explain briefly how the formulae of the Greeks may be derived from Black-Scholes option pricing model

Expert Solution

Black Scholes option pricing model is basically a differential equation to quote prices for option contracts. it estimates the theoritical prices for a call on the basis of speculations in various variables such as kinds of options available, underlying price of stock etc. conclusively, it helps to diminish the scope of arbitrage.

it was originated by Fischer Black, Robert Merton and Myron Scholes. It is based on defined assumptions -

1) firstly that its usage is limited at expiration as it is european option.

2) it has benefit of non payment of dividend till the option's life.

3) it is largely used by option traders such as stock market.

under this model, traders buy the options whose price is calculated by using this formulae and then they sell those options when the price of such options is increased as per this formula only.

Formulae is :

C=StN(d1)−Ke−rtN(d2)

in this formulae,

C is the price of a call option,

P is the price of a put option,

S is the Current Stock Price

T is the time of maturity

N is the standard Normal Distribution

K is the Strike price

I is the risk free interest rate

jeff jeffy answered 1 year ago

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