The Black—Scholes Theory of Option Prices
We now turn to the determination of the prices of derivative securities such as forwards, futures, or options in the presence of fluctuations in the price of the underlying. Such investments for speculative purposes are risky. Bachelier’s work on futures already shows that for relative prices, even the deterministic movements of the derivative are much stronger than those of the bond, and it seems clear that an investment into a derivative is then associated with a much higher risk (see also Bachelier’s evaluation of success rates) than in the underlying security, although the opportunities for profit would also be higher.
KeywordsStock Price Option Price Fractional Brownian Motion Implied Volatility Strike Price
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