Question

4.

1. (a) Explain the features of an interest rate swap, illustrating your answer with a simple numerical example. What benefits could a firm obtain from using interest rate swaps? (150 words)

2. (b) Why must the price of an American call option on a stock that pays no dividends always be higher than its intrinsic value? How can the price of an American call option be determined from the price of a European call option on the same stock with the same time to expiry? Explain. (180 words)

3. (c) Is it ever optimal to exercise an American put option before its expiration date, assuming the underlying stock pays no dividends? Explain your answer with reference to the put-call parity relationship. (150 words)

   (Total = 25 marks)

Answer 1

Explain the features of an interest rate swap, illustrating your answer with a simple numerical example. What benefits could a firm obtain from using interest rate swaps?

An interest rate swap is a forward contract in which one stream of future interest payments is exchanged for another based on a specified principal amount. Interest rate swaps usually involve the exchange of a fixed interest rate for a floating rate, or vice versa, to reduce or increase exposure to fluctuations in interest rates or to obtain a marginally lower interest rate than would have been possible without the swap.

Interest rate swaps are the exchange of one set of cash flows for another. Because they trade over the counter (OTC), the contracts are between two or more parties according to their desired specifications and can be customized in many different ways. Swaps are often utilized if a company can borrow money easily at one type of interest rate but prefers a different type.

There are three different types of interest rate swaps: Fixed-to-floating, floating-to-fixed, and float-to-float.

Fixed to Floating

For example, consider a company named TSI that can issue a bond at a very attractive fixed interest rate to its investors. The company's management feels that it can get a better cash flow from a floating rate. In this case, TSI can enter into a swap with a counterparty bank in which the company receives a fixed rate and pays a floating rate. The swap is structured to match the maturity and cash flow of the fixed-rate bond and the two fixed-rate payment streams are netted. TSI and the bank choose the preferred floating-rate index, which is usually LIBOR for a one-, three- or six-month maturity. TSI then receives LIBOR plus or minus a spread that reflects both interest rate conditions in the market and its credit rating.

Floating to Fixed

A company that does not have access to a fixed-rate loan may borrow at a floating rate and enter into a swap to achieve a fixed rate. The floating-rate tenor, reset and payment dates on the loan are mirrored on the swap and netted. The fixed-rate leg of the swap becomes the company's borrowing rate.

Float to Float

Companies sometimes enter into a swap to change the type or tenor of the floating rate index that they pay; this is known as a basis swap. A company can swap from three-month LIBOR to six-month LIBOR, for example, either because the rate is more attractive or it matches other payment flows. A company can also switch to a different index, such as the federal funds rate, commercial paper or the Treasury bill rate.

Real World Example of an Interest Rate Swap

Suppose that PepsiCo needs to raise $75 million to acquire a competitor. In the U.S., they may be able to borrow the money with a 3.5% interest rate, but outside of the U.S., they may be able to borrow at just 3.2%. The catch is that they would need to issue the bond in a foreign currency, which is subject to fluctuation based on the home country's interest rates.

PepsiCo could enter into an interest rate swap for the duration of the bond. Under the terms of the agreement, PepsiCo would pay the counterparty a 3.2% interest rate over the life of the bond. The company would then swap $75 million for the agreed upon exchange rate when the bond matures and avoid any exposure to exchange-rate fluctuations.

A swap can also involve the exchange of one type of floating rate for another, which is called a basis swap.

Why must the price of an American call option on a stock that pays no dividends always be higher than its intrinsic value? How can the price of an American call option be determined from the price of a European call option on the same stock with the same time to expiry?

An American option is a version of an options contract that allows holders to exercise the option rights at any time before and including the day of expiration. Another version or style of option execution is the European option that allows execution only on the day of expiration.

An American style option allows investors to capture profit as soon as the stock price moves favorably. The names American and European have nothing to do with the geographic location but only apply to the style of rights execution.

American Options Explained

American options outline the timeframe when the option holder can exercise their option contract rights. These rights allow the holder to buy or sell—depending on if the option is a call or put—the underlying asset, at the set strike price on or before the predetermined expiration date. Since investors have the freedom to exercise their options at any point during the life of the contract, American style options are more valuable than the limited European options. However, the ability to exercise early carries an added premium or cost.

The last day to exercise a weekly American option is normally on the Friday of the week in which the option contract expires. Conversely, the last day to exercise a monthly American option is normally the third Friday of the month.

The majority of exchange-traded options on single stocks are American, while options on indexes tend to be European style.

American Call and Put Options

A call option gives the holder the right to demand delivery of the underlying security or stock on any day within the contract period. This feature includes any day leading up to and the day of expiration. As with all options, the holder does not have an obligation to receive the share if they choose not to exercise their right. The strike price remains the same specified value throughout the contract.

If an investor purchased a call option for a company in March with an expiration date at the end of December of the same year, they would have the right to exercise the call option at any time up until its expiration date. American options are helpful since investors don't have to wait to exercise the option when the asset's price rises above the strike price. However, American style options carry a premium—an upfront cost—that investors pay and which must be factored into the overall profitability of the trade.

American put options also allow the execution at any point up to and including the expiration date. This ability gives the holder the freedom to demand the buyer takes delivery of the underlying asset whenever the price falls below the specified strike price.

When to Exercise Early

In many instances, holders of American style options do not utilize the early exercise provision, since it's usually more cost-effective to either hold the contract until expiration or exit the position by selling the option contract outright. In other words, as a stock price rises, the value of a call option increases as does its premium. Traders can sell their option back to the options market if the current premium is higher than the initial premium paid at the onset. The trader would earn the net difference between the two premiums minus any fees or commissions from the broker.

However, there are times when options are typically exercised early. Deep-in-the-money call options—where the asset's price is well above the option's strike price—will usually be exercised early. Puts can also be deep-in-the-money when the price is significantly below the strike price. In most cases, deep prices are those that are more than $10 in-the-money.

Early execution can also happen leading up to the date a stock goes ex-dividend. Ex-dividend is the cutoff date by which shareholders must own the stock to receive the next scheduled dividend payment. Option holders do not receive dividend payments. So, many investors will exercise their options before the ex-dividend date to capture the gains from a profitable position and get paid the dividend.

The reason for the early exercise has to do with the cost of carry or the opportunity cost associated with not investing the gains from the put option. When a put is exercised, investors are paid the strike price immediately. As a result, the proceeds can be invested in another security to earn interest.

However, the drawback to exercising puts is that the investor would miss out on any dividends since exercising would sell the shares. Also, the option itself might continue to increase in value if held to expiry, and exercising early might lead to missing out on any further gains.

Pros

• Ability to exercise at any time

• Allows exercise before an ex-dividend date

• Allows profits to be put back to work

Cons

• Charges a higher premium

• Not available for index option contracts

• May miss out on additional option appreciation

Real World Example of an American Option

An investor purchased an American style call option for Apple Inc. (AAPL) in March with an expiration date at the end of December in the same year. The premium is $5 per option contract—one contract is 100 shares ($5 x 100 = $500)—and the strike price on the option is $100. Following the purchase, the stock price rose to $150 per share.

The investor exercises the call option on Apple before expiration buying 100 shares of Apple for $100 per share. In other words, the investor would be long 100 shares of Apple at the $100 strike price. The investor immediately sells the shares for the current market price of $150 and pockets the $50 per share profit. The investor earned $5,000 in total minus the premium of $500 for buying the option and any broker commissions.

Let's say an investor believes shares of Facebook Inc. (FB) will decline in the upcoming months. The investor purchases an American style July put option in January, which expires in September of the same year. The option premium is $3 per contract (100 x $3 = $300) and the strike price is $150.

Facebook's stock price falls to $90 per share, and the investor exercises the put option and is short 100 shares of Facebook at the $150 strike price. The transaction effectively has the investor buying 100 shares of Facebook at the current $90 price and immediately selling those shares at the $150 strike price. However, in practice, the net difference is settled, and the investor earns a $60 profit on the option contract, which equates to $6,000 minus the premium of $300 and any broker commissions.

A European option is a version of an options contract that limits execution to its expiration date. In other words, if the underlying security such as a stock has moved in price an investor would not be able to exercise the option early and take delivery of or sell the shares. Instead, the call or put action will only take place on the date of option maturity.

Another version of the options contract is the American options, which can be exercised any time up to and including the date of expiration. The names of these two versions should not be confused with the geographic location as the name only signifies the right of execution.

European Options Explained

European options define the timeframe when holders of an options contract may exercise their contract rights. The rights for the option holder include buying the underlying asset or selling the underlying asset at the specified contract price—the strike price. With European options, the holder may only exercise their rights on the day of expiration. As with other versions of options contracts, European options come at an upfront cost—the premium.

It is important to note that investors usually don't have a choice of buying either the American or the European option. Specific stocks or funds might only be offered in one version or the other, and not in both. Also, most indexes use European options because it reduces the amount of accounting needed by the brokerage. Many brokers use the Black Scholes model (BSM) to value European options.

European index options halt trading at business close Thursday before the third Friday of the expiration month. This lapse in trading allows the brokers the ability to price the individual assets of the underlying index. Due to this process, the settlement price of the option can often come as a surprise. Stocks or other securities may make drastic moves between the Thursday close and market opening Friday. Also, it may take hours after the market opens Friday for the definite settlement price to publish.

European options normally trade over the counter (OTC), while American options usually trade on standardized exchanges.

European Calls and Puts

A European call option gives the owner the liberty to acquire the underlying security at expiry. A call option buyer is bullish on the underlying asset and expects the market price to trade higher than the call option's strike price before or by the expiration date. The option's strike price is the price at which the contract converts to shares of the underlying asset. For an investor to profit from a call option, the stock's price, at expiry, has to be trading high enough above the strike price to cover the cost of the option premium.

A European put option allows the holder to sell the underlying security at expiry. A put option buyer is bearish on the underlying asset and expects the market price to trade lower than the option's strike price before or by the contract's expiration. For an investor to profit from a put option, the stock's price, at expiry, has to be trading far enough below the strike price to cover the cost of the option premium.

Is it ever optimal to exercise an American put option before its expiration date, assuming the underlying stock pays no dividends? Explain your answer with reference to the put-call parity relationship.

Put-call parity is a principle that defines the relationship between the price of European put options and European call options of the same class, that is, with the same underlying asset, strike price, and expiration date.

Put-call parity states that simultaneously holding a short European put and long European call of the same class will deliver the same return as holding one forward contract on the same underlying asset, with the same expiration, and a forward price equal to the option's strike price. If the prices of the put and call options diverge so that this relationship does not hold, an arbitrage opportunity exists, meaning that sophisticated traders can theoretically earn a risk-free profit. Such opportunities are uncommon and short-lived in liquid markets.

Understanding Put-Call Parity

Put-call parity applies only to European options, which can only be exercised on the expiration date, and not American options, which can be exercised before.

Say that you purchase a European call option for TCKR stock. The expiration date is one year from now, the strike price is $15, and purchasing the call costs you $5. This contract gives you the right—but not the obligation—to purchase TCKR stock on the expiration date for $15, whatever the market price might be. If one year from now, TCKR is trading at $10, you will not exercise the option. If, on the other hand, TCKR is trading at $20 per share, you will exercise the option, buy TCKR at $15 and break even, since you paid $5 for the option initially. Any amount TCKR goes above $20 is pure profit, assuming zero transaction fees.

Say you also sell (or "write" or "short") a European put option for TCKR stock. The expiration date, strike price, and cost of the option are the same. You receive $5 from writing the option, and it is not up to you to exercise or not exercise the option since you don't own it. The buyer has purchased the right, but not the obligation, to sell you TCKR stock at the strike price; you are obligated to take that deal, whatever TCKR's market share price. So if TCKR trades at $10 a year from now, the buyer will sell you the stock at $15, and you will both break even: you already made $5 from selling the put, making up your shortfall, while the buyer already spent $5 to buy it, eating up his or her gain. If TCKR trades at $15 or above, you have made $5 and only $5, since the other party will not exercise the option. If TCKR trades below $10, you will lose money—up to $10, if TCKR goes to zero.

The profit or loss on these positions for different TCKR stock prices is graphed below. Notice that if you add the profit or loss on the long call to that of the short put, you make or lose exactly what you would have if you had simply signed a forward contract for TCKR stock at $15, expiring in one year. If shares are going for less than $15, you lose money. If they are going for more, you gain. Again, this scenario ignores all transaction fees.