BASICS OF OPTION PRICING

Option prices are never fixed by any stock exchanges or regulator (SEBI) or anybody for that matter. Price discovery is a very critical and basic component of markets. Stock exchanges only provide a platform where buyers and sellers meet, and regulators role is to ensure smooth functioning of our markets. As long as the option is not expired, there will always be some time value. Intrinsic value may or may not be there, depending upon whether the option is ITM, ATM or OTM.

Any change in option price whether increases or decreases depending upon different market variables. Each variable has its own impact on the option prices. The impact can be same or may differ for a call and put option. As discussed in the previous chapters option premium is the sum of both intrinsic value and time value. As long as the option is not expired, there will always be some time value. Intrinsic value may or may not be there, depending upon whether the option is ITM, ATM or OTM.

Time value of the option in turn depends upon how much time is remaining for the option to expire and how volatile is the underlying.

Parameters

There are five fundamental parameters on which the option price depends:

1) Spot price of the underlying asset

2) Strike price of the option

3) Volatility of the underlying asset’s price

4) Time to expiration

5) Interest rates

These factors affect the premium/ price of options (both American & European) in several ways.

Spot price of the underlying asset

The option price is influenced by the price changes in the underlying assets. If price of the underlying asset goes up the price of the call option increases while the price of the put option decreases. Similarly, if the price of the underlying asset falls, the price of the call option decreases while the price of the put option increases (If all other factor remain constant).

Strike Price

If the strike price of option increases, intrinsic value of the call option will decrease and hence its price will also decrease. On the other hand, with all the other factors remaining constant, increase in strike price of option increases the intrinsic value of the put option which in turn increases its option value.

Volatility

It is the amplitude of movement in the underlying asset’s price, either up or down. It impacts both call and put options in the same way. Higher the volatility of the underlying stock, higher the premium because there is a higher the possibility that the option will move in-the-money during the life of the contract.

Higher volatility = Higher premium, Lower volatility = Lower premium (for both call and put options).

Time to expiration

The impact of time to expiration on both call and put options premium is similar. Generally, longer the maturity of the option greater is the uncertainty and hence higher the option premiums. If all other factors affecting an option’s price remains constant, the time value portion of an option’s premium will decrease with the passage of time. This is also known as time decay. Due to this property options are also known as “wasting assets”. There time value gradually falls to zero with passage of time.

Also note that of the two component of option pricing (time value and intrinsic value), one part is naturally biased towards reducing in value, i.e., time value. So, if all parameters remain constant throughout the contract period, the option price will always fall in price towards expiry. Thus, option sellers/writers are at a natural advantage as compared to option buyers as there is an inherent tendency in the price to go down.

Interest Rates

Interest rates are slightly difficult because they affect different options, differently. For example, interest rates have a greater impact on options with individual stocks and indices compared to options on commodity market. To put it in simpler way high interest rates will result in an increase in the value of a call option and a decrease in the value of a put option.

Options Pricing Models

There are several option pricing models which traders use to arrive at the proper value of the option. Two of the most common models are briefly discussed below:

The Binomial Pricing Model

This model was developed by William Sharpe in 1978. It has proved over time to be the most flexible, intuitive, and famous method to price option. The binomial model represents the price evolution of the option’s underlying asset as the binomial tree of all possible prices at equally spaced time steps from today under the assumption that at each step, the price can only move up and down at fixed rates and with respective simulated probabilities. This is a very accurate model as it is iterative, but also very lengthy and time consuming.

The Black & Scholes Model: This model was published in 1973 by Fisher Black and Myron Scholes. It is one of the most popular, relatively simple, and fast modes of calculation. Unlike the binomial model, it does not rely on calculation by iteration. This model is used to determine theoretical call price (ignoring the dividends paid during the life of the option) using the five key determinants of an option’s price: underlying asset price, strike price of the option, volatility of underlying, time to expiration, and short-term (risk free) interest rate.

The original formula for calculating the theoretical Option Price (OP) is:

OP = SN(d1)-Xe^rtN(d2)

 Where,

D1=[In(s/n)+(r+(v²/2)t]/ 

vÖt D2 = d1-vÖt

And the variables are

·         S = Underlying Asset price

·         X = Strike price of the option

·         t = time remaining until expiration, (in years)

·         r = current continuously compounded risk-free interest rate

·         v = annual volatility of stock price (the standard deviation of the short-term                     returns over one year)

·         In = natural logarithm

·         N(x) = standard normal cumulative distribution function

·         e = the exponential function