Question: Given below is the Option Pricing Model (OPM) derived by Black and Scholes in 1973 for predicting the market price of call options. C =

Given below is the Option Pricing Model (OPM) derived by Black and Scholes in 1973 for predicting the market price of call options. C = ( ) ( ) d1 Xe F N d2 SN r T Where d1 = ( ) T In S X rFT T / + + d2 = d1 T C = Market price of the option N(d1) and N(d2) = the cumulative probabilities for a unit normal variable S = Underlying stocks price X = The exercise price T = Time to maturity in years = The instantaneous variance rF = The risk-free rate 2 In = Natural logarithm

Required:

a) State and briefly explain the relationship between a call options price and the following determinants: i. The underlying stocks price. (2 Marks) ii. The exercise price (2 Marks) iii. The time to maturity (2 Marks) iv. The risk-free rate. (2 Marks)

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