Consider an Option to Buy €12,500 for £10,000 Calculate the Current €/£ Spot Exchange Rate

question 22

Essay

Consider an option to buy €12,500 for £10,000.In the next period,the euro can strengthen against the pound by 25 percent (i.e.,each euro will buy 25 percent more pounds)or weaken by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.

$\begin{array}{lll}&spot Rates&Risk-tree Rates\\S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \\S_{0}\left(\$ / £)\right. & \$ 2.00=£ 1.00&i €4.00 \% \\S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%\end{array}$ Calculate the current €/£ spot exchange rate.

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Definitions:

Utility Function

A mathematical representation of how different quantities of goods or services are ranked according to their desirability for a consumer.

Initial Endowment

The initial distribution of income, wealth, or resources that individuals or organizations possess before entering into any market transactions.

Numeraire

A unit of account in which prices are expressed in an economic model, facilitating comparison and calculation.

Competitive Equilibrium Price

The price level at which the quantity supplied equals the quantity demanded in a competitive market, ensuring no excess supply or demand.