22 Jun
Options Valuation | CA Final SFM
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.
Example 1
Market price of the share today
1 year call option is available at an exercise price of
Risk free rate of interest
The probable market price at the end of the year will be
Determine the value of call option using Portfolio Replication Model.
Solution
As per Portfolio Replication Model, the investor can simply create a stock portfolio by purchasing an equity share at the prevailing market price, i.e. ` 165. Therefore, the present value of investment under stock portfolio will be ` 165.
The value of this stock portfolio by the year end can be either of the following:
MP1 = 190
MP2 = 200
The investor can alternatively create an option portfolio by purchasing a call option and simultaneously investing the PV of Exercise price in risk free investment.
Let the call option premium be ‘C’
PV of investment in such option portfolio will be
C + PV of Exercise Price
The value of such option portfolio by the end of the year will be as below:
| Market Price | Value of option (A) | Value of RFI(B) | Total (A + B) |
|---|---|---|---|
| MP1 = 190 | 14 | 176 | 190 |
| MP2 = 200 | 24 | 176 | 200 |
It is observed that the value of the option portfolio is matching with that of the stock portfolio by the year end i.e. to say the option portfolio appears to be a complete replication of the stock portfolio. If the two portfolios result into same values at year end, then the PV of the two portfolios should also be equal.
160 + C = 165
C = 165 – 160
C = 5
Conclusion: The value of call option in today’s term will be 5
Example 2
Market price of the share today
1 year call option is available at an exercise price of
Risk free rate of interest
The probable market price at the end of the year will be
Determine the value of call option using Portfolio Replication Model.
Solution
As per Portfolio Replication Model, the investor can simply create a stock portfolio by purchasing an equity share at the prevailing market price, i.e. ` 165. Therefore, the present value of investment under stock portfolio will be ` 165.
The value of this stock portfolio by the year end can be either of the following:
MP1 = 152
MP2 = 200
The investor can alternatively create an option portfolio by purchasing a call option and simultaneously investing the PV of Exercise price in risk free investment.
Let the call option premium be ‘C’
PV of investment in such option portfolio will be
C + PV of Exercise Price
The value of such option portfolio by the end of the year will be as below:
| Market Price | Value of option (A) | Value of RFI(B) | Total (A + B) |
|---|---|---|---|
| MP1 = 152 | 0 | 176 | 176* |
| MP2 = 200 | 24 | 176 | 200 |
*It is observed that there is a mismatch in the portfolio values at the lower probable price. To remove this mismatch an alteration is required in the option portfolio i.e. instead of investing the PV of exercise price, in risk free investment, the amount to be invested should be PV of lower probable price i.e.
The PV of such option portfolio will then be = C + 138.18
The value of such option portfolio by the end of the year will be as below:
| Market Price | Value of option (A) | Value of RFI(B) | Total (A + B) |
|---|---|---|---|
| MP1 = 152 | 0 | 152 | 152 |
| MP2 = 200 | 48 | 152 | 200 |
The option portfolio should comprise of 2 call options + PV of lower probable price.
The PV of option portfolio will be = 2C + 138.18
It is observed that the modified option portfolio as above replicates the stock portfolio. The PV of the two portfolio must be equal.
2C + 138.18 = 165
2C = 26.82
C = 13.41
Tips by CA Harish Wadhwani (Scored 93 marks in SFM)
February 02, 2021
Securitization CA Final SFM (Strategic Financial Management)
February 02, 2020
Things you should do before your CA Final Exams
April 04, 2019
Latest Posts
Tips by CA Harish Wadhwani (Scored 93 marks in SFM)
Congratulations…!! CA Harish Wadhwani for scoring 93 marks in SFM (CA Final)
Securitization CA Final SFM (Strategic Financial Management)
Securitization CA Final SFM Securitisation a chapter in Strategic Financial Management (SFM). This is an important chapter from the CA Exam point of view as well. The concept has been explained with a comprehensive example, to make sure the concepts are very clear. It mainly talks about Debt Securitisation, Mortgage-Backed Securities, Securitisation Process, Credit Rating Continue reading
Things you should do before your CA Final Exams
Things you should do before your CA Final Exams Clearing CA Final Exam is clearly not a simple cake walk. You need to be extremely committed to attending your CA final coaching classes. As the subjects are numerous, you need to study your lessons as and when they’re taught your respective CA final Coaching class. Continue reading
CA Final SFM, quick preparation tips
CA final SFM has a few topics which carry a fine weight-age in each trial which are Foreign Exchange Risk Management, Capital Budgeting, Derivatives, and Portfolio Management. But in its place of starting with a topic keeping huge concepts start with a bit lighter note and extremely interesting niche i.e. Bold Valuation. Thereafter full acquisition Continue reading
Two Way Quotes | Forex | CA Final SFM
A Two way Quote indicates a set of two different rates of exchange known as Bid Rate and Ask Rate. In a Two Way Quotes, the rate at which bank will buy the currency and the customer will sell the currency is known as Bid Rate. The rate at which bank will sell the Continue reading
What is an Exchange Rate | Direct Quote & Indirect Quote
Exchange Rate A rate at which one currency can be exchanged with the other. It is a rate at which one currency expressed in terms of the other. It is a rate at which a currency can be bought or sold. Direct Quote & Indirect Quote
Corporate Valuation Basics | CA Final SFM
Need for Corporate Valuation Along with the enterprise growth, number of stakeholders also grows. Presentation of annual financial statements becomes. Curiosity of the stakeholders to understand the ‘true worth’ of their enterprise becomes translated to the concept of ‘valuation’. The market analysts, financial intermediaries, and the academicians, also attempt to apply their valuation approaches Continue reading
Interest Rate Futures | Derivatives | CA Final SFM
When Forward Interest Rate Agreements are regulated through the “Exchange”, it will become Interest Rate Futures. However, the mechanism of IRF is different from FRA. The system is designed in a manner that interest rate is made up as a marketable product. The following example, will clarify as to how interest rate futures are Continue reading
