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Home arrow Business & Finance arrow Frequently Asked Questions in Quantitative Finance

Passport option

is a call option on the trading account of an individual trader, giving the holder the amount in his account at the end of the horizon if it is positive, or zero if it is negative. For obvious reasons they are also called perfect trader options. The terms of the contract will specify what the underlying is that the trader is allowed to trade, his maximum long and short position, how frequently he can trade and for how long. To price these contracts requires a small knowledge of stochastic control theory. The governing partial differential equation is easily solved by finite differences. Monte Carlo would be quite difficult to implement for pricing purposes. Since the trader very quickly moves into or, more commonly, out of the money, the option is usually hedged with vanilla options after a while.

Put option

is the right to sell the underlying stock. See the 'Call option' since comments about pricing methodology, embedded features, etc., are equally applicable. Deep out-of-the-money puts are commonly bought for protection against large downward moves in individual stocks or against market crashes. These out-of-the-money puts therefore tend to be quite expensive in volatility terms, although very cheap in monetary terms.

Quanto

is any contract in which cash flows are calculated from an underlying in one currency and then converted to payment in another currency. They can be used to eliminate any exposure to currency risk when speculating in a foreign stock or index. For example, you may have a view on a UK company but be based in Tokyo. If you buy the stock you will be exposed to the sterling/yen exchange rate. In a quanto the exchange rate would be fixed. The price of a quanto will generally depend on the volatility of the underlying and the exchange rate, and the correlation between the two.

Rainbow option

is any contract with multiple underlyings. The most difficult part of pricing such an option is usually knowing how to deal with correlations.

Range note

is a contract in which payments are conditional upon an underlying staying within (or outside) a specified range of values.

Ratchet

is a feature that periodically locks in profit.

Repo

is a repurchase agreement. It is an agreement to sell some security to another party and buy it back at a fixed date and for a fixed amount. The price at which the security is bought back is greater than the selling price and the difference implies an interest rate called the repo rate. Repos can be used to lock in future interest rates.

Reverse repo

is the borrowing of a security for a short period at an agreed interest rate.

Straddle

is a portfolio consisting of a long call and a long put with the same strike and expiration. Such a portfolio is for taking a view on the range of the underlying or volatility.

Strangle

is a portfolio of a call and a put, the call having a higher strike than the put. It is a volatility play like the straddle but is cheaper. At the same time it requires the underlying to move further than for a straddle for the holder to make a profit.

STRIPS

stands for Separate Trading of Registered Interest and Principal of Securities. The coupons and principal of normal bonds are split up, creating artificial zero-coupon bonds of longer maturity than would otherwise be available.

Swap

is a general term for an over-the-counter contract in which there are exchanges of cash flows between two parties. Examples would be an exchange of a fixed interest rate for a floating rate, or the exchange of equity returns and bond returns, etc.

Swaption

is an option on a swap. It is the option to enter into the swap at some expiration date, the swap having predefined characteristics. Such contracts are very common in the fixed-income world where a typical swaption would be on a swap of fixed for floating. The contract may be European so that the swap can only be entered into on a certain date, or American in which the swap can be entered into before a certain date or Bermudan in which there are specified dates on which the option can be exercised.

Total Return Swap (TRS)

is the exchange of all the profit or loss from a security for a fixed or floating interest payment. Periodically, one party transfers the cash flows plus any positive value change of a reference asset to the other party, this includes interest payments, appreciation, coupons, etc., while the other party pays a fixed or floating rate, probably with some spread. The difference between a total return swap and a default swap is that a default swap simply transfers credit risk, by reference to some designated asset whereas a total return swap transfers all the risks of owning the designated asset. Total return swaps were among the earliest credit derivatives. TRSs existed before default swaps, but now default swaps are the more commonly traded instruments. The maturity is typically less than the maturity of the underlying instrument. A TRS therefore provides a means of packaging and transferring all of the risks associated with a reference obligation, including credit risk. TRSs are more flexible than transactions in the underlyings. For example, varying the terms of the swap contract allows the creation of synthetic assets that may not be otherwise available. The swap receiver never has to make the outlay to buy the security. Even after posting collateral and paying a high margin, the resulting leverage and enhanced return on regulatory capital can be large.

Ultras

give a multiple of an index's performance on a daily basis, and that multiple can be positive or negative. Suppose you have an ultrashort giving a multiple of minus two and suppose that the returns on an index over a week are 2%, 3%,

— 1%, 2% and —3%. The ultrashort would then have a value given by the compounding of —4%, —6%, 2%, —4% and 6%.

Variance swap

is a swap in which one leg is the realized variance in the underlying over the life of the contract and the other leg is fixed. This variance is typically measured using regularly spaced data points according to whatever variance formula is specified in the term sheet. The contract is popular with both buyers and sellers. For buyers, the contract is a simple way of gaining exposure to the variance of an asset without having to go to all the trouble of dynamically delta hedging vanilla options. And for sellers it is popular because it is surprisingly easy to statically hedge with vanilla options to almost eliminate model risk. The way that a variance swap is hedged using vanillas is the famous 'one over strike squared rule. The variance swap is hedged with a continuum of vanilla options with the quantity of options being inversely proportional to the square of their strikes. In practice, there does not exist a continuum of strikes, and also one does not go all the way to zero strike (and an infinite quantity of them).

The volatility swap is similar in principle, except that the payoff is linear in the volatility, the square root of variance. This contract is not so easily hedged with vanillas. The difference in prices between a volatility swap and a variance swap can be interpreted via Jensen's Inequality as a convexity adjustment because of volatility of volatility. The VIX volatility index is a representation of SP500 30-day implied volatility inspired by the one-over-strike-squared rule.

 
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