# Put Values and Stock Prices

The same price-change characteristics apply to puts that apply to calls with one major difference: Put values are inversely correlated with stock prices. Thus put values fall as stock prices rise and rise as stock prices fall. Table 3-4 contains theoretical values of a 100 Put at various stock prices and days to expiration.The stock price is 100, the put has 90 days to expiration,and the theoretical value of the 100 Put is 5.31.

If the stock price falls by 1 to 99 (row 5, column1) and the other factors are unchanged, the theoretical value of the 100 Put increases by 0.45 to 5.76. If the stock price rises by 1 to 101, the put value decreases to 4.88. In both cases,the put price changes less than the stock price, and this relationship is always true for puts, just as it is for calls. Furthermore, the ratio of the change in put price to change in stock price varies with stock price and with time.

For example, when the stock price falls by 1 from 99 to 98 at 45 days, the put value rises from 4.36 to 4.89, or approximately 53 percent of the stock-price change. In another situation, when the stock rises from 103 to 104 at 60 days, the put falls from 3.23 to 2.89, or approximately 34 percent of the stock-price change.The upper line (curved) reflects put values at 90 days to expiration,like column 1 in Table 3-4.

The middle line (curved) contains put values at 45 days to expiration, like column 4 in Table 3-4; and the lower line (two straight sections) contains put values at expiration, like column 7 in Table 3-4. Like Table 3-4, Figure 3-2 illustrates that put values are inversely correlated with stock prices and that the level of correlation varies depending on the relationship of the stock price to the strike price.

Put values are near zero when the stock price is significantly above the strike price. Put values rise gradually as the stock price declines toward the strike price. The values then rise faster and faster as the stock price reaches and then falls below the strike price. Finally, as the stock price drops significantly below the strike price, the change in put value approaches a one-for-one relationship with change in stock price. In theory, however, put values never change exactly one for one with stock prices because, in theory, the value of a put always will contain at least a slight time premium.

Delta:The ratio of option-price change to stock-price change is an important aspect of option-price behavior, and it is referred to as the delta of an option. Specifically, delta is the change in option theoretical value given a one-unit change in price of the underlying stock. This chapter introduces delta, but Chapter 4 will discuss it in detail.Recall the example from Table 3-3. When the stock price rose from 100 to 101 at 90 days to expiration, and the 100 Call rose 0.58 from 6.53 to 7.11, this call would be described as having a “delta of 58.”

Actually, the delta is 0.58, or 58 percent. This means that the 100 Call is estimated to change in price by an amount equal to 58 percent of the stock-price change. Look at a different example from Table 3-4, where the stock price declined from 100 to 99, and the 100 Put rose by 53 cents. This put would be described as having a “delta of 53,” or negative 53 percent. This means that the 100 Put is estimated to change in price by 53 cents when the stock price changes by \$1.

Call Values Relative to Put Values:The relationship between call and put values confuses many traders.Intuition may tell you that calls and puts with the same strike price and the same expiration should have the same value if the stock price is equal to the strike price. Actually, however, this parity does not happen. Assuming no dividends, call prices always will be greater than put prices because they contain an interest component that puts lack.

Evidence of this disparity appears from a comparison of Tables 3-3 and 3-4. Row 6 in both tables shows option values with the stock price at \$100. At 90 days (column 1), the 100 Call has a value of 6.53, but the 100 Put has a value of 5.31. The call value is also greater than the put value in every cell of row 6. These differences stem from an interest factor that is part of the call price but which is not part of the put price. When arbitrage strategies are explained in Chapter 6, the reason for the interest factor will become clear.