Implied Volatility and Call Option Pricing

Very Hard Derivative Markets And Instruments Exchange-traded Derivatives

In the context of exchange-traded derivatives, investors often utilize various strategies to manage risk and enhance returns. Consider a hypothetical derivative product traded on an exchange, which provides payoff structures based on the underlying asset price movements. Assume that this derivative is a European-style call option on a stock index, which is set to expire after six months. The option has a strike price of 1,000 and the underlying index is currently trading at 950.

Now, an investor expects the underlying index to rise to 1,050 by expiration and wants to determine the financial implications of this expectation. However, in addition to this, the investor also analyzes the potential impact of increased volatility in the underlying index, which could affect the option's pricing.

Given this scenario, what is the theoretical relationship between the implied volatility of the option and the price as the expiration date approaches, assuming all else remains constant?

As implied volatility increases, the price of the call option decreases.

As implied volatility increases, the price of the call option increases.

The price of the call option remains unchanged regardless of changes in implied volatility.

Hint

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