BHP Billiton Case Study - Evaluate the Percentage Change - Finance Assignment Help

Assignment Task :

Question 1, Option pricing  

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. 

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. Identify if there is arbitrage opportunity. Construct an arbitrage strategy if there is an arbitrage opportunity.  

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.

Question 2, Duration and Banking  

Consider a 5-year bond with annual coupon payments. The bond that has a face value of $100 and sells for $95. The coupon rate is 3%. Coupon rate is the ratio between the coupon value and the face value. The face value is paid at the maturity year in addition to the last coupon payment. 

1. Calculate the the bond’s yield to maturity (YTM).  

2. Calculate the bond’s duration using its YTM.  

3. Suppose the bond’s YTM changes in correspondence to 5-year T-bill interest rate. Use the bond’s duration to evaluate the percentage change in the 5-year bond’s value if the interest rate on 5-year T-bills falls by one basis point, that is, by 0.01%.  

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