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.

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.

2. Construct an arbitrage strategy.
 

Date 3 Jul 2019 3 Jun 2019 3 May 2019 3 Apr 2019 4 Mar 2019 4 Feb 2019 3 Jan 2019 3 Dec 2018 5 Nov 2018 4 Oct 2018 4 Sep 2018 3 Aug 2018 BHP stock price Vol.(%) VIX 58.93 19.5 12.6 52.38 18.9 52.81 17.1 56.30 19.3 13.7 52.79 16.4 14.6 51.12 35.3 15.7 46.39 33.9 16.4 46.50 36.3 20.0 48.40 32.4 14.2 50.01 23.2 13.2 47.24 27.6 11.6 50.38 31.2 16.1 18.9 12.9 Iron ore price 123.16 93.97 89.15 87.60 78.98 77.85 74.30 67.82 74.17 70.79 68.28 67.87 Date 3 Jul 2019 3 Jun 2019 3 May 2019 3 Apr 2019 4 Mar 2019 4 Feb 2019 3 Jan 2019 3 Dec 2018 5 Nov 2018 4 Oct 2018 4 Sep 2018 3 Aug 2018 BHP stock price Vol. (%) 58.93 52.38 52.81 56.30 52.79 51.12 46.39 46.50 48.40 50.01 47.24 50.38 VIX 12.6 19.5 18.9 17.1 19.3 13.7 16.4 14.6 35.3 15.7 33.9 16.4 36.3 20.0 32.4 14.2 23.2 13.2 27.6 11.6 31.2 16.1 18.9 12.9 Iron ore price 123.16 93.97 89.15 87.60 78.98 77.85 74.30 67.82 74.17 70.79 68.28 67.87