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Option Valuation (How we calculate the value of a option)?

Although we know that options can be used by investors to anticipate future levels of security prices. the key to understanding how they are valued comes from recognizing that they also are risk reduction tools. Specifically, in this section we show that and options theoretical value depends on combining it with its underlying security  to create a synthetic risk-free portfolio. That is, it always is theoretically possible to use the option as a perfect hedge against fluctuations in the value of the asset on which it is based.
The primary differences between put-call parity and what follows are twofold. First, the hedge portfolio implied by the put-call parity transaction did not require special calibration; it simply consisted of one stock long, one put long and one call short-a mixture that required no adjustment prior to the expiration date. However, hedging an underlying asset positions risk with a single option position whether it is a put or a call-often involves using multiple contracts and frequent changes in the requisite number to maintain the risk-less portfolio. Second, the put-call parity paradigm did not demand a forecast of the underlying assets future price level whereas the following analysis will. Indeed, we will see that forecasting the volatility  of future asset prices is the most important input the investor must provide in determining option values. 

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