Options time value

A number of factors dictate whether an option is exercised or not. The first is the asymmetric profit-loss profile of option holders their potential gain is theoretically unlimited when the price of the underlyir asset rises, but they lose only their initial investment if the price falls. This asymmetry fevors runnir an option position. Another consideration favorir holdir is the fact that the options time value is lost if it is exercised early. In callable bonds, the call price often decreases as the bond approaches mamriry. This creates an incentive to delay exercise until a lower strike price is available. Coupon payments, on the other hand, may fevor earlier exercise, since, in the case of a normal, nonembedded option, this allows the holder to earn interest sooner. 

For an example of the kinds of decisions that involve the time value of money, examine the advertisement in Figure 3.1. For which option do you receive the most value Answers to this and similar questions sometimes may be quickly resolved using a calculator or computer without much thought. To understand the underlying assumptions and concepts behind file calculations, however, you need to account for cash flows in and out using the investment time line diagram for a project. Look at Figure 3.2. 

Although the economic downturn of 2001-2003 was accompanied by massive losses on the stock markets, this development did not reflect to the same degree in the prices paid for acquisitions in the specialty chemicals sector. Since at the same time the economic outlook for most specialty chemicals markets offered considerably lower growth expectations than in the 1990s, major acquisitions at high multiples seemed an increasingly unattractive option for value generation. 

Figure 2 shows examples of how the data from PEPT can be treated, in this case from a spouted bed. The simplest data output is a continuous trajectory, consisting of a large file of x, y, z, time values, plus optional continuously recorded user-defined parameters such as speed or blade position. Velocity values can be obtained from this data file, in practice by a multi-point weighted averaging technique, and time averaged velocity profiles can then be derived. It is also possible to obtain values of... 

The relation (15.5) is known as the compound-interest formula. The relation (15.6) is the reciprocal that allows the comparison of different options on the same basis, the present value. A simple numerical exploration shows that the variation of the future value F over years depends strongly on the interest rate. Figure 15.3 presents the evolution of a monetary unit over 20 years at different interest rates. The time-value of money change considerably, particularly for higher interest rates and longer times. 

The original MTM system is now known as MTM-1. Subsequent modifications were later developed to provide easier and quicker systems by condensing emd reducing the number of motion options and time values. MTM-2 and MTM-3 are exeunples of second-level and third-level MTM data. In addition, the MTM family of systems include MTM-V, MTM-C, MTM-M, MTM-TE, MTM-MEK, and MTM-UAS. 

Determining the Value of an Embedded Option The value of an embedded option is found through the binomial tree model. The first step is to forecast the value of the underlying security in which the price S of a security can move, respectively, in the upstate and downstate with a probability of p and 1 p. The change in price occurs in discrete time interval At and will depend on the level of volatility assumed. An option written on the asset, with maturity T will move in discrete steps as the movements of the share prices. The process can be carried on for any number of time intervals (Figure 9.6). 

Time Value—Option premiums normally exceed their intrinsic value. For example, the premium for a call option struck at 98 on a bond trading at 101 might be 4, not 3. The time value of an option is the... 

The time value of at-the-money options is the greatest. This is not so apparent from Exhibit 17.8 which shows the total premiums, comprising intrinsic value and time value. Exhibit 17.9 shows the time value component by itself, which makes this feature obvious. With OTM options, the entire premium is time value—this applies to the 117-strike calls and the 116-strike puts, for example. With ITM options, the time value is the total premium less the intrinsic value. For example, the intrinsic value for the April 2003 call option struck at 115 is 1.42 (116.42 less 115). Subtracting this from the total premium of 1.53 gives the time value of 0.11 shown in the table. 

EXHIBIT 17.9 Time Values for Euro-BUND Options on 7 March 2003... 

Why is time value greatest for ATM options Think first abont OTM and ITM options. For deep ITM options, the owner is virtn-ally certain to exercise the option, so the right to tear up the option instead is minimal. In a similar way, the owner of a deep OTM option is virtually certain to let the option expire unexercised, so the right to exercise the option instead is also minimal. For ATM options there is no snch certainty on the contrary, uncertainty is at its greatest, so the right to decide later whether or not to exercise is also highest at this strike level. 

Time value is greatest for the ATM options struck at 97.750, equalling 0.100 for both puts and calls. The 97.875 strike options have a time value of 0.055, while the 97.625 strike options have a time value of only 0.050. As we will see when we examine hedging applications, this makes the economic cost of ATM options the highest. 

The option premium has two constituents intrinsic value and time value. Intrinsic value equals the difference berween the strike price and the underlying assets current price. It is what the options holders would realize if they were to exercise it immediately. Say a call option on a bond futures contract has a strike price of 100 and the contract is trading at 105. A holder who exercises the option, buying the futures at 100 and selling the contract immediately at 105, earns a profit of 5 that is the options intrinsic value. A put options intrinsic value is the amount by which the current underlying assets price is below the strike. Because an option holder will exercise it only if there is a benefit to so doing, the intrinsic value will never be less than zero. Thus, if the bond future in the example were trading at 95, the intrinsic value of the call option would be zero, not —5. 

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. 

Time value The difference between the current price of the option and its intrinsic value... 

The premium of the call option, 1.15, is composed entirely of time value. 

As noted in chapter 8, the value of an option is a function of five factors The price of the underlying asset The option s strike price The options time to expiry... 

The price of an option is composed of intrinsic value and time value. An option s intrinsic value is clear. Valuation models, therefore, essentially price time value. 

At-the-money options have the greatest time value in-the-money contracts have more time value than out-of-the-money ones. These relationships reflect the risk the different options pose to the market makers that write them. Out-of-the-money call options, for instance, have the lowest... 

At-the-money options—which constitute the majority of OTC contracts—are the riskiest to write. They have 50—50 chances of being exercised, so deciding whether or not to hedge them is less straightforward than with other options. It is this uncertainty about hedging that makes them so risky. Accordingly, at-the-money options have the highest time values. 

In theory, American options should have greater value than equivalent European ones, because they can be exercised before maturity. In practice, however, early exercise rarely happens. This is because option holders realize only their contracts intrinsic value when they exercise. By selling their contracts in the market, in contrast, holders can realize their full value, including time value. 

Some option strategies exploit theta. Writing a short-term option and simultaneously purchasing a longer-term one with the same strike price, for instance, represents a play on the options theta if the time value of the longer option decays at a slower rate than that of the short-dated option, the trade will be profitable. 

An option s value, or price, is composed of two elements its intrinsic value and its time value. The intrinsic value is what the holder would realize if the option were exercised immediately—that is, the difference between the strike price and the current price of the underlying asset. To illustrate, if a call option on a bond has a strike price of 100 and the underlying bond is currently trading at 103, the option has an intrinsic value of 3. The holder of an option will exercise it only if it has intrinsic value. The intrinsic value is never less than zero. An option with intrinsic value greater than zero is in the money. An option whose strike price is equal to the price of the underlying is at the money one whose strike price is above (in the case of a call) or below (in the case of a put) the underlying s price is out of the money. 

An option s time value is the difference between its intrinsic value and its premium. Stated formally. 

The premium of an option with zero intrinsic value is composed solely of time value. Time value reflects the potential for an option to move more deeply into the money before expiry. It diminishes up to the option s... 

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