Question 4 [Total marks 25]

Task 1 [10 marks]

Define a function called european_put() that prices a put option.

1. Test that it is able to price a put option correctly. With the following parameters, the price of the put should be 3.44 Here are the inputs: european_put(S0=15, T=2,m=4,rf=0.05,E=18,sigma=0.3)

2, Graph the convergence of the binomial put option price to the Black-Scholes price for the put option with time steps ranging from 2 to 500 for the option above. For completeness I have included the function for the Black Scholes put option in the assignment.

3. Graph the pricing error (Binomial Price/Black-Scholes Price minus 1) on the y-axis with the number of time-steps on the x-axis. (Max 100 words)