(Requires Numerical Analysis) 

(a) Write down the probability density function of the risk-neutral terminal distribution of returns for stocks in the Black-Scholes model. 

(b) Then write down the expression for the value of a call option on a stock in integral (expectation) form under the risk-neutral probability measure. 

(c) For the following parameter values, undertake the integration using Octave and price the call option: S = 100, strike K = 102, volatility σ = 0.3, risk-free rate r = 0.02, and maturity T = 0.5. There are no dividends.