Question

On December 1st, 2018, a client placed the following order on an online trading provider:

Short 20 European call currency option contracts on Australian dollars with maturity June 2019 and strike 0.8000
Short 10 European put currency options contracts on Australian dollars with maturity June 2019 and strike 0.7500. Each contract has a size of 10,000 Australian dollars.

On December 1st, 2018, the spot exchange rate was quoted at 0.7792 USD per AUD, the US interest rate was 1.95% p.a. and the AUD interest rate was 3.08% p.a. with continuous compounding. The exchange rate volatility was 32% p.a..

1. a) Use the Black Scholes’s model to estimate the premium involved to trade theseoptions. Did the client pay or receive this premium?

2. b) Identify the strategy that the client used and provide the table and the diagram of the expected profit/loss generated by the strategy.

3. c) Discuss the profit and loss potential associated with this strategy. What was the client’s expectation on market volatility and direction (bull or bear) when he placed the order?

4. d) Calculate the losses made if he exercises in June 2019 when the spot exchange rate is 0.9170.

5. e) Calculate the delta and gamma of the client’s options portfolio on December 1st, 2018. Interpret these numbers.

6. f) Your recommendation is to hedge his portfolio and you are considering two alternatives: i) a delta hedge only and ii) a delta-gamma hedge. What positions on currency options (with delta of 0.25, gamma of 3.35 and value of AU$200) and Australian dollars are required to make his portfolio

   1. i) delta neutral, or

   2. ii) delta – gamma neutral?

   What is the cost of each hedge? Assume that the hedge is set up on December 1st, 2018.

7. g) Discuss the benefits and drawbacks of each hedging strategy considered in part f). What hedge is more effective for the client’s options portfolio and why?

Answer 1

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