Valuation of options

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In finance, a price (premium) is paid or received for purchasing or selling options. This price can be split into two components.

These are:

  • Intrinsic value
  • Time value

Intrinsic value[edit]

The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call option, the option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price. For a put option, the option is in-the-money if the strike price is higher than the underlying spot price; then the intrinsic value is the strike price minus the underlying spot price. Otherwise the intrinsic value is zero.

For example, when a DJI call (bullish/long) option is 18,000 and the underlying DJI Index is priced at $18,050 then there is a $50 advantage even if the option were to expire today. This $50 is the intrinsic value of the option.

In summary, intrinsic value:

= current stock price – strike price (call option)
= strike price – current stock price (put option)

Time value[edit]

The option premium is always greater than the intrinsic value. This extra money is for the risk which the option writer/seller is undertaking. This is called the Time value.

Time value is the amount the option trader is paying for a contract above its intrinsic value, with the belief that prior to expiration the contract value will increase because of a favourable change in the price of the underlying asset. The longer the length of time until the expiry of the contract, the greater the time value. So,

Time value = option premium – intrinsic value

Other factors affecting premium[edit]

There are many factors which affect option premium. These factors affect the premium of the option with varying intensity. Some of these factors are listed here:

  • Price of the underlying: Any fluctuation in the price of the underlying (stock/index/commodity) obviously has the largest effect on premium of an option contract. An increase in the underlying price increases the premium of call option and decreases the premium of put option. Reverse is true when underlying price decreases.
  • Strike price: How far is the strike price from spot also affects option premium. Say, if NIFTY goes from 5000 to 5100 the premium of 5000 strike and of 5100 strike will change a lot compared to a contract with strike of 5500 or 4700.
  • Volatility of underlying: Underlying security is a constantly changing entity. The degree by which its price fluctuates can be termed as volatility. So a share which fluctuates 5% on either side on daily basis is said to have more volatility than e.g. stable blue chip shares whose fluctuation is more benign at 2–3%. Volatility affects calls and puts alike. Higher volatility increases the option premium because of greater risk it brings to the seller.
  • Payment of Dividend: Payment of Dividend does not have direct impact on value of derivatives but it does have indirect impact through stock price. We know that if dividend is paid, stock goes ex-dividend therefore price of stock will go down which will result into increase in Put premium and decrease in Call premium.

Apart from above, other factors like bond yield (or interest rate) also affect the premium. This is because the money invested by the seller can earn this risk free income in any case and hence while selling option; he has to earn more than this because of higher risk he is taking.

Pricing models[edit]

Because the values of option contracts depend on a number of different variables in addition to the value of the underlying asset, they are complex to value. There are many pricing models in use, although all essentially incorporate the concepts of rational pricing, moneyness, option time value and put-call parity.

Amongst the most common models are:

The Black Scholes Model which was developed by Black Scholes and Merton in 1977

Monte Carlo Option Model involves very easy computations and could be coded easily in any programming language of your choice. The method simply randomly generates stock prices based on a declared number of simulations.The stock prices generated is used to calculate the payoff which is simply given as max(S-K,0) in the case of a call option and max(K-S,0) for a put option.The payoffs are then sum and divided by the number of simulations.The Monte Carlo Method provides a good calculation of the option value with a higher number of simulations.

Finite Difference Method is a type of numerical approach that approximate all the derivatives with differences.There are three types of difference thus; 1.Forward Difference 2.Backward Difference 3.Central Difference Formulas for the above methods could be found in ref></ref>. The finite Difference also have the following schema; 1.Explicit Schema 2.Implicit Schema 3.Crank Nicolson Schema

Other approaches include:

Value adjustments[edit]

Post the financial crisis of 2008, the "fair-value" is computed as before, but using the Overnight Index Swap (OIS) curve for discounting. (The OIS is chosen here as it reflects the rate for overnight unsecured lending between banks, and is thus considered a good indicator of the interbank credit markets.) Relatedly, this risk neutral value is then adjusted for the impact of counterparty credit risk via a credit valuation adjustment, or CVA, as well as various other X-Value Adjustments which may also be appended.