How are Options Priced?

In the options market, you often come across terms like the intrinsic value, the time value, etc. In addition, you also hear the popular Black & Scholes model. Our focus will be on options valuation and in understanding how are options priced in the F&O market. After all, options valuation lies at the core of pricing options and is key to understanding how are options priced.

The options pricing mechanism is at the core of the F&O market and is the basis for making decisions on whether to buy or sell the option. But option pricing by itself is fairly complex and nuanced. Here we look at the idea of options contract pricing and how the various market concepts like intrinsic value and time value go into options contract pricing.

About Options Priced?

Before we get into the discussion of options contract pricing, we will look at two very important types of value viz. intrinsic value and time value. No discussion on options pricing and options valuation is complete without understanding the concepts of intrinsic value and time value in options contract pricing. The option premium can broadly be broken up into intrinsic value and time value. This is the key to options contract pricing.

In options contract pricing, what exactly do we understand by intrinsic value. How can an option being a contract have an intrinsic value? The intrinsic value of an option refers to the amount by which the option is in the money. Now, what exactly does that mean? It is the amount that the option buyer will realize, without adjusting for a premium paid, if exercised right now. Remember that when it comes to options pricing Only ITM options have intrinsic value whereas ATM options and OTM options have zero intrinsic value. Now, in options pricing, the intrinsic value of an option can be zero but it can never be negative. In the case of a call option, intrinsic value is the excess of the spot price (S) over the strike price (X), i.e., intrinsic value = (S - X). The reverse is true in the case of put options. Input options contract pricing, the intrinsic value is (X – S)

Then what exactly is time value? Time value is the residual option premium left from the market price of the option after the intrinsic value is removed. We have already seen in our discussion of options pricing that ATM and OTM options will have only time value because the intrinsic value of such options is zero. It is only in the case of ITM options that you will get to see the existence of intrinsic value and time value. When it comes to options contract pricing, we often talk of time decay in options. Here we are referring to decay in the time value of the option. This is very important when it comes to options contract pricing.

How are options priced using the Black & Scholes Model?

Remember that in options pricing, we value the right to buy or sell an asset. Options pricing is important for the same reason as you value stocks. After all, it is this options pricing or option valuation that helps you identify underpriced and overpriced options contracts. Black & Scholes Model, provides the theoretical underpinnings to calculate the intrinsic value of an option based on a set of parameters and forms the basis of options pricing. The calculation of the Black & Scholes model is a complex formula at the back-end but it is sufficient to understand the logic of the formula since trading platforms have an automated calculator.

Key assumptions underlying Black & Scholes model

There is 6 assumption underlying the Black & Scholes model.

  • The first assumption is that the underlying stock pays no dividends during the option's life. One way is to adjust the stock price with the dividend yield to make the model a tad more realistic.
  • Black & Scholes is cut out for European options where the options can only be exercised on the expiry date and not before that. The model will not work in the case of American options that can be exercised ahead of expiry.
  • The model assumes that markets are efficient. That means you cannot consistently predict the direction of the market or the stock with certainty. So, where prices are more of a random process around a certain median value.
  • Another rather unrealistic assumption is zero commission charged, which is not practical as there is a commission and also statutory charges that distort valuations. However, this is a model for ideal conditions.
  • Interest rates do not change, which can be interpreted both ways. While the statutory rates don’t change the yields tend to change and also fluctuate wildly.
  • The last and most important assumption is that the returns are lognormally distributed. This assumption of the normal distribution is fairly reasonable and practical.

5-Factor Black & Scholes Model

Broadly, 5 factors go into option valuation, and this is how each of the factors would affect the valuation of the option. This is the core of the Black & Scholes model for the pricing of options.

Option Valuation Factor How it impacts call options How it impacts put options
Underlying Stock Price If spot price goes up call option value goes up If spot price goes up to put option value goes down
Exercise Price As you move to higher strikes, the call option value goes down As you move to higher strikes, the put option value goes up
Volatility As volatility goes up, the value of the call option goes up As volatility goes up, the value of the put option goes up
Time to expiry As the time to expiry reduces, the value of the call option goes down As the time to expiry reduces, the value of the put option goes down
Interest rates Higher interest rates will reduce the present value of the strike price and increase the value of the call option Higher interest rates will reduce the present value of the strike price and hence reduce the value of the put option

How is the Black & Scholes valuation arrived at?

To understand the Black and Scholes valuation model of options pricing, we divide it into two parts. The first part, SN(d1), derives the expected benefit from acquiring a stock outright. This is determined by multiplying stock price [S] by the change in the call premium concerning a change in the underlying stock price [N(d1)]. Now for the second part. The second part of the Black & Scholes model, Ke(-rt)N(d2), gives the present value of paying the exercise price on the expiration day. The fair market value of the call option or the options pricing is then calculated by taking the difference between these two parts. The final output is the options pricing or the option valuation.

Finally, we move on to Option Greeks

Option Greeks are sensitivities and some of the Greeks are derived from the options pricing as put out by the Black & Scholes model. Here are key options for Greeks.

  1. Option Delta is a key aspect of options pricing and it represents the sensitivity of option price to movements in the price of the underlying asset. For example, if a call option has a delta of 0.7, you can interpret saying that if the underlying price increases by Rs.10, the option price will increase by Rs.7. Put options have a negative delta since put options pricing is related negatively to the stock price. Delta of call option ranges between 0 and 1 while delta of put option ranges between 0 and -1.
  2. Options Gamma is the second level and measures the sensitivity of option delta to changes in the underlying prices. If option delta measures the speed, then option gamma measures the acceleration momentum.
  3. Option Vega measures the option price sensitivity to changes in volatility. It represents a change in the price of an option for a 1% change in underlying volatility. For example, if the Vega of an option is 1.4, it means that if the volatility of the underlying were to increase by 1%, then the option price will increase by Rs.1.40.
  4. Option Theta or time decay in options pricing is the measure of change in option value relative to the change in the time to maturity. It measures how much the option value wastes for each passing day to expiry. Theta is always negative.
  5. A lesser-used green is the Option Rho in options pricing. Rho measures the sensitivity of option value with the changes in the risk-free interest rate. For instance, if the Rho of a call is 0.5, it indicates that a 1% increase in risk-free interest rate will increase option value by Rs.0.50. Put options have negative Rho.

Benefits of option trading

Options trading allow traders to take a leveraged position in the market with lower capital and also limit their risk to the extent of the premium paid only. These options allow traders to trade on volatility rather than just on price.

Uses of option contracts

Options contracts can be used to trade and speculate on prices with smaller margins. They can also be used to arbitrage and earn riskless profits. But the biggest contribution of options is in hedging the risk of traders underlying positions in the market using options as offsetting positions.

Frequently Asked Questions Expand All

Option valuations are done by the forces of volatility, time to expiry and the price movements and are purely market determined. The prices of options reflect the intrinsic value of options as close as possible.

Volatility works in favour of the option buyer and against the option seller. Higher the volatility, higher chances of the price movement being in favour of the buyer and higher the chances of the prices being against the seller of the option.