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Question 1, Option pricing (6 marks) BHP Billiton (BHP), 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 the BHP's stock prices in USD and the annualised historical volatility (Vol. for short) of BHP on NYSE, VIX Index, the iron ore prices in USD at given dates below. Table 1 Date NYSE:BBL BBL Vol. (%) VIX Iron Ore 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 16.39 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 with underlying stock BHP's strike price of $65 is traded at $1.46 on 3 July 2019, expiring on 17 Jan 2020. A European put option with underlying stock BHP's strike price of $65 is traded at $8.55 on 3 July 2019, expiring on 17 Jan 2020. The risk-free rate of interest is 2.15%. 1. Compute the implied volatility of both put and call options using the Black-Scholes Options. Compare the implied volatilities of call and put options, and provide an economic rational to explain the difference. (2 marks) 2. Identify if there is arbitrage opportunity. Construct an arbitrage strategy if there is an arbitrage opportunity. (2 marks) 3. Evaluate the vega of the call option for the period based on the period from 3 June 2019 to 3 July 2019. Comment on your results. (2 marks) Useful links: A report on surging iron ore here, and market index here