ACCA AFM Syllabus B. Advanced Investment Appraisal - Pricing of options - Notes ^{1 / 7}

Writers of options need to establish a way of pricing them.

This is important because there has to be a method of deciding what premium to charge to the buyers.

Factors determining the value(price) of option

The major factors determining the price of options are as follows:

1. The price of the underlying item

   For a call option, the greater the price for the underlying item the greater the value of the option to the holder. 

   For a put option the lower the share price the greater the value of the option to the holder.

   The price of the underlying item is the market prices for buying and selling the underlying item. 

   However, mid-price is usually used for option pricing, for example, if price is quoted as 200–202, then a mid-price of 201 should be used.

2. The exercise price

   For a call option the lower the exercise price the greater the value of the option. 

   For a put option the greater the exercise price, the greater the value of the option.

3. Time to expiry of the option

   The longer the remaining period to expiry, the greater the probability that the underlying item will rise in value. 

   Call options are worth more the longer the time to expiry (time value) because there is more time for the price of the underlying item to rise. 

   Put options are worth more if the price of the underlying item falls over time.

4. Prevailing interest rate

   The seller of a call option will receive initially a premium and if the option is exercised the exercise price at the exercised date. 

   If interest rate rises the present value of the exercise price will diminish and he will therefore ask for a higher premium to compensate for his risk.

   The risk free rate such as treasury bills is usually used as the interest rate.

5. Volatility of underlying item

   The greater the volatility of the price of the underlying item the greater the probability of the option yielding profits.

   The volatility represents the standard deviation of day-to-day price changes in the underlying item, expressed as an annualized percentage.

The following steps can be used to calculate volatility of underlying item, using historical information:

1. Calculate daily return = Pi/Po, 

   where 
   Pi = current price and 
   Po = previous day’s price

2. Take the ‘In’ of the daily return using the calculator

3. Square the result above to get, say, X

4. Calculate the standard deviation as

   =√ ((∑X² /n)−(∑X/n)²)

5. Then annualise the result using the number of trading days in a year.

   The formula = daily volatility x √trading days

Illustration

Solution

Standard deviation = Daily volatility 
= √( 0.00170875 − (0.02155)²)
= 0.035
= 4%

Since there are five trading days in a week and 52 weeks in a year, we assume the trading days in a year is 52 x 5 = 260 days. 

Annualised volatility = 4% x √260= 64.5%.