Finance: Option pricing - call

This is a non-mathematical approach to explaining the movement of option prices with regards to the underlying asset. Since the arithmetic expression requires substantial knowledge of statistics and stochastic finance which probably exceeds the typical undergraduate course of study, we will leave that out for perhaps a future post.

A call option exposes the call buyer to gains of increase in share prices but not the loss when share price decreases. The seller of this call option will then subsequently be exposed the counterparty compensation should the buyer makes a profit, thus the seller have to charge a fair price in order to ensure the option price matches the risk undertaken.

For an option with high underlying asset volatility, the odds of the asset price increasing by a large amount are higher than that of a low volatility. Therefore the call buyer has a higher chance of making a big profit at the expense of the seller; while not losing should the asset price falls drastically.

This would require the seller to charge a higher price for the option.

For an option with a longer time to expiration, there is a longer duration for the underlying asset to move in favour of the call buyer; against the seller. As mentioned, there is no way an option can cause the buyer to lose more money than the option price itself, thus a longer duration to shift against the seller’s favour would require the seller to charge a higher fee for it.

Assuming an at-the-money option, the upside AUC is larger when volatility is higher (1 and 2 vs 3 and 4) and when duration is longer, vice versa. The increase in downside AUC is not borne by the buyer thus it is only advantageous to the option buyer when the underlying asset is volatile and also with a longer option duration. This advantage would have to be accordingly compensated by paying a higher option price.

Note that should share price falls into the negative region, neither the buyer nor seller would be exposed to any further risks no matter how much it falls since a) The buyer will simply let the option expires worthless and b) The seller doesn't have to compensate anything.

The only gains(risks) to either party comes from the share price increasing which will result in the profit(loss) of the buyer(seller). This will be the inverse for a put option.