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 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. Date 3 Jul 2019 BHP stock price Vol.(%) VIX Iron ore price 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. 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%. Using what you learnt from the course, answer the following questions. 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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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 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.
Date
3 Jul 2019
BHP stock price Vol.(%) VIX
Iron ore price
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. 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%. Using what you learnt from the
course, answer the following questions. 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)
Transcribed Image Text: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 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. Date 3 Jul 2019 BHP stock price Vol.(%) VIX Iron ore price 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. 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%. Using what you learnt from the course, answer the following questions. 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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