Price Volatility of Share
Volatility in the share price influences the call option value. In operational terms, the greater is the possibility of extreme outcomes, the greater is the call option value to its holder, all other things remaining that is. In statistical terms, the greater is the variance/standard deviation of the financial returns on it associated share, the more is the worth of the option to its owner. The reason is that a decrease 1 the lower possible share price, say, to Rs 130 (from Rs 140) does not cause to the call owner as the call option worth remains zero both the levels of price. However, at possible increase in the upper share price (say, to Rs 170 from Rs 160) makes the option worth more as the call option is in the money.
To make things more value of is determined with reference to new set of possible market prices of the underlying share for the fans contained in the steps involved are as follows:
(i) The investor is required to invest in risk free security/treasury bills equivalent to the present value of the lower share price (Rs 130 in this case); the amount of investment is Rs 121.11 (discount rate is 7 per cent). In addition, he is to buy 1.6 call options (explained in step ii), In case, the share price ends up at Rs 130, the tall option has no value as the exercise price is Rs 141.
(ii) In case the share price turns out to be Rs 170, the call option has worth of (Rs 170 - Rs 145) Rs 25. The investor would get Rs 130 from his investments in risk-free asset. He would fall short of Rs 40 to make his portfolio worth of Rs 170 (equal to the share price). Since, one call is worth of Rs 25, the required number of calls to be purchases is (Rs 40/Rs 25) 1.6.
(iii) Alternatively, the number of call options to be purchased to make it equal to the price of a share can be determined by Equation 5.11.
Since the variance of the financial return associated with the security has increased (in view of greater span of plausible price range, now of Rs 130 and Rs 170 vis-a-vis Rs 140 and 160 earlier) the call value has risen to Rs 8.4 as shown below.