Question 2. Option pricing (3 marks) BHP Billiton, the leading Australian iron ore mining giant, is listed on New York Stock Exchange. The iron ore prices have almost doubled from $67.87 on 3 August 2018 to $123.16 on 3 July 2019. The following table shows BHP stock prices in $ and the an- nualised historical volatility (Vol.) of BHP, VIX Index, the iron ore prices in $ at given dates. For simplicity, we assume one price, i.e., no bid-ask spread. Date BHP stock price Vol.(%) VIX Iron ore price 3 Jul 2019 58.93 19.5 12.6 123.16 3 Jun 2019 52.38 18.9 18.9 93.97 3 May 2019 52.81 17.1 12.9 89.15 3 Apr 2019 56.30 19.3 13.7 87.60 4 Mar 2019 52.79 16.4 14.6 78.98 4 Feb 2019 51.12 35.3 15.7 77.85 3 Jan 2019 46.39 33.9 16.4 74.30 3 Dec 2018 46.50 36.3 20.0 67.82 5 Nov 2018 48.40 32.4 14.2 74.17 4 Oct 2018 50.01 23.2 13.2 70.79 4 Sep 2018 47.24 27.6 11.6 68.28 3 Aug 2018 50.38 31.2 16.1 67.87 A European call option on BHP stock that expired on 3 Jan 2020 and had a strike price of $65 was traded at $1.46 on 3 July 2019. A European put option on BHP stock that expired on 3 Jan 2020 and had a strike price of $65 was traded at $8.55 on 3 July 2019. The annual risk-free rate of interest was 2.15%. Use discrete compounding if you need to compute semi-annual interest rate. 1. Show that there was an arbitrage opportunity with these options. (1 mark) 2. Construct an arbitrage strategy. (2 marks)