What is ' Option ' ?
An Option is a contract, which gives to it's owner, the right ( but not the obligation ) to purchase or sale an underlying asset on or before a specific date and at a predetermined price.
Example :- Mr. A sell an call option to Mr. B, for 1 BTC at a price of $11,000 and the exercise date is 31/Oct/2020.
Here Mr. B has a right to purchase 1BTC on 31/Oct/2020, but he don't have obligation to purchase. It means if on 31/Oct/2020, if price of 1BTC is more than $11,000, then he will purchase and if price is less than $11,000, he will not purchase.
Various valuation model are used to Value Option, I am giving few of them.
(1) Price difference method.
Under this method,
Value of Option = Present Value of Strike Prices - Spot price of the underlying asset on the date of valuation.
(2) Expected Gain Method
Under this method,
Value of Option = Present Value of Expected Gain to the Option buyer.
Under this method, expected gain are calculated ignoring the Option premium.
(3) Binomial Model
This model assumes that the, there can be only two prices of the underlying asset on the date of maturity.
One will be higher than strike price and other will be lower than strike price.
Under this method, Value of Option is calculated, from the Option writer's point of view.
Option premium calculated under this method, provides Risk-free rate of return, at either of the prices, on the Investment made by the Option writer.
Note :- If price breaks the prices i.e higher than upper price and lower than lower price, then Option writer's have to bear loss.
(4) Risk neutral method.
This method is an alternative method of Binomial Model i.e it provides the same result as Binomial Model.
Steps
(a) Find the probabilities of two possible prices of underlying asset, which will result in expected gain equal to Risk-free rate of return on investment made by Investor in underlying asset.
(b) Calculate Option Value by using expected gain method.
Probability (p) = (R-d)/(u-d)
Where,
'R' is the amount to which an investment equal to spot price of the underlying asset will grow, if invested at the Risk-free rate of return for the duration of call.
'u' is expected upper price and 'd' is expected lower price.
(5) Black Scholes model
Under this method,
Value of European Call Option = [ Spot price X N(D1) ] - [ Present Value of Strike Prices X N(D2) ]
Value of N(D1) and N(D2) are calculated using Normal distribution table.
D1 = [ ln (Spot price/ Strike Price) + ( r + 0.5 SD^2)t ]/ SD√t
D2 = D1 - SD√t
Thank you for reading.
