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.(%) 58.93 19.5 52.38 18.9 52.81 17.1 56.30 19.3 52.79 16.4 51.12 35.3 46.39 33.9 46.50 36.3 48.40 32.4 50.01 23.2 47.24 27.6 50.38 31.2 VIX 12.6 18.9 12.9 13.7 14.6 15.7 16.4 20.0 14.2 13.2 11.6 16.1 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