7. Let P(S, t; E,T) denote the value at time t of a European put option on the underlying asset S expiring at time T wit

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7 Let P S T E T Denote The Value At Time T Of A European Put Option On The Underlying Asset S Expiring At Time T Wit 1 (51.72 KiB) Viewed 14 times

7. Let P(S, t; E,T) denote the value at time t of a European put option on the underlying asset S expiring at time T with exercise price E. I (a) You are given the following inequality P(S. t; Ê, T) P(S. t; E, T). which mean that this inequality must hold as a Using no-arbitrage arguments, find the values of no-arbitrage condition on option prices. [4 marks] (b) You are given the following inequality P(S. t: E, T) 2P(S. t; 2E.T) - P(S. t; E, T). Using no-arbitrage arguments, find the values of E which mean that this inequality must hold as a no-arbitrage condition on option prices. [8 marks] - (c) Consider the case where the current share price is So £56.76, a put option with E= £40 is priced at £13, a put with E £80 is priced at £46, and a put with E= £120 is priced at £72, all of the options have one year left until expiry. The current risk free interest rate is a constant 2% per annum. Construct a portfolio to exploit the arbitrage opportunity and calculate the profit made. [6 marks]