Collateralized Debt Obligation squared (CDO2)
is a CDO-like contract in which the underlyings are other CDOs instead of being the simpler risky bonds.
Collateralized Mortgage Obligation (CMO)
is a pool of mortgages securitized into one financial instrument. As with CDOs there are different tranches allowing investors to participate in different parts of the cash flows. The cash flows in a mortgage are interest and principal, and the CMOs may participate in either or both of these depending on the structure. The different tranches may correspond to different maturities of the underlying mortgages, for example. The risk associated with CMOs are interest rate risk and prepayment risk, therefore it is important to have a model representing prepayment.
is an option on an option, such as a call on a put which would allow the holder the right to buy a specified put at a later date for a specified amount. There is no element of choice in the sense of which underlying option to buy (or sell).
Contingent premium option
is paid for at expiration only if the option expires in the money, not up front. If the option expires below the strike, for a call, then nothing is paid, but then nothing is lost. If the asset is just slightly in the money then the agreed premium is paid, resulting in a loss for the holder. If the underlying ends up significantly in the money then the agreed premium will be small relative to the payoff and so the holder makes a profit. This contract can be valued as a European vanilla option and a European digital with the same strike. This contract has negative gamma below the strike (for a call) and then positive gamma at the strike and above, so its dependence on volatility is subtle. The holder clearly wants the stock to end up either below the strike (for a call) or far in the money. A negative skew will lower the price of this contract.
is a bond issued by a company that can, at the choosing of the holder, be converted into a specified amount of equity. When so converted the company will issue new shares. These contracts are a hybrid instrument, being part way between equity and debt. They are appealing to the issuer since they can be issued with a lower coupon than straight debt, yet do not dilute earnings per share. If they are converted into stock that is because the company is doing well. They are appealing to the purchaser because of the upside potential with the downside protection. Of course, that downside protection may be limited because these instruments are exposed to credit risk. In the event of default the convertible bond ranks alongside debt, and above equity.
These instruments are best valued using finite-difference methods because that takes into account the optimal conversion time quite easily. One must have a model for volatility and also risk of default. It is common to make risk of default depend on the asset value, so the lower the stock price the greater the probability of default.
Credit Default Swap (CDS)
is a contract used as insurance against a credit event. One party pays interest to another for a prescribed time or until default of the underlying instrument. In the event of default the counterparty then pays the principal in return. The CDS is the dominant credit derivative in the structured credit market. The premium is usually paid periodically (quoted in basis points per notional). Premium can be an up-front payment, for short-term protection. On the credit event, settlement may be the delivery of the reference asset in exchange for the contingent payment or settlement may be in cash (that is, value of the instrument before default less value after, recovery value). The mark-to-market value of the CDS depends on changes in credit spreads. Therefore they can be used to get exposure to or hedge against changes in credit spreads. To price these contracts one needs a model for risk of default. However, commonly, one backs out an implied risk of default from the prices of traded CDSs.