Robustness of Volatility
Last Thursday we looked at a stock with historical annualized 100-day volatility of 60%, selling $100, with a September call with strike price 100 selling for $4.50, and saw that normal interest rate variation did not make a lot of difference in the call value. An interest rate of 4% gave the call a value of $7.73, whereas an interest rate of 0% gave it a value of $7.55, not very much different, in the scheme of things. Any reasonable estimate of the current riskless interest rate would reside in this region of approximately 0% to 4%.
However, the story with volatility was different. A volatility of 10% gave it a value of $1.36, whereas a volatility of 60% gave it a value of over $7.00. Now a volatility of 10% in the next 40 or so days might well be considered unreasonable. But even if the volatility turned out to be 30%, the call would be worth only $3.87. How reasonable is a volatility of 30% in the next 45 days?
There are many ways to answer this question, which we will be discussing in the near future, but the point that I want to make today is that, of the five quantities that determine the value of the call under the Black-Scholes model, only volatility is subject to a lot of argument or difference of opinion.
The five quantities are: underlying price, strike price, time to expiration, interest rate and volatility. The is little doubt about the current underlying price. The last trade or yesterday’s close is available to everyone, and although there may be some doubt about the next price the doubt is small in magnitude and does not affect the option value much. Similarly, the strike price is known with absolute certainty, as is the time to expiration. There is little dispute about the current riskless interest rate, and what dispute there is has little effect on the value of the option, as demonstrated above and last Thursday. The value of the call is robust relative to the riskless interest rate.
The major difference of opinion among traders is about the volatility. And the value of the call is not robust relative to the volatility. You might think this unfortunate, in that you cannot determine the option’s value with exactitude. However it is this uncertainty that gives the astute trader an advantage over the market.
I will be discussing ways to estimate volatility in the next few commentaries, and I will give you some very intuitive approaches which should give you faith in their results.
BTW, the answer to the question I posed on Thursday is: the implied volatility.