Problem 20.6 On Call Options Based On Chapter 20

Problem 20 6 On Call Options Based On Chapter 20

Analyze various options-related problems based on Chapter 20, including calculating payoffs for call and put options at expiration, drawing payoff diagrams, computing option returns and break-even prices, applying the Black-Scholes valuation model, evaluating swap strategies for debt issuance, and assessing futures contracts for commodities. Provide thorough explanations, calculations, diagrams, and discuss strategies related to options, swaps, and futures to demonstrate understanding of options pricing, payoff profiles, and hedging techniques.

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Introduction to Options and Derivatives Instrumentation

Financial derivatives such as options, swaps, and futures are pivotal tools in the modern financial landscape, enabling investors and firms to hedge risk, speculate, or enhance returns. Understanding the mechanisms of these instruments involves analyzing their payoffs, valuation models, and strategic applications. This paper provides a comprehensive review of various derivatives-based problems, including calculating option payoffs, constructing payoff diagrams, applying the Black-Scholes model, and evaluating strategies for firms in debt management and commodity hedging.

Option Payoffs and Diagrams

Call Option Payoff Analysis

The first problem involves a call option on Intuit stock with a strike price of $40, expiring in three months. The payoff for a call option at expiration depends on the stock price relative to the strike price. If the stock price surpasses the strike, the payoff equals the difference; otherwise, it is zero. For instance, if the stock trades at $55, the payoff is (55 - 40) = $15. Conversely, if the price declines to $35, the payoff becomes zero since exercising would yield no profit. The payoff diagram for a call option at expiration is a convex function, starting at zero for stock prices below $40, and increasing linearly beyond that point, illustrating the asymmetric upside potential (Hull, 2012).

Put Option Payoff Analysis

Similarly, for a put option on Ford stock with a strike of $10, expiring in six months, the payoff is the maximum of zero and strike minus stock price. If Ford stock is at $8, the payoff is ($10 - $8) = $2; if the stock is at $23, the payoff is zero — as exercising would be unprofitable. The payoff diagram for a put resembles a downward-sloping convex curve, with the maximum payoff equal to the strike price when stock price approaches zero (Natenberg, 1994).

Options Return and Break-even Analysis

Calculating Break-even Stock Prices

Considering IBM call and put options, the break-even point occurs when the total profit from exercising equals zero, which combines the premium paid and the stock price at expiration. For a call, this is the strike plus the premium; for a put, it is the strike minus the premium (McMillan, 2004). Such calculations are crucial for assessing risk and potential profit margins.

Return Analysis

The most likely options to yield a -100% return are out-of-the-money options at expiration, where the stock price remains below (for puts) or above (for calls) the strike price, rendering the options worthless. If IBM's stock price reaches $216, the in-the-money options will deliver the highest returns, as intrinsic value increases with stock price movements (Cox, Ross, & Rubinstein, 1979).

Black-Scholes Model for European Call and Put Valuation

The Black-Scholes formula is fundamental in options valuation, taking into account parameters like current stock price, strike price, volatility, risk-free rate, and time to expiration. Applying the Black-Scholes formula for Up, Inc.'s call with given parameters yields an estimated fair value which can be compared to market prices for arbitrage opportunities. Using put-call parity, the corresponding put value can be deduced, facilitating complete options strategy analysis (Black & Scholes, 1973; Merton, 1973).

Interest Rate Swaps and Corporate Borrowing Strategies

In managing corporate debt, firms can choose between short-term borrowing and issuing long-term bonds. Implementing a swap agreement, where fixed-rate debt is converted into floating rate or vice versa, allows firms to hedge against interest rate fluctuations while potentially reducing the effective cost of capital. If market conditions improve, refinancing via swaps can lock in favorable rates, thus stabilizing borrowing costs over extended periods. Calculating the optimal strategy involves analyzing spreads over LIBOR, treasury yields, and swap quotations, aligning with the firm's risk preferences and credit outlook (Tuckman & Serrat, 2011).

Futures Contracts for Commodity Hedging

Managing Oil Price Risk

Using futures contracts, a utility company seeking to hedge against rising oil prices can lock in purchase prices. Going long futures contracts ensures that if oil prices increase, the gains on futures offset higher purchase costs. The daily mark-to-market profits or losses depend on the futures price changes, which can be tabulated over the 10 days. The total profit or loss after 10 days aggregates these daily changes, illustrating the effectiveness of futures in risk mitigation (Hull, 2012).

Risk of Cumulative Losses

While futures provide protection against price increases, they entail potential losses if prices decline. The maximum cumulative loss occurs if the futures prices drop consistently, and the company must purchase at higher-than-market spot prices, highlighting the importance of monitoring market movements and considering stop-loss strategies (Kolb & Overdahl, 2007).

Conclusion

Derivatives like options, swaps, and futures are valuable financial instruments that, when used effectively, can hedge risk, speculate, and optimize capital structure. Proper understanding and strategic application require analyzing payoffs, valuation models, and market conditions. This comprehensive review underscores the importance of these tools in modern financial management, emphasizing the need for accurate calculations, risk assessment, and strategic planning to maximize benefits and mitigate potential losses.

References

• Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654.
• Cox, J., Ross, S., & Rubinstein, M. (1979). Option Pricing: A Simplified Approach. Journal of Financial Economics, 7(3), 229–263.
• Hull, J. C. (2012). Options, Futures, and Other Derivatives (8th ed.). Pearson Education.
• Kolb, R. W., & Overdahl, J. A. (2007). Financial Derivatives: Pricing and Risk Management. Wiley.
• Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4(1), 141–183.
• McMillan, L. G. (2004). Options as a Strategic Investment. Pearson Education.
• Natenberg, S. (1994). Option Volatility & Pricing. McGraw-Hill.
• Tuckman, B., & Serrat, A. (2011). Fixed-Income Securities: Tools for Today's Markets (3rd ed.). Wiley.