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Foreign Exchange Option Pricing: A Practitioner's Guide by Iain J. Clark

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Chapter 10

Multicurrency Options

Most FX options that trade are single currency products, but there is a definite demand for options that depend upon a number of FX spot rates. Whereas single currency pair exotics often trade in the interbank market, or with hedge funds, multicurrency FX options are more often tailored to the needs of a corporate client – either due to a structuring request or as an embedded product within a trade note.

The typical example is a basket option, which a client can use to hedge the FX risk of a number of different currency exposures simultaneously and more cheaply than by buying an FX option for each of the FX rates separately.

An example may make this clearer. Consider a hypothetical Japanese sporting goods exporter, who sells athletic equipment (running shoes, athletics wear, etc.) both in their domestic market and internationally. On the basis of prior sales and internal forecasts, they expect to realise first quarter revenues of about 3 billion yen in Europe and 8 billion yen in their North American sales region.

To make the arithmetic easier, let’s suppose that USDJPY is trading at 90.00 and EURJPY is trading at 110.00.

This fixes EURUSD at 1.2222 in order to avoid arbitrage, and the expected revenues in units of local currency are EUR 27.3 million and USD 88.9 million respectively.

The goods for sale are obviously priced in EUR and USD in the local markets, thus giving rise to currency risk in each of the two factors EURJPY and USDJPY. Clearly ...

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