Consider an Option to Buy £10,000 for €12,500 USING RISK NEUTRAL VALUATION (I

question 30

Essay

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.

$\begin{array}{lll}&spot Rates&Risk-tree Rates\\S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \\S_{0}\left(\$ / £)\right. & \$ 2.00=£ 1.00&i €4.00 \% \\S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%\end{array}$ USING RISK NEUTRAL VALUATION (i.e.,the binomial option pricing model)find the value of the call (in euro).

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Definitions:

Private-Value Auction

An auction in which the value of the item being bid on is subjective and differs for each bidder, based on their private evaluation.

Dutch Auction

A market structure where the price of an item is lowered until it meets a bid, opposite of the traditional auction format where prices ascend.

Second-Highest Willingness

The concept of determining the price or value of an item based on the highest bid that did not win in an auction or competitive bidding process.

Winner's Curse

A phenomenon in auctions, suggesting that the winning bidder tends to overpay due to incomplete information or overly optimistic value assessments.