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) |
---|---|---|---|

MP_{1} = 190 |
14 | 176 | 190 |

MP_{2} = 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) |
---|---|---|---|

MP_{1} = 152 |
0 | 176 | 176^{*} |

MP_{2} = 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) |
---|---|---|---|

MP_{1} = 152 |
0 | 152 | 152 |

MP_{2} = 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