option price calculation

7/31/2019 Option Price Calculation

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Option Price Calculation

The price of an option contract is the premiumthat is acceptable to the seller of the option.

The seller decides about this with the assumptionand calculation that the seller will have no profit-no loss by accepting this premium to bear the riskof an option contract.


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Binomial Model of Calculating Option Price

One-step Binomial Method Two-step Binomial Method

Option equivalent method

Risk neutral method

Risk neutral method


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Binomial Model

Binomial method is based on the fundamentalthat price of the underlying share can eitherincrease or decrease in the future incomparison to current spot price.

One-step Binomial Process

Under this model, one-time step is considered

for calculating the price of option: Option equivalent method

Risk neutral method


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Option equivalent method

The option equivalent method assumes that theoutcomes for a particular share on which anoption contract has been written can result into

either a high value or low value.

Option equivalent method is based on the concept of hedge ratio, hedge

ratio implies that the seller of the option should have position in the

underlying asset equal to the hedge ratio for the quantity for which option


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Price of a call option

Option equivalent method assumes that the outcome for aparticular share on which an option contract has beenwritten, can result into any two values, i.e., high value or lowvalue, depending on the movement of spot price likely to takeplace during the time duration of option contract.

Steps taken to calculate the price of call option:

Estimate highest value of call assuming that the spot price ofunderlying asset on the expiration date will increase to a certain levelin future.


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Estimate lowest value of call assuming that spot

price of underlying asset on the expiration date

will decrease to a certain level in future.

Calculation of hedge ratio symbolized as [h] or

By hedge ratio, we mean a ratio of difference between the highest and the

lowest value of call option and the difference of the maximum andminimum price of underlying share.


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Estimating funds to be borrowed at present to

create a hedge portfolio


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Calculation of price of call using formula


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Risk neutral method

Risk neutral method assumes that investorsexpect returns from an investment at leastequal to the risk-free interest rate.

Steps taken to calculate value of a call option:Estimate highest value of call assuming that the

spot price of underlying asset on the expirationdate will increase to a certain level in future.


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Risk neutral method

Estimate lowest value of call assuming that

spot price of underlying asset on the

expiration date will decrease to a certain level

in future.


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Risk neutral method (Cont.)

Estimate the probability of increase in the

spot price of underlying shares on the

expiration date


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Calculate expected future value of the call option with the help of

probability

Calculate present value of call: Done by discounting the future value of

call as calculated in the previous step.


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Price of a Put Option

Once we have calculated price of call option itis much easier to calculate the price of putoption. The formula is as follows:


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Two-step binomial process

Under this model, two-time steps are consideredfor calculating the price of the option.

It is perceived that price of the underlying sharehas a probability of rise or fall during each of thetwo successive time periods.

Price can be calculated by using Risk neutralmethod


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Black and Scholes Model for Option Price Calculation

This model of option price/value calculation is based on the fundamental that inthe future, the price of the underlying asset will either increase or decrease ascompared to the spot price of the underlying asset.

This model has the following assumptions: The call option for which value is being calculated in European style

Price of the underlying share change continuously

Share price has a log normal distribution

Transaction costs and taxes do not exist

No restriction on short selling

Funds can be borrowed at risk-free rate of return to create risk neutralportfolio

During the time period to maturity of the call option, dividend is not declaredby the company


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Steps taken to calculate the price of the option

Calculation of d1


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Steps taken to calculate the price of the option

Calculation of d2.


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Steps taken to calculate the price of the option (Cont.)

Application of the formula to calculate

value/price of call option

Value/Price of a put option

The price so calculated is called equilibrium price and it is expected to be

maintained because of the arbitrage process. It is the arbitrage process, whichforces it to be maintained.


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Valuation Mechanism for Futures Contract

In a market, there is always a difference between the spotprice of the share and price of the same share for a futurescontract.

Difference is on account of many factors expectation aboutthe future market trends, i.e., bullish or bearish, expected

performance of the company, rate of interest, inflation rate,market imperfections, carrying cost, volatility of the shareprices, time till expiration and others.

All these factors have a collective influence in deciding thefutures price.

A model called COST OF CARRY MODEL has been developedto estimate futures price.


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The Cost of Carry Model

Cost of carry model takes into consideration the spot price

and the effective cost of carrying the hedge position in

underlying asset.

Assumptions

The price of the underlying share change continuously

Transaction costs and taxes do not exist

No restriction on short selling

Funds can be borrowed at risk-free rate of return to create risk neutral

portfolio i.e. zero cash flow portfolio. During the time period to maturity of the call option, dividend is not

declared by the company; even if it is declared, it can be adjusted in

the formula.


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Futures price

Price of futures contract

option price calculation

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