Factors affecting value of options
November 22, November 23, Options are an asset to the buyer and a liability to factors determining the cost of options seller. Hence, the buyer must pay a premium to the seller up front to compensate him for taking the risk. A European option is an option that can be exercised only at expiration.
This simplifies the valuation because we only need to determine the option value at expiry. A call option has value to a buyer only when the spot price at expiration ST is greater than the exercise price X otherwise its value is zero. In other words, the value of a call option to the buyer is a maximum of 0 or any excess of future spot price over exercise price ST — X.
This is called intrinsic value or exercise value of the option, i. A put option has value only if the buyer can sell the underlying at an exercise price X which is greater than the spot market price ST otherwise it is better to let the option expire and sell the underlying in open market. A put option value at expiration is Max 0, X — ST.
Effect of the value of underlying The value of a European call option increases while a European put option decreases with an increase in the price of the underlying and vice versa. This is because a call option is equivalent to buying the underlying while the put option is equivalent to selling it. If the exercise price is low, there is a greater chance that a call option shall be in-the-money i.
Effect of time to expiration A European call option is more valuable when the time to expiration is longer. It is because, over a longer duration, there is a greater chance that the spot price will rise about the exercise price.
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- Rise in Volatility leads to rise in Option Premiums.
- Effect of the value of the underlying: The call option can be viewed as buying the underlying and the put option can be viewed as selling the underlying.
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Further, since the holder of a call option is required to make payment, delaying factors determining the cost of options payment has time-value-of-money benefits. A European put option benefits from a longer time period because there is a greater probability of spot price falling below the exercise price, but this effect may be offset by the time value of money effect of the proceeds from the exercise of put.
This is because when a buyer exercises a put, he sells the underlying and receives cash whose present value is lower if the time period is longer, the interest rate is higher and where the option is deep-in-the-money when the difference between X and ST is larger. Effect of the risk-free rate of interest Since the buyer of a European option can earn interest on the money which will be used to buy the underlying when he eventually exercises the option, a higher risk-free interest rate over a longer time period means higher option value.
The value of a European put option is inversely related to the risk-free interest rate. It is because a higher interest rate means a lower present value of the exercise price when the option is exercised.
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When the options are not exercised, the level of risk-free interest rate becomes irrelevant. Effect of volatility of the underlying When volatility of the underlying is high, a there is a greater chance that the spot price will go above the exercise price in case of a European call option, and b the difference will be larger.
However, if the spot price declines further below the exercise price, it does not matter regarding an option-holder decision.
This is why volatility and option value are directly related. The value of a European put option responds similarly to the volatility of the underlying.
Factors affecting value of an option
Due to high dispersion as measured by the rangethere is a greater chance that the spot price goes below the exercise price by a bigger margin. If the spot price is above the exercise price and it goes further up, it does not affect the option value adversely because it is already zero.
Effect of payments on the underlying and cost of carry Since the value of underlying falls as soon as it pays dividends or interest, the value of a European call option responds negatively to any such payments. However, they benefit from any cost of carry because the option holders do not have to bear those costs.
Factors That Determine Option Pricing