A quanto is a type of

derivative In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is t ...

in which the

underlying In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements: # an item (the "underlier") that can or must be bou ...

is denominated in one

currency A currency is a standardization of money in any form, in use or circulation as a medium of exchange, for example banknotes and coins. A more general definition is that a currency is a ''system of money'' in common use within a specific envi ...

, but the instrument itself is settled in another currency at some rate. Such products are attractive for speculators and investors who wish to have exposure to a foreign asset, but without the corresponding

exchange rate In finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of ...

risk. Quantos are attractive because they shield the purchaser from exchange rate fluctuations. If a US investor were to invest directly in the Japanese stocks that comprise the Nikkei, he would be exposed to both fluctuations in the Nikkei index and fluctuations in the USD/JPY exchange rate. Essentially, a quanto has an embedded currency forward with a variable notional amount. It is that variable notional amount that give quantos their name—"quanto" is short for "quantity adjusting option". Quanto options have both the strike price and underlier denominated in the foreign currency. At exercise, the value of the option is calculated as the option's intrinsic value in the foreign currency, which is then converted to the domestic currency at the fixed exchange rate. Another type of structure is called Quanto in the weather/energy markets. In these markets, a Quanto is a weather-contingent energy (or commodity) derivative. Weather contingent means that a payoff is triggered if some weather variable (typically temperature, but also precipitation or any other weather variable) crosses (from above or from below) a specified strike value. For the structure to be called Quanto, the payoff must depend on the market price of a publicly traded commodity. A typical example of a buyer of a Quanto is a retailer in a liberalized

electricity market An electricity market is a system that enables the exchange of electrical energy, through an electrical grid. Historically, electricity has been primarily sold by companies that operate electric generators, and purchased by consumers or electr ...

, with a customer base to which they deliver to a fixed contracted price. The retailers do buy most of their electricity forward, but have to go and purchase from the expensive spot market whenever they need to deliver more than what they've planned to. This situation typically occurs if the weather is hotter (colder) than expected and a substantial number of households turn on the airconditioning (heating). As electricity demand rises sharply in such a situation, spot prices spike while the revenue from the sales side remains constant. Buying a quanto allows the retailer to hedge against that risk. Common types of quanto include: * Quanto

futures contract In finance, a futures contract (sometimes called futures) is a standardized legal contract to buy or sell something at a predetermined price for delivery at a specified time in the future, between parties not yet known to each other. The item tr ...

s, such as a futures contract on a European

stock market index In finance, a stock index, or stock market index, is an Index (economics), index that measures the performance of a stock market, or of a subset of a stock market. It helps investors compare current stock price levels with past prices to calcul ...

which is settled in US dollars. * Quanto options, in which the difference between the underlying and a fixed strike price is paid out in another currency. * Quanto swaps, in which one

counterparty A counterparty (sometimes contraparty) is a Juristic person, legal entity, unincorporated entity, or collection of entities to which an exposure of financial risk may exist. The word became widely used in the 1980s, particularly at the time of the ...

pays a non-local

interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...

to the other, but the

notional amount The notional amount (or notional principal amount or notional value) on a financial instrument is the nominal or face amount that is used to calculate payments made on that instrument. This amount generally does not change and is thus referred to a ...

is in local currency. The second party may be paying a fixed or floating rate. For example, a swap in which the notional amount is denominated in

Canadian dollar The Canadian dollar (currency symbol, symbol: $; ISO 4217, code: CAD; ) is the currency of Canada. It is abbreviated with the dollar sign $. There is no standard disambiguating form, but the abbreviations Can$, CA$ and C$ are frequently used f ...

s, but where the floating rate is set as USD

LIBOR The London Inter-Bank Offered Rate (Libor ) was an interest rate average calculated from estimates submitted by the leading Bank, banks in London. Each bank estimated what it would be charged were it to borrow from other banks. It was the prim ...

, would be considered a quanto swap. * Quanto credit default swap, in which default protection is purchased on a notional amount specified in one currency, but the regular protection payment is denominated in a different currency.

Pricing Quanto Derivatives

Pricing quanto derivatives involves modeling financial variables (stocks, interest rates etc.) in a currency which is different from their actual currency. In order to write the dynamics of the modeled financial variables under foreign currency pricing measure one has to apply

Girsanov theorem In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it explains how to ...

leading to a drift term which depends on its volatility, the FX rate volatility (FX rate between the pricing currency and the modeled variable currency) and correlation between both.D. Papaioannou (2011): "Applied Multidimensional Girsanov Theorem", SSRN
/ref> This drift term leads to an adjustment in the pricing that is referred to as "quanto adjustment" and falls into the more general category of what is called in mathematical finance convexity adjustments.

References

External links

Pantz, Julien 2011 Quantos and FX Skew * https://ssrn.com/abstract=1895474 Brigo, Damiano; Pede, Nicola; Petrelli, Andrea 2015 Multi Currency Credit Default Swaps: Quanto effects and FX devaluation jumps * {{arXiv, 1512.07256 Turfus, Colin 2018 Analytic Pricing of Quanto CDS * https://www.researchgate.net/publication/325070862_Analytic_Pricing_of_Quanto_CDS Chung, Tsz-Kin; Gregory, Jon 2018 CVA Wrong Way Risk: Calibration Using Quanto CDS Basis * https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3406004_code2921783.pdf Derivatives (finance) Swaps (finance)