Options premium

Option Premiums Stochastic Risk Risk to Workout... 

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. 

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 exhibit shows the option premiums quoted to the nearest 0.005 and strike prices separated by 0.125 intervals as required by the contract specification. The underlying June 2003 future settled at 97.745 that day (implying a 3-month interest rate in June of 2.255%), so the table highlights the 97.750 ATM options. 

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. 

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. 

Essentially, the premium represents the buyer s expected profit. Like insurance premiums, option premiums depend on how the option writers assess the likelihood of the payout equaling the premium. That, in turn, is a function of the probability of the option being exercised. An option s price is, therefore, a function of the probability that it will be exercised, from which is derived an expected outcome and a fair value. 

The level of interest rates. As noted above, the option premium, in theory, equals the present value of the gain the buyer expects to realize at exercise. The discount rate used therefore affects the premium, although it is less influential than the other factors discussed. 

The profit-loss profile for option buyers is quite different from that for option sellers. Buyers potential losses are limited to the option premium, while their potential profits are, in theory, unlimited. Sellers potential profits are limited to the option premium, while their potential losses are, in theory, unlimited at the least, they can be very substantial. (For a more in-depth discussion of options profit-loss profile, see chapter 8.)... 

Gamma is the only major Greek that does not measure the sensitivity of the option premium instead, it measures the delta sensitivity. Since delta determines an option s hedge ratio, gamma indicates how much this... 

Insurance Expenses - Depending upon the project, insurance expenses could either increase or decrease. Insurance premiums can be increased depending on the technology option chosen for a plant design. 

Finally, there are the house brands of each supermarket, with very little description of their source and treatment. Wegman s Spring Water comes from Concord, New York, and sells for 0.17 per quart, which is 10 times less than the premium imported water. The source may be municipal or well water, with very little claim to high-tech processing, and is the lowest cost option to tap water. 

Specific comparisons may help to explain the variety of options available to enrollees. In 2007, there were three American Association of Retired Persons (AARP)-associated plans Medicare Rx had an average monthly premium of 27.83, Medicare Rx Saver had a premium of 17.83, and Medicare Rx Enhanced had a premium of 46.30 (Hoadley et al., 2006). Humana also had three plans with premiums of 15.17, 22.03, or 80.43 for standard, enhanced, and complete coverage, respectively. As well as variation in premiums, there also was variation in other benefit cost-sharing characteristics, such as copays and tiered medications. 

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