Further information: Option: Model implementation

In finance

Finance

"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...

, a price (premium) is paid or received for purchasing or selling option

Option (finance)

In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

s. This price can be split into two components.

These are:

• Intrinsic Value
• Time Value

Intrinsic Value

If the market value is more than the strike price, then a call option is 'In the Money'. The difference between the two is called the Intrinsic Value.

In simple words, it is the value by which is already available in the market. If you are holding NIFTY 5000 Call (Bullish/Long) option and NIFTY is at 5050 level then you already have 50 Rs advantage even if the option expires today. These 50 Rs is the intrinsic value of option.

Conversely if you are holding a put option and NIFTY is below strike price then your option has an intrinsic value equalling the difference between the strike price and NIFTY value. So,

Intrinsic Value

= Current Stock Price – Strike Price (Call Option)

= Strike Price – Current Stock Price (Put Option)

Time Value

The option premium is always greater than 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. Obviously, the longer the amount of time until the expiry of the contract, the greater the time value. So,

Time Value = Option Premium – Intrinsic Value

There are many factors which determine 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 impact 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 has an impact on option premium. Say, if NIFTY goes from 5000 to 5100 the premium of 5000/5100 strike will change a lot compared to a contract with strike of 5500 or 4700.
• Time till expiry: Lesser the time to expiry, option premium follows the intrinsic value more closely. On the expiry date Time Value approached zero.
• 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 let’s say a 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.

Apart from above, other factors like bond yield (or interest rate

Interest rate

An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

) also affect the premium. This is due to the fact that 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.

Sometimes dividend payment by an underlying is also factored in to the premium as it affects the cost of buying those shares directly rather than buying the option.

Pricing models

Because the values of option

Option (finance)

In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

 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

Moneyness

In finance, moneyness is a measure of the degree to which a derivative is likely to have positive monetary value at its expiration, in the risk-neutral measure. It can be measured in percentage probability, or in standard deviations....

, Option time value

Option time value

In finance, the time value of an option is the premium a rational investor would pay over its current exercise value , based on its potential to increase in value before expiring. This probability is always greater than zero, thus an option is always worth more than its current exercise value...

and Put-call parity.

Amongst the most common models are:

• Black–Scholes and the Black model
  Black model
  The Black model is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing bond options, interest rate caps / floors, and swaptions...
  
  
• Binomial options pricing model
  Binomial options pricing model
  In finance, the binomial options pricing model provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. Essentially, the model uses a “discrete-time” model of the varying price over time of the underlying...
  
  
• Monte Carlo option model
  Monte Carlo option model
  In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features....
  
  
• Finite difference methods for option pricing
  Finite difference methods for option pricing
  Finite difference methods for option pricing are numerical methods used in mathematical finance for the valuation of options. Finite difference methods were first applied to option pricing by Eduardo Schwartz in 1977....
  
  

Other approaches include:

• Heston model
  Heston model
  In finance, the Heston model, named after Steven Heston, is a mathematical model describing the evolution of the volatility of an underlying asset...
  
  
• Heath-Jarrow-Morton framework
  Heath-Jarrow-Morton framework
  The Heath–Jarrow–Morton framework is a general framework to model the evolution of interest rate curve – instantaneous forward rate curve in particular . When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian...
  
  
• Variance Gamma Model (see variance gamma process
  Variance gamma process
  In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma process , also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments distinguishing it from many Lévy processes. There is no diffusion...
  
  )