The correct answer is: D. high volatility
An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a specified date. The price at which the option can be exercised is called the strike price. The price paid for the option is called the premium.
The value of an option depends on a number of factors, including the strike price, the underlying asset price, the time to expiration, interest rates, and volatility.
Volatility is a measure of how much the price of the underlying asset is expected to fluctuate. A high-volatility asset is one whose price is expected to fluctuate a lot. A low-volatility asset is one whose price is expected to fluctuate very little.
The value of an option increases with volatility. This is because a high-volatility asset is more likely to reach the strike price before expiration, which gives the option holder a greater chance of making a profit.
For example, consider an option to buy a share of stock at $50 per share. The stock is currently trading at $40 per share. The option premium is $5.
If the stock price remains at $40 per share, the option will expire worthless and the option holder will lose the $5 premium.
However, if the stock price rises to $55 per share, the option holder can exercise the option and buy the stock at $50 per share. The option holder can then sell the stock at the market price of $55 per share, making a profit of $5.
The higher the volatility of the stock, the more likely it is that the stock price will reach the strike price before expiration. This means that a high-volatility stock option is more valuable than a low-volatility stock option.
In conclusion, an increase in value of option leads to low present value of exercise cost only if it has high volatility.