The Option Speculator Mini Case Is Designed To Test Your Kno

The Option Speculator Mini Case Is Designed To Test Your Knowledge Of

The Option Speculator Mini-Case is designed to test your knowledge of speculation with currency options. A speculator is considering the purchase of five three-month Japanese yen call options with a strike price of 96 cents per 100 yen. The premium is 1.35 cents per 100 yen. The spot price is 95.28 cents per 100 yen and the 90-day forward rate is 95.71 cents. The speculator believes the yen will appreciate to $1.00 per 100 yen over the next three months.

As the speculator's assistant, you have been asked to prepare the following:

1. In Excel, diagram the call option, profit (or loss) on the y-axis and future spot price on the x-axis.

2. Determine the speculator's profit if the yen appreciates to $1.00/100 yen.

3. Determine the speculator's profit if the yen appreciates only to the forward rate.

4. Determine the future spot price at which the speculator will only break even.

Introduction

Currency options are vital instruments in international financial markets, enabling traders and speculators to hedge against exchange rate risk or to profit from anticipated currency movements. In this case, a speculator considers buying Japanese yen call options to benefit from an expected appreciation of the yen over the upcoming three months. Analyzing the profitability of these options involves understanding the option payoff structure, the influence of exchange rate movements, and the calculation of break-even points.

Understanding Call Options in Currency Trading

A call option grants the holder the right, but not the obligation, to buy a specified amount of foreign currency at a predetermined strike price within a certain timeframe. For yen options, the payoff depends on the future spot rate relative to the strike price. If the spot rate appreciates above the strike, exercising the option is profitable; otherwise, the option expires worthless, and the loss is limited to the premium paid.

The Setup of the Case

The speculator considers purchasing five Japanese yen call options with a strike of 96 cents, a premium of 1.35 cents, and an expiration of three months. The current spot is 95.28 cents, with a forward rate of 95.71 cents, indicating market expectations of slight appreciation. The key question is whether the economic benefit from yen appreciation exceeds the cost of the options, factoring in the premiums paid.

Diagramming the Call Option Payoff in Excel

The first step involves graphing the call option's profit/loss versus the future spot price. In Excel, this can be achieved by creating a table with various potential future spot rates, calculating the profit or loss at each point, and then plotting these values using a scatter plot with straight lines and markers. This graph visually demonstrates the breakeven point, potential gains, and maximum loss.

Calculating Profits at Different Appreciation Levels

Profit if Yen Appreciates to $1.00/100 Yen:

If the yen appreciates to 100 cents per 100 yen, the intrinsic value of the option is:

\[ \text{Intrinsic Value} = (100\, \text{cents} - 96\, \text{cents}) = 4\, \text{cents} \]

The total profit from one option:

\[ (4\, \text{cents} - 1.35\, \text{cents}) \times 100\, \text{yen} = 2.65\, \text{cents} \]

Given five options, total profit:

\[ 5 \times 2.65\, \text{cents} = 13.25\, \text{cents} \]

Profit if Yen Appreciates only to the Forward Rate (95.71 cents):

This appreciation does not surpass the strike, so the intrinsic value is:

\[ (95.71\, \text{cents} - 96\, \text{cents}) = -0.29\, \text{cents} \]

Because it's less than the strike, the option expires worthless, resulting in a total loss of the premium paid:

\[ 5 \times 1.35\, \text{cents} = 6.75\, \text{cents} \]

Break-Even Future Spot Price:

The break-even occurs when the intrinsic value equals the premium paid:

\[ \text{Future spot} = \text{strike} + \text{premium} \]

\[ 96\, \text{cents} + 1.35\, \text{cents} = 97.35\, \text{cents} \]

Thus, the yen must appreciate to at least 97.35 cents per 100 yen for the investor to break even.

Conclusion

This case illustrates how fluctuations in currency exchange rates influence the profitability of currency options. The graphical representation in Excel provides a clear visualization of potential gains and losses across different future spot rates. The calculations underscore the importance of accurately forecasting currency movements and understanding the cost structure governed by option premiums, which together determine the success of currency speculation strategies.

Sample Paper For Above instruction

Financial Strategies in Currency Options: A Case Study Analysis

Currency options serve as pivotal tools in international finance, allowing entities and investors to hedge against adverse currency movements or to speculate on future exchange rate fluctuations. The examined mini-case focuses on a specific scenario where a speculator considers entering into Japanese yen call options, aiming to profit from an anticipated appreciation of the yen against the US dollar in the upcoming three months. Analyzing this scenario provides insights into the mechanics of currency options, their payoff structures, and strategic considerations essential for profitable speculation.

Background and Context

The scenario involves a speculator contemplating the purchase of five three-month Japanese yen call options, each with a strike price of 96 cents per 100 yen. The premium for each option is 1.35 cents, and current market data indicate a spot rate of 95.28 cents and a forward rate of 95.71 cents. The central premise is the expectation that the yen will strengthen to reach a dollar equivalence of 1.00 per 100 yen, presenting potential gains if the market moves as anticipated. This situation encapsulates core concepts of foreign exchange derivatives, including how the initial premium, strike price, and underlying currency movements influence profitability.

Understanding the Mechanics of Currency Call Options

Currency call options give the holder the right to purchase foreign currency at a predetermined strike price. The payoff at expiration depends on the future spot rate: if the yen's appreciation surpasses the strike, exercising the option yields a profit. Conversely, if the yen's value remains below the strike, it is optimal to let the option expire worthless, limiting losses to the premium paid. Graphically, the payoff structure resembles a kinked line, with a flat section when the spot rate is below the strike (option is out-of-the-money) and rising linearly as the spot exceeds the strike (option is in-the-money).

Graphical Representation in Excel

To visualize the payoff, one should construct a data table in Excel, plotting possible future spot rates against corresponding profits or losses. Key points include the strike price, the current spot, the forward rate, and a range of scenarios at regular intervals above and below the strike. Calculations involve determining the intrinsic value: (future spot rate - strike price) multiplied by the number of units, minus the premium paid. The profit is zero if the future spot rate is below the strike (since options expire worthless), and positive above the strike considering the premium deduction. Use a scatter plot with straight lines and markers to visualize the payoff profile effectively.

Calculations for Specific Exchange Rates

1. Profit if Yen Appreciates to $1.00/100 Yen

At a future rate of 100 cents per 100 yen, the intrinsic value per option is:

(100 cents - 96 cents) = 4 cents per 100 yen.

For five options, total profit before considering premium:

5 × 4 cents = 20 cents. Subtracting the premium cost per option (1.35 cents), the net profit per option is 2.65 cents, and for all five, total profit is:

5 × 2.65 cents = 13.25 cents.

Converted to dollar terms, this represents a profitable scenario, indicating the speculator's expectation is justified if the yen reaches a dollar per 100 yen.

2. Profit if Yen Appreciates Only to the Forward Rate ($0.9571)

The intrinsic value at this rate is:

(95.71 cents - 96 cents) = -0.29 cents, resulting in no intrinsic value. Given the option expires worthless, the total loss equals the premium for five options:

5 × 1.35 cents = 6.75 cents.

This scenario demonstrates the importance of the estimated market value exceeding the strike plus premium for profitability.

3. Break-Even Future Spot Price

The break-even point occurs when intrinsic value equals the premium paid:

Future spot = Strike + Premium = 96 cents + 1.35 cents = 97.35 cents.

Above this rate, the call provides net gains; below, it results in a net loss, aligning with the basic principle that options are profitable only when the underlying moves favorably beyond costs.

Implications and Strategic Considerations

This analysis underscores critical factors influencing FX options trading, including market expectations, currency volatility, and the cost of premiums. The graphical depiction supports investors’ ability to visualize risk-reward profiles, facilitating better decision-making. Strategic awareness of the breakeven point and potential profit scenarios enhances the efficacy of speculation strategies in forex markets.

Conclusion

This mini-case illustrates the practical application of currency options in international finance. Understanding the payoff structures, effective visualization through Excel, and precise calculations of profits at different exchange rates empower traders and investors to make informed decisions. As currency markets are influenced by multiple unpredictable factors, comprehensive analysis remains key to optimizing outcomes when engaging with currency derivatives.

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