Using python

Task 3 [5 marks]

The put-call parity is a condition that must hold for arbitrage to be ruled out in option markets.

The underlying idea is that if two different investment positions have exactly the same payoff, then they must also have the same price.

We can state it as follows: S + P = PV(K) + C

Where: P = Price of a European put option (with strike price K)

S = The underlying stock price

PV(K) = Present value of the strike price of the option (i.e. a bond investment equal to the strike price)

C = Price of a European call option (with strike price K)

We can of course rearrange the terms and compute the price of for example a call option using the put-call parity as: C = P + S PV(K) The calculated price should be equal to that from using the binomial tree to compute the call price.

a) Explain graphically and with words how the put-call parity works. Write maximum 2/3 of a page of text. Also make sure to visualize the equivalence graphically. (Max 300 words)

b) Write a function that uses the put-call parity to compute the price of a European call option. Verify that the outcome is identical to pricing the call option directly with the binomial tree (up to approximately 6 decimals or so).