# 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

*(EP) is termed the*

**exercise price of the option***(IV) of the option.*

**intrinsic value**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

*(P) of an option and its*

**premium***(IV):*

**intrinsic value**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

*If the option is exercised now (i.e. at LCC 60), the intrinsic value is gained,*

**probability that the intrinsic value could increase between the time of the purchase and the expiration date.***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.*

**but time value is forgone.**# 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.