The prices of stocks and options are influenced by demand and supply pressures and fluctuate at each trading interval. As an option contract is derived from a stock (or index), all factors affecting the value of its underlying stock (or index) influence its value. Also, since the distinguishing features of options are dependent on their built-in right (call/put) and nature (American/European), one must understand the factors that affect its value. The estimate of a fair or true value of an option plays a vital role in exploiting arbitrage, hedging and speculative opportunities. Let's look at the factors directly affecting an option's value.
Price or value of underlying security: The price of a call option increases with the rise in the price of its underlying security. This is because the higher the underlying price relative to the strike price on the day of exercising it, the higher the pay-off. So a call option is more valuable as the price of its underlying stock or index rises, and vice versa. However, the price of a put option rises with the fall in the underlying security's price as the lower the latter's price relative to the strike price on the exercise day, the higher the pay-off. So a put option becomes more valuable if the price of its underlying security falls and its value erodes if this price rises.
Time to expiration: The longer the period before expiry, the higher the value of call and put options, and vice versa. This is because the option with more days left for expiry has a higher probability of finishing in the money (ITM). There is a greater chance for the underlying security's price move to be favourable. Such a relationship works for American options, but is undefined or indeterminate for European options.
Volatility: Volatility implies uncertainty in the movement of the underlying security. Both put and call options demand higher premium when volatility is high. This is because uncertainty forces option sellers to ask for a higher risk premium to grant the exercise right to buyers. However, call and put option buyers are willing to pay more as the chances of prices moving in any direction are high. As the risk is limited to the amount of premium, buyers of both call and put expect the prices to move in their favour.
Risk-free rate: If one assumes the risk-free rate to rise independently of the underlying security's price, it will increase the value of a call option and decrease the value of a put option. This is because the increased risk-free rate reduces the present value of expected future benefits, which is beneficial for call option buyers, but not for put option buyers. Mostly, interest rates and stock prices do not move independently, and the rise in interest rates reduces stock prices, and vice versa. This reduces the value of a call and increases that of a put. The relationship reverses if the movement of interest rates and stock prices is inter-related.
Future dividends: Dividends reduce the price of a stock on the payout date, which benefits put buyers and is detrimental to call buyers. If dividends are anticipated, the value of a call option is affected negatively, and that of a put option, positively.
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