5. (a) Write a MATLAB program to evaluate the Black-Scholes formula (1) for a Eu- ropean...

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5. (a) Write a MATLAB program to evaluate the Black-Scholes formula (1) for a Eu- ropean Call option using appropriate special functions of MATLAB. Your code should be fully explained with comments. (b) Produce three plots, each showing three curves that compare how changes to parameters affect option prices. Your plots should be clear, with appro- priate titles, labels, legends etc. Use the following combinations of para- meters: = 75, with = 0.15, 4% (per annum), and time E = 35, E = 55, E four months to maturity. = 0.05, = 0.15 and = time four months to maturity. 0.3, with E = 55, r = = 4% (per annum), and r = 1%, r = = 4% and r = 10%, with E = 55, = 0.15, and time four months to maturity. (c) Describe how the option price changes in each of these cases. Give a financial interpretation and a mathematical explanation for the changes. 5. (a) Write a MATLAB program to evaluate the Black-Scholes formula (1) for a Eu- ropean Call option using appropriate special functions of MATLAB. Your code should be fully explained with comments. (b) Produce three plots, each showing three curves that compare how changes to parameters affect option prices. Your plots should be clear, with appro- priate titles, labels, legends etc. Use the following combinations of para- meters: = 75, with = 0.15, 4% (per annum), and time E = 35, E = 55, E four months to maturity. = 0.05, = 0.15 and = time four months to maturity. 0.3, with E = 55, r = = 4% (per annum), and r = 1%, r = = 4% and r = 10%, with E = 55, = 0.15, and time four months to maturity. (c) Describe how the option price changes in each of these cases. Give a financial interpretation and a mathematical explanation for the changes.