specified date in the future it is usually paid for as soon as the contract is entered into. In a Black-Scholes world, even with time-dependent volatility, these contracts have simple closed-form formula for their values. Provided the strike is set to be a certain fraction of the underlying at the start date then the value of a vanilla call or put at that start date is linear in the price of the underlying, and so prior to the start date there is no convexity. This means that forward-start options are a way of locking in an exposure to the volatility from the option s start date to the expiration.

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