Option pricing

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 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.
1. Show that there was an arbitrage opportunity with these options. (1 mark)
2. Construct an arbitrage strategy. (2 marks)

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