التفاصيل البيبلوغرافية
| العنوان: |
The Calculation of Implied Variances from the Black-Scholes Model: A Note. |
| المؤلفون: |
MANASTER, STEVEN, KOEHLER, GARY |
| المصدر: |
Journal of Finance (Wiley-Blackwell); Mar1982, Vol. 37 Issue 1, p227-230, 4p |
| مصطلحات موضوعية: |
STOCK options, ECONOMIC equilibrium, VARIANCES, INTEREST rates, RATE of return, ALGORITHMS, PRICES, OPTIONS (Finance), FINANCE education, MATHEMATICAL models |
| مستخلص: |
Black and Scholes have derived a model for the equilibrium price of a European Stock Purchase option. According to the Black and Scholes model, equilibrium option prices are a function of the time to maturity of the option, the exercise price, the current price of the underlying stock, the risk free rate of interest, and the instantaneous variance of the stock's rate of return. Of these five variables, only the first four can be directly observed; the instantaneous variance of the stock's return can only be estimated. Recently, several authors, rather than estimating a variance from past data, have attempted to employ the Black-Scholes option pricing formula to derive an “implied variance.” An implied variance is the value of the instantaneous variance of the stock's return which, when employed in the Black-Scholes formula, results in a model price equal to the market price. Unfortunately, the implied variance cannot be calculated explicitly, and previous researchers have used numerical methods such as the Newton-Raphson method and its variants. However for many options, no values of implied variance could be found to justify the observed option prices. In this note, necessary and sufficient conditions for the existence of a positive implied variance are given. An algorithm is presented which converges monotonically and quadratically to the (unique) implied variance, when it exists. The most valuable feature of this algorithm is that it provides a starting value for the first iteration of the Newton-Raphson procedure. If one applies the Newton-Raphson procedure without the correct starting value, solutions that do exist can be overlooked. [ABSTRACT FROM AUTHOR] |
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