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 annualised 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.

Show that there was an arbitrage opportunity with these options, then construct an arbitrage strategy