Options Valuation

Option valuation refers to the amount of premium to be determined. In other words, what should be the fair amount of an option premium? Determining such fair value or fair premium is known as option valuation.

Once option valuation is made, one will come to know as to what should be the premium for a particulars option. On comparing such fair premium with the actual premium, the investor can decide whether he should buy such options or sell such options.

Consider the following situations:

1. If actual premium is more than the fair premium, the option premium is considered to be overpriced and the investor will prefer selling or writing such option.
2. If actual premium is less than the fair premium, the option premium is considered to be underpriced and the investor will prefer buying or holding such option.

For determining fair value of an option, there are various approaches or models. These are mentioned below:

1. Portfolio Replication Model
2. Risk Neutral Model
3. Binomial Model
4. Black & Scholes Model

All the above approaches can be used for determining the value of call options only. For determining the value of put options, the following procedure should be used:

1. Determine the value of call option for the same exercise price.
2. Use ‘Put-Call Parity’ Theory for determining the value of put option through the value of call option.

Portfolio Replication Model

This model creates a portfolio of stock and then creates a replica of such stock portfolio through options (Call Options). In other words, the created option portfolio should appear as a replication of the stock portfolio. The stock portfolio will contain a single equity share whose option valuation is required. The option portfolio on the other hand will contain one or more than one option to match with the stock portfolio. Through this created match, the value of a call option can be determined.

Risk Neutral Model

As per Risk Neutral Model the risk free rate of interest is a weighted average of rate of returns at higher and lower probable prices where the weights used represents the probabilities of rise and fall in prices.

Binomial Model

C = Value of Call Option at present

Cu = value of call option on expiry when price goes up

Cd = Value of call option on expiry when price goes down

I = 1 + i ( 1 + Risk free Interest rate)

U = 1 + ROR when Price goes up

D = 1 + ROR when price goes down