One Year Ago You Sold A Put Option On 100,000 Euros

One Year Ago You Sold A Put Option On 100000 Euros With An Expiratio

One year ago, you sold a put option on 100,000 euros with an expiration date of 1 year. You received a premium on the put option of $0.04 per unit. The exercise price was $1.22. Assume that 1 year ago, the spot rate of the euro was $1.20, the 1-year forward rate exhibited a discount of 2 percent, and the 1-year futures price was the same as the 1-year forward rate. From 1 year ago to today, the euro depreciated against the dollar by 4 percent.

Today the put option will be exercised (if it is feasible for buyer to do so). a) Determine the total dollar amount of your profit or loss from your position in the put option. b) Now assume that instead of taking a position in the put option 1 year ago, you sold a futures contract on 100,000 euros with a settlement date of 1 year. Determine the total dollar amount of your profit or loss.

Paper For Above instruction

The scenario presented involves two different financial instruments—selling a put option and selling a futures contract—both linked to the euro-dollar exchange rate. The analysis compares the outcomes of these positions over a one-year period, considering initial conditions, changes in exchange rates, and the implications on profit and loss. This paper aims to evaluate the profitability of each approach, given the exchange rate movements and related market factors.

Introduction

Foreign exchange derivatives, such as options and futures, are widely used by investors and corporations to hedge against currency risk or speculate on future movements. Understanding their profitability depends on initial conditions, market movements, and the specific contractual features. This paper examines a scenario where an investor sells a put option and a futures contract on euros, analyzing the profit or loss resulting from each position after one year, considering the depreciation of the euro against the dollar.

Initial Market Conditions and Contract Details

One year ago, the initial spot exchange rate was $1.20 per euro, with the option's exercise (strike) price at $1.22 per euro. The premium received for the put option was $0.04 per euro, and the futures and forward prices were aligned at a 2% discount relative to the spot rate, indicating a forward/futures price of approximately $1.176 per euro. The total exposure involved was 100,000 euros, placing the total initial premium income at $4,000 (100,000 euros × $0.04).

Part A: Profit or Loss from Selling a Put Option

The key to understanding the profit or loss lies in the relationship between the spot price today and the exercise price. One year ago, the spot was $1.20, but over the year, the euro depreciated by 4%, making the current spot rate approximately $1.152 per euro ($1.20 × 0.96).

Since the current spot rate ($1.152) is below the exercise price ($1.22), the put option is exercised by the holder. The option holder will sell euros at $1.22, while the market price is only $1.152, incurring a loss on each euro equal to the difference. The gross loss per euro is:

• Difference in price = $1.22 - $1.152 = $0.068

The total loss from the exercise is thus:

• Loss = 100,000 euros × $0.068 = $6,800

Net profit or loss for the writer of the put option is the loss minus the premium received:

• Net loss = $6,800 - $4,000 = $2,800

Therefore, the total dollar amount of your profit or loss from the put option position is a net loss of $2,800, considering the premium received offsets part of the exercise loss.

Part B: Profit or Loss from Selling a Futures Contract

When selling a futures contract, the trader enters into an obligation to sell euros at the agreed-upon futures price ($1.176) in one year. Over the year, the euro depreciates from an initial spot of $1.20 to $1.152, constituting a decrease of $0.048 per euro.

The profit or loss for the futures position is determined by the difference in futures price at initiation and settlement. Given the initial futures price was aligned with the forward rate ($1.176), and the futures contract settles at the actual spot price ($1.152), the position incurs a loss of:

• Loss per euro = $1.176 - $1.152 = $0.024

The total loss is:

• Loss = 100,000 euros × $0.024 = $2,400

Since you sold the futures contract, the loss is a financial loss. Correspondingly, the total profit/loss is the negative of this amount:

• Total loss = $2,400

Discussion and Conclusion

The analysis reveals contrasting outcomes of the two instruments in response to currency depreciation. Selling a put option resulted in a net loss of $2,800 mainly because the euro depreciated below the strike, rendering the option exercisable at a loss after accounting for the premium. Conversely, selling a futures contract resulted in a loss of $2,400, driven directly by the euro's depreciation from $1.20 to approximately $1.152.

Both instruments effectively provided exposure to exchange rate movements, with the futures contract exposing the seller to losses when the euro depreciates. The put option sale allowed some offset through the premium, but the depreciation was sufficient to produce losses in both cases. Such analyses are crucial for hedgers and speculators to understand potential risks and outcomes associated with currency derivatives. Proper hedging strategies can help mitigate these risks, but as demonstrated, markets can move unfavorably despite initial hedging intentions.

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