Options Pricing: Determinants of options pricing, the Binomial Model- Volatility in the
Binomial Model - One-Period Model Two-Period Model; The Black Scholes Model for
Options Pricing.
Options Pricing: An Introduction
In the previous CO you have got an idea of the options markets and its mechanisms. The present
CO is devoted to options pricing. Any option holder takes decision on the basis of price of the
option. If he finds price favourable, then he can either hedge or arbitrage. Pricing of an option
involves complex mathematical calculations and treatment.
As discussed in the previous chapter, the price that an option buyer pays to the option seller for
buying an option is called option premium. Since the strike price of options is constant
throughout their lives they are quoted in the market on premium basis.
In this CO, let us understand the determination of individual option prices from information
about the underlying. With options, exercise occurs only if this is in the holder’s interest. For
European options, this depends on the underlying asset’s price at maturity. For American
options, it depends on the entire pattern of evolution of the asset’s price since exercise may
occur at any time.
Over the years, a number of alternative models have been proposed in the option pricing
literature. Two particularly popular ones are the binomial model and the Black-Scholes
model. Both are used widely in practice for pricing options on equities, indices, exchange rates,
and other underlying assets. The Black-Scholes model is very well known and, indeed, is
almost synonymous with option pricing, but it is somewhat technical and does not offer much
intuition about option pricing and hedging. It also has some limitations; for example, it
cannot easily handle early exercise. The binomial model, in contrast, is an ideal starting point
for understanding option pricing.
,Determinants of Options Pricing
Logically, like the price of any other product premium of an option should also be determined
by demand and supply factors in the market. However, theoretically as seen earlier, option
premium is a combination of intrinsic value and time value. Intrinsic value in turn is a function
of the difference between strike price and cash market price of the underlying asset and time
value is a function of volatility of the price of underlying asset, time to expiration of the option
and prevailing interest rate in the economy. Therefore fundamentally, there are following five
basic determinants of options pricing:
1. Cash price of asset (St)
2. Strike price (X)
3. Volatility of underlying asset’s prices
4. Time to expiration (T)
5. Interest rates (r)
These factors affect the premium/price of both American and European options in several
ways.
1. Cash Price (or) Current Price (or) Spot Price of Asset (St)
Keeping all other factors constant, if cash market price of underlying asset goes up value of the
call option increases but value of the put option diminishes.
For instance, call option with strike price Rs 100 would worth more when cash market price of
stock is Rs 110 than in the situation when cash market price of stock is Rs 100. This point may
be derived from the intrinsic value concept, which maintains that keeping the strike price
constant an increase in the market price of underlying asset results in an increase in intrinsic
value of call option.
Similarly, value of a put option decreases with an increase in market price of underlying asset
due to decrease in the intrinsic value of this option.
,2. Strike Price (K)
If all other factors remain constant but the strike price of option increases, intrinsic value of the
call option will decrease and hence its value will also begin to decrease. On the other hand,
with all other factors remaining constant, increase in strike price will increase the intrinsic
value of the put option and it will therefore become dearer.
Now for a call option, the lower the strike price, the more beneficial it is for the buyer and vice
versa for a put option. As options are struck at higher (lower) exercise prices, they will become
lesser (more) useful for the buyer to profit from the call (put) option.
Consider two October call options on Infosys - one with a strike price of ` 1620 and the other
with a strike price of ` 1740. If these two options are available, any buyer would like to pay the
minimum possible amount and consequently chooses the 1620 call over the 1740 call.
Therefore, the price of the call with a lower exercise price will be more than the call with a
higher exercise price. A similar logic (but in opposite direction) applies in the case of put
, option, i.e., options at higher strikes will be preferred by put buyers since they can sell the
underlying stock at higher prices.
3. Volatility of underlying asset’s prices
The second part of an option’s price is the time value - given as the difference between option
price and the intrinsic value. The time value is the amount that the buyers are willing to pay for
the possibility that the option may become profitable to exercise sometime before expiration.
In other words, option buyers believe that the price may be unattractive today but price
fluctuations in the future may make the option profitable. Therefore, longer the time to expiry,
the greater is the probability that at expiry the asset price will be significantly different from
the exercise price.
The greater the expected movement in the price (higher the volatility) of the underlying asset,
the greater the chance of the asset rising largely over (for a call) or below (for a put) the exercise
price at expiry which leads to profitable exercise and hence the more valuable the option for
its holder. This movement in the asset prices is termed as volatility. One may wonder higher
volatility may also work against the holder, i.e., higher volatility may lead to a steeper fall (rise)
in the underlying asset price but an option buyer need not worry about this and it will not hurt
him since he will not exercise the option to buy (sell) the underlying asset.
Volatility in the price of underlying asset affects both call and put options in the same way. As
higher volatility escalates the chances of an option going in-the-money at any point in time
Binomial Model - One-Period Model Two-Period Model; The Black Scholes Model for
Options Pricing.
Options Pricing: An Introduction
In the previous CO you have got an idea of the options markets and its mechanisms. The present
CO is devoted to options pricing. Any option holder takes decision on the basis of price of the
option. If he finds price favourable, then he can either hedge or arbitrage. Pricing of an option
involves complex mathematical calculations and treatment.
As discussed in the previous chapter, the price that an option buyer pays to the option seller for
buying an option is called option premium. Since the strike price of options is constant
throughout their lives they are quoted in the market on premium basis.
In this CO, let us understand the determination of individual option prices from information
about the underlying. With options, exercise occurs only if this is in the holder’s interest. For
European options, this depends on the underlying asset’s price at maturity. For American
options, it depends on the entire pattern of evolution of the asset’s price since exercise may
occur at any time.
Over the years, a number of alternative models have been proposed in the option pricing
literature. Two particularly popular ones are the binomial model and the Black-Scholes
model. Both are used widely in practice for pricing options on equities, indices, exchange rates,
and other underlying assets. The Black-Scholes model is very well known and, indeed, is
almost synonymous with option pricing, but it is somewhat technical and does not offer much
intuition about option pricing and hedging. It also has some limitations; for example, it
cannot easily handle early exercise. The binomial model, in contrast, is an ideal starting point
for understanding option pricing.
,Determinants of Options Pricing
Logically, like the price of any other product premium of an option should also be determined
by demand and supply factors in the market. However, theoretically as seen earlier, option
premium is a combination of intrinsic value and time value. Intrinsic value in turn is a function
of the difference between strike price and cash market price of the underlying asset and time
value is a function of volatility of the price of underlying asset, time to expiration of the option
and prevailing interest rate in the economy. Therefore fundamentally, there are following five
basic determinants of options pricing:
1. Cash price of asset (St)
2. Strike price (X)
3. Volatility of underlying asset’s prices
4. Time to expiration (T)
5. Interest rates (r)
These factors affect the premium/price of both American and European options in several
ways.
1. Cash Price (or) Current Price (or) Spot Price of Asset (St)
Keeping all other factors constant, if cash market price of underlying asset goes up value of the
call option increases but value of the put option diminishes.
For instance, call option with strike price Rs 100 would worth more when cash market price of
stock is Rs 110 than in the situation when cash market price of stock is Rs 100. This point may
be derived from the intrinsic value concept, which maintains that keeping the strike price
constant an increase in the market price of underlying asset results in an increase in intrinsic
value of call option.
Similarly, value of a put option decreases with an increase in market price of underlying asset
due to decrease in the intrinsic value of this option.
,2. Strike Price (K)
If all other factors remain constant but the strike price of option increases, intrinsic value of the
call option will decrease and hence its value will also begin to decrease. On the other hand,
with all other factors remaining constant, increase in strike price will increase the intrinsic
value of the put option and it will therefore become dearer.
Now for a call option, the lower the strike price, the more beneficial it is for the buyer and vice
versa for a put option. As options are struck at higher (lower) exercise prices, they will become
lesser (more) useful for the buyer to profit from the call (put) option.
Consider two October call options on Infosys - one with a strike price of ` 1620 and the other
with a strike price of ` 1740. If these two options are available, any buyer would like to pay the
minimum possible amount and consequently chooses the 1620 call over the 1740 call.
Therefore, the price of the call with a lower exercise price will be more than the call with a
higher exercise price. A similar logic (but in opposite direction) applies in the case of put
, option, i.e., options at higher strikes will be preferred by put buyers since they can sell the
underlying stock at higher prices.
3. Volatility of underlying asset’s prices
The second part of an option’s price is the time value - given as the difference between option
price and the intrinsic value. The time value is the amount that the buyers are willing to pay for
the possibility that the option may become profitable to exercise sometime before expiration.
In other words, option buyers believe that the price may be unattractive today but price
fluctuations in the future may make the option profitable. Therefore, longer the time to expiry,
the greater is the probability that at expiry the asset price will be significantly different from
the exercise price.
The greater the expected movement in the price (higher the volatility) of the underlying asset,
the greater the chance of the asset rising largely over (for a call) or below (for a put) the exercise
price at expiry which leads to profitable exercise and hence the more valuable the option for
its holder. This movement in the asset prices is termed as volatility. One may wonder higher
volatility may also work against the holder, i.e., higher volatility may lead to a steeper fall (rise)
in the underlying asset price but an option buyer need not worry about this and it will not hurt
him since he will not exercise the option to buy (sell) the underlying asset.
Volatility in the price of underlying asset affects both call and put options in the same way. As
higher volatility escalates the chances of an option going in-the-money at any point in time
