## What is Extrinsic Value of an Option?

Extrinsic value of the option is one of the components of the total value of the option due to time value and the impact of volatility of the underlying asset. This part of the option value does not consider intrinsic value that accounts for the difference between the spot price and exercise price of the underlying security.

### Components

Following hierarchy shows the contributors to the option value and the factors affecting these components:

- Intrinsic value is impacted by the spot price at the time of maturity, the exercise price of the option, cashflows of the underlying and the risk-free rate used for discounting
- This is affected by the time to maturity or the expiry of the option and the volatility of the underlying

### Factors Affecting the Extrinsic Value

- Time value, also known as the time value of decay, represented by the option greek ‘theta’ and therefore also known as theta decay, exists because the option buyer believes that in the given time to maturity the price of the underlying might become favorable and therefore, it is believed that longer the time to expiry, greater is the time value
- And as the time to expiry keeps on reducing, this value keeps on decaying, at the time of expiry, this value is equal to zero and this is the reason why it is known as the time value of decay
- Volatility (option greek: ‘vega’) of the underlying has a direct relationship with the extrinsic value too because the buyer of the option buys it to hedge himself and if he believes that the value of the underlying is not too volatile, he would never be willing to pay the price of purchasing the option.
- Therefore, if the underlying is highly volatile, the buyer can benefit from it as options have the unilateral risk that is, if the option is in the money, it will be exercised while if it is out of the money, it will not be exercised. So higher the volatility of the underlying asset, higher is the risk for hedgers and higher is the extrinsic value leading to higher option value.
- Having explained the factors and their relationship with the extrinsic value, we still need to understand that measuring the extrinsic value is not an easy process and at times, there are different option values from different analysts because of their difference in opinion about the volatility measure.

### Extrinsic Value Example

- As we have mentioned in the introduction, an option value has two components, intrinsic and extrinsic. When the investor purchases the option, the exercise price determined is either equal to or lower (higher) than the current spot price of the underlying for a call (put) option. This implies that the intrinsic value is 0. In case of a call (put) option, the option has a positive payoff when the spot price at maturity is greater (lower) than the exercise price.
- Even with a 0 intrinsic value, the investor pays the premium to purchase the option. So at this time, the entire premium is due to the extrinsic value.
- For example, if the exercise price for a call option is $100 and the Spot price of the underlying is either $100 or less, the payoff is 0. Let’s suppose, during the time of the option, the spot price becomes 110, then the payoff is 110-100 = $10 and let us say there are 3 months to expiry, we feel that the underlying can go up to $120 so the option price will be higher than the current payoff of 10, maybe $15, this addition $5 is due to extrinsic value, more precisely time value if volatility is constant.

### Option Pricing Methods

Based on the lengths of the interim time periods from the time of purchase of the option till the time of maturity, there are two popular methods used for option pricing, the binomial method when the time periods are discrete such as 2 years and the BSM method and its variants such as the Black method, when the desired pricing is continuous.

The price arrived at any of these methods encompasses both the intrinsic and extrinsic value of the option. If the market price is even higher than this price then there can be two reasons for this:

- Either there is an arbitrage opportunity.
- Or the estimates of volatility are amiss. At times we back-calculate the volatility from the current market price op the option and such volatility is known as the implied volatility, whereas there is another method for volatility calculation known as the historical method.

### Assumptions of Black Scholes Model

We need to also look at a few assumptions of the BSM because some of these are very simplistic as compared to a real-world scenario:

- We assume that the volatility of the underlying is known and constant
- The risk-free rate is known and constant
- The underlying has no cash flows
- There are no transaction cost or taxes

However, these assumptions do not always hold true in the real world and therefore the BSM model requires adjustments to be made to incorporate such variance. Such adjustments vary from analyst to analyst and therefore there might be a possibility that the price calculated from these methods may vary from the current market price.

What we need to understand from this is that it is not always the case that the market price – intrinsic value = extrinsic value and here is the difference between the terms price and value of the option. Price may refer to the market price, the value may refer to the calculated price from one of these models and premium may refer to the amount paid at the time of the purchase of the option.

The formula for BSM for calculation of a call option price is below for understanding:

**Source:** Wikipedia.org

- Without going in too much depth, we only should understand the points from the perspective of this article
- The standard deviation is the symbol for volatility and the T-t is the time till expiry, therefore the formula suggests that the price calculated using this model incorporates for extrinsic value variables along with intrinsic value variables.

### Conclusion

- We understand that the extrinsic value of the option is one of the components of the total value of the option, existing due to time value and the impact of volatility of the underlying asset.
- Calculation of extrinsic value may not always be easy because of the variation in calculation of the volatility input of the option pricing methodology, however, if we use the market price of the option to back-calculate the volatility, such volatility is known as the implied volatility.
- Implied volatility can only be calculated only if we know the market price and therefore can’t be predicted with accuracy, making the predictability of extrinsic value extremely difficult.

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