Options payoff profile

The simplest hedge against a drop in bond prices is to buy put options on the bond. Let s first consider using the June 2003 put option struck at 116.50, which are priced at 1.26, or 627,480 for 498 contracts. Exhibit 17.20 shows the payoff profile for the bond, the put option, and the combination. The kink in the option payoff profile at an option strike price of 116.50 corresponds to a price of around 105.75 in the bond being hedged. 

An options payoff profile is unlike that of any other instrument. Compare, for instance, the profiles of a vanilla call option and of a vanilla bond futures contract. Traders who buy one lot of the bond futures at 114 and hold it for a month before selling it realize a profit if the contracts price at the end of the month is above 114 and a loss if it is below 114. The amount of the gain or loss is 1,000 for each point above or below ll4. The same applies in reverse to those with short positions in the futures contract. The futures payoff profile is thus linear, for both the long and the short position. This is illustrated in FIGURE 8.1. 

Exhibit 17.3 shows the payoff profiles for the buyer and seller of the bond option, once the option premium— 2 in this example—is taken into account. If the underlying bond is trading below 98, the option will expire worthless, and the option buyer will now be 2 down, as the chart shows. It is this premium income that provides the incentive for option sellers. As Exhibit 17.3 shows, so long as the bond trades at a price of 100 or lower when the option expires, the option seller ends up with a profit. 

EXHIBIT 17.3 Payoff Profiles for Option Buyer and Seller (with Premiums)... 

Put Option— This gives the holder the right to sell the underlying asset. Exhibit 17.4 contrasts the payoff profile from a call with that of a put. In both cases, the fixed price at which the bond may be bought (for the call) or sold (for the put) is 98. For illustrative purposes, the call premium is 2, while the put premium is 3. 

The simplest way to speculate is simply to buy bond call options. The ATM calls struck at 116.50 are priced at 1.18, so buying these options on a notional bond face value of 100 million would involve buying 996 contracts, and would cost 1.18 million. Exhibit 17.23 illustrates the resulting payoff profile. 

When volatility rises, it is because option writers are more uncertain about the future, and increase their quotations for option premiums. Buyers of straddles—holding both puts and calls—will therefore benefit, as Exhibit 17.26 shows. Here we chart the payoff profile of the original straddle, and compare this with the profile after volatility has risen by 1%. The gap between these lines is around 400,000—the profit generated by the straddle from a 1% increase in volatility. 

This example illustrates that the holders of long and short positions in options, unlike holders of other financial instruments, have asymmetrical payoff profiles. Call option buyers benefit if the price of the underlying asset rises above the strike by at least the amount of the premium bur lose... 

Traders who wish to benefit from a fall in the market level but don t want to short the market might buy put options. Put options have the same asymmetrical payoff profiles for buyers and sellers as call options, but in the opposite direction. Put buyers profit if the market price of the underlying asset falls below the strike but lose only the premium they paid if the price remains above the strike. Put writers do not profit from moves in the underlying, whatever direction these moves take, and lose if the market falls below the strike by more than the premium amount. The premium they earn on the option sale is their compensation for taking on this risk. 

The time value of an option is the amount by which the option value exceeds the intrinsic value. Because of the risk they are taking on, illustrated in the payoff profiles above, option writers almost always demand premiums that are higher than the contracts intrinsic value. The value of an option that is out of the money is composed entirely of time value. Time value reflects the potential for an option to move into, or more deeply into, the money before expiry. It diminishes up to the option s expiry date, when it becomes zero. The price of an option on expiry is composed solely of intrinsic value. FIGURE 8.4 lists basic option market terminology. 

Bond investors can use credit options to hedge against rating downgrades and similar events that would depress the value of their holdings. To ensure that any loss resulting from such events will be offset by a profit on their options, they purchase contracts whose payoff profiles refiect their bonds credit quality. The options also enable banks and other institutions to take positions on credit spread movements without taking ownership of the related loans or bonds. The writer of credit options earns fee income. 

Other derivatives, such as forward-rate agreements and swaps, have similar profiles, as, of course, do cash instruments such as bonds and stocks. Options break the pattern. Because these contracts confer a right but impose no obligation on their holders and impose an obligation but confer no right on their sellers, the payoff profiles for the two parties are different. If, instead of the futures contract itself, the traders in the previous example take long and short positions in a call option on the contract at a strike price of 114, their payoff profiles will be those shown in FIGURE 8.2. 

FIGURE 8.2 Payoff Profiles for Long and Short Positions in a Call Option Contract ... 

This example illustrates that the holders of long and short positions in options, unlike holders of other financial instruments, have asymmetrical payoff profiles. Call option buyers benefit if the price of the underlying asset rises above the strike by at least the amount of the premium but lose only what they paid for the option if it fails to do so. The option sellers suffer a loss if the price of the underlying asset rises above the strike by more than the premium amount but realize only the funds received for writing the option if it fails to do so. 

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