### Quanto, Composites and FX foreign market derivatives

There are variety of ways an investor can gain exposure to foreign market indices and stocks, this article hopes to give you an introduction to these fx based structures and their implications from modelling perspective. Essentially we are talking about derivatives contracts which have payment currencydifferent to the currency of the underlying. We shall talk about three basic types of FX exposures, namely Quantos, Composites and FX foreign market derivatives. To begin with lets describe these major FX expsuer types:

##### Quantos

These are derivative contracts in which the payoff is based on a foreign index/stock in local currency. Imagine a call option again on NIFTY 50 based in USD (hence they are also called ADR style) with strike 123.88 so that the payoff is Max[0,S_{usd}-123.88]. To highlight the difference in the case of composites, At expiry suppose the NIFTY climbs from 5600 in INR to 5800 but the USD weakens against INR from 45.2043 to 48.2010 (1 USD = 48.2010 INR) resulting S_{usd}=120.32 so that the call payoff=0. So even though the index climbs in the local currency, its the index value in the foreign currency that determines the payoff i.e. both exchange rate and spot should be modelled together for pricing purposes.

Essentially then the payoffs for a composite forward, call option and put option are respectively:

The effective volatility of a composite option is given by

##### FX market derivatives

FX market derivatives are derivatives whose payoffs are driven by the underlyings in the local currency but the final settlement is made in the foreign currency.

Imagine a call option again on NIFTY 50 based in INR which makes the final settlement in USD based on existing exchange rate at expiry. If we revisit the above example, lets say the call option has the strike 5600 (corresponding to the strike 123.88 in the example above). At expiry lets say the NIFTY climbs from 5600 to 5800 and at the same time the USD weakens against INR from 45.2043 to 48.2010 (1 USD = 48.2010 INR). So that the final payoff = USD 4.15.

Essentially then the payoffs for a FX market forward, call option and put option are respectively:

From pricing perspective, we can model the FX and Equity seperately.