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# Intrinsic value and time value

## Introduction

The price or premium (P) of an option has two parts, i.e.:

• Intrinsic value (IV).

• Time value (TV).

Therefore:

Figure 6: short put option

## Intrinsic value

The difference between the spot price of the underlying asset (SP) and the exercise price of the option (EP) is termed the intrinsic value (IV) of the option.

As seen, there are 3 categories in this regard:

• In-the-money (ITM) options (have an intrinsic value)

• At-the-money (ATM) options (have no intrinsic value)

• Out-the-money (OTM) options (have no intrinsic value).

ITM options are:

• Call options where: SP > EP

• Put options where: SP < EP.

Clearly, the following options have no intrinsic value (OTM):

• Call options where: SP < EP

• Put options where: SP > EP

• Call options where: SP = EP

• Put options where: SP = EP.

Thus:

IV = SP - EP (call options); positive when SP > EP IV = EP - SP (put options); positive when EP > SP.

A summary is provided in Table 2.

Table 2: Payoff profiles: ITM, ATM and OTM options

## Time value

Figure 7: time value of option

The time value (TV) of an option is the difference between the premium (P) of an option and its intrinsic value (IV):

P = IV + TV

TV = P - IV.

An example is required:

Option = call option

Underlying asset = ABC share

Underlying asset spot market price (SP) = LCC 70

Option exercise price (EP) = LCC 60

Intrinsic value (IV) = SP - EP = IV = LCC 70 - LCC 60 = LCC 10 Premium (P) = LCC 12

Time value (TV) = P - IV = TV = LCC 12 - LCC 10 = LCC 2.

The option has time value of LCC 2, and this indicates that there is a probability that the intrinsic value could increase between the time of the purchase and the expiration date. If the option is exercised now (i.e. at LCC 60), the intrinsic value is gained, but time value is forgone. It will be apparent that as an option moves towards the expiration date, time value diminishes, and that at expiration time value is zero. This is portrayed in Figure 7.

# Option valuation/pricing

## Introduction

There are two main option pricing / valuation models that are used by market participants:

• Black-Scholes model.

• Binomial model.

Below we also mention the other pricing models and define the so-called "Greeks".

## Black-Scholes model

### Introduction

The Black-Scholes model was first published in 1973 and essentially holds that the fair option price (or premium) is a function of the probability distribution of the underlying asset price at expiry. It has as its main constituents the following (see the valuation formula below)46:

• Spot (current) price of underlying asset (assume share) (SP).

• Exercise (strike) price (EP).

• Time to expiration.

• Risk free rate (i.e. treasury bill rate).

• Dividends expected on the underlying asset during the life of the option.

• Volatility of the underlying asset (share) price.

Each of these elements is covered briefly below.

### Spot (current) price of underlying asset and exercise price

If a call option is exercised the profit is:

SP - EP (obviously if SP < EP, there is no profit).

Call options are therefore more valuable as the SP of the underlying asset increases (EP a given) and less valuable the higher EP is (SP a given). The opposite applies in the case of put options. The profit on a put option if exercised is:

EP - SP (obviously if EP < SP there is no profit).

Put options are therefore more valuable as the SP of the underlying asset decreases (EP a given) and less valuable the lower EP is (SP a given).

### Time to expiration

The longer the time to expiration the more valuable both call and put options are. The holder of a short-term option has certain exercise opportunities. The holder of a similar long-term option also has these opportunities and more. Therefore the long option must be at least equal in value to a short-term option with similar characteristics. As noted above, the longer the time to expiration the higher the probability that the price of the underlying assets will increase/decrease.

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