Question

(a)

Briefly outline how a change in the following factors can influence the price of both call and put options:

1. Interest Rates
2. Exercise price of the option
3. Volatility of the underlying asset

Please support your answer with an illustrative example.

Answer 1

Solution:-

I. Impact of interest rates on prices of call and put options:

We must note that all assets are valued in the market based on their expected rates of return. Higher the expected rate of return from an asset, lower would be its value in the market and vice-versa. Now, the expected rates of returns from assets are completely benchmarked on the interest rates in the economy (i.e. risk free rate). When interest rates go up, the market value of all assets go down to adjust their yields higher in line with increased interest rates and vice-versa.

Therefore, when the interest rates go down, the market value of shares go up. When the market value of shares go up, the price of call options go up while the price of put options go down. Similarly, when the interest rates go up, the market value of shares go down which results in an increase in the prices of put options and decrease in the prices of call options.

Example:

Let's say that interest rates in an economy are cut by 100 basis points by the central bank which results in a 5% increase in the value of shares in the stock market. Let's say that before the interest rate cut, the price of a March 2020 call option for strike price $100 with current stock price $110 was $12. Now, if as a result of interest rate cut, the current stock price goes to $115.5, the price of call option will also go up as a result of the increase in share price

II. Impact of change in exercise price of the option on the option prices:

When the exercise price of the option goes up, it results in a fall in prices of call option and increase in the prices of put options. This is because the call options are rights to buy the underlying shares at the exercise price on a future date and put options are rights to sell underlying shares at the exercise price on a future date. So, when exercise price goes up, the opportunity of making profits from call options goes down and opportunity to make profits from put options go up.

Example:

Let's say that the price of a March 2020 call option for strike price $100 with current stock price $110 was $12. This means that if the stock price remains above $100, the option would stay in the money and would be exercised, however if the exercise price goes up to let's say $108, the option would only be able to be profitably exercised as long as the share price stays above $108. Thus, the opportunity to make money from call options goes down which results in fall in their market prices.

III. Volatility of the underlying asset:

Volatility of the underlying asset refers to the pace and quantum at which the prices of underlying assets are expected to move. If the volatility is high, it means that the prices of underlying assets can move substantially and quicker, and vice-versa.

The value of an option is equal to the sum of its time value and intrinsic value. Intrinsic value is simply equal to the difference between exercise prices and current stock prices. On the other hand, time value refers to the value of the option attributable due to the time gap between present and option maturity date which presents risk to the intrinsic value of the option that stands today.

When the volatility of underlying assets goes up, it means that there could be a fast and substantial movement in the prices of underlying assets which means higher risk for the option seller, higher time value of options and thus higher option prices as a result.

Example:

Let's say that the price of a March 2020 call option for strike price $100 with current stock price $110 was $12. This means that the $12 price of option is composed of intrinsic value of $10 (i.e. $110-$100) and time value $2. Time value exists because as an example in this case, the option has an intrinsic value of $10 today but if the stock price falls before the option maturity, the intrinsic value of the option would go down, thus time value represents the threats to intrinsic value of options.

If the volatility of underlying assets goes up, it increases the risk of potential impact of changes in stock prices, increasing the time value of an option, thus increasing the prices of option.

Therefore, an increase in volatility of underlying assets increases prices of both call and put options,