This is an assessment that I need to be asked for help. All questions are details as below and all answers I need to be with the progress not only f

This is an assessment that I need to be asked for help. All questions are details as below and all answers I need to be with the progress not only for a number and an answer. Thank you!

Problem A2: Option Valuation and Properties of Options (27 marks)

In this question, you need to price options with different valuation approaches and comment on your results. You will consider puts and calls on a share with a spot price of $150. Strike price is $148. The risk-free interest rate is 4% per annum with continuous compounding.

Binomial trees:

Furthermore, assume that over each of the next two three-month periods, the share price is expected to go up by 5% or down by 5%.

Draw a two-step binomial tree and populate the individual nodes with the share price values at each node. [2 marks]

Use the two-step binomial tree from a. to calculate the value of a six-month European call option using the no-arbitrage approach. [3 marks]

Use the two-step binomial tree from a. to calculate the value of a six-month European put option using the no-arbitrage approach. [3 marks]

Show whether the put-call-parity holds for the European call and the European put prices you just calculated in b. and c. [2 mark]

Use the two-step binomial tree from a. to calculate the value of a six-month European call option using risk-neutral valuation. [2 marks]

Use the two-step binomial tree from a. to calculate the value of a six-month European put option using risk-neutral valuation. [2 marks]

Verify whether the no-arbitrage approach and the risk-neutral valuations lead to the same results. [1 mark]

Use the two-step binomial tree from a. to calculate the value of a six-month American put option.

[2 marks]

Without calculations: What is the value of a six-month American call option with a strike price of

$148? Why? [2 marks]

Notes:

When you use no-arbitrage arguments, you need to show in detail how to set up the riskless portfolios at the individual nodes of the binomial tree.

Black-Scholes-Merton model:

Furthermore, assume that the volatility of the underlying asset is 10%.

What is the Black-Scholes-Merton price of a six-month European call option? [2 marks]

What is the Black-Scholes-Merton price of a six-month European put option? [2 marks]

Without calculations: What would happen to the option prices you just calculated in i. and j. if the interest rate increases to 6%? Why? [2 marks]

Comparison across models:

Compare the call option prices you just calculated in e. and i. Compare also the put option prices you just calculated in f. and j. Do expect these prices to be the same? Why/Why not? [2 marks]

Part C: Risk Management Case Study (25 marks)

Suppose you are a risk management specialist employed by WeManageYourRisk, a company specialised in providing mining companies with expert advice regarding their various risk management needs.

Assume it is 1 September 2022. Mr Walter Pinkman who is a new treasurer of WeMineGold contacts you to discuss the companys financial risk management. WeMineGold is an Australian gold mining company producing gold in north-eastern Australia, with plans to increase its size and valuation over the next few years. WeMineGold is a growth company that has invested in developing goldfields and commenced extracting gold and gold production from its underground mines. WeMineGolds profit and loss is subject to the price change of gold which is known to be quite volatile. WeMineGold is planning to sell its output of 100,000 ounces of gold on 1 March 2023. The company regularly transacts with the WeTradeDerivatives Bank which is also available as a counterparty of forward and option contracts with gold as an underlying asset.

Walter has a basic understanding of how derivatives like forwards, futures and options work but would like to receive detailed advice about derivatives positions and potential outcomes of various strategies. Walter is considering following strategies:

Strategy A: Using forwards with the WeTradeDerivatives bank as a counterparty Strategy B: Using options with the WeTradeDerivatives bank as a counterparty Strategy C: Doing nothing

Walter is expecting the gold price to rise over the next six months and is hoping to find a strategy which will provide protection against unfavorable price movements while at the same time allowing to benefit from a potential gold price increase. Furthermore, while Walter knows that derivatives are mainly used to manage financial risks, he shares that he had recently heard in a podcast that one could use them for arbitrage trading strategies too and is interested to understand how these strategies work.

Following further information is available:

Profit margin is defined as (Revenue Cost of Goods Sold) / Revenue.

The company has a target profit margin of 18%.

The cost of mining one ounce of gold is $1,350.

The spot price of gold on 1 September 2022 is $1,708 per ounce.

The risk-free interest rate for all maturities is 1.5% (cont. comp.).

Following option contracts expiring on 1 March 2023 are available (each option is on one ounce of gold):

Option Type Strike price Option Premium

Put option $1,700 $38.24

Call Option $1,700 $58.94

Based on the information given above, please address following questions:

What is the profit margin of WeMineGold if the current spot price is used? [1.5 marks]

What should be the gold price at which WeMineGold achieves exactly its target rate? [1.5 marks]

What would be the forward price for a contract expiring on 1 March 2023? [1 mark]

Provide an explanation (without calculations) what option contracts (puts or calls) and what positions (long or short) are suitable for the needs of the company, should the company decide to go with strategy B. [3 marks]

For each of these three hedging strategies A, B and C, calculate the profit margin for the following two scenarios:

The spot price of gold on 1 March 2023 is $1,900 per ounce.

The spot price of gold on 1 March 2023 is $1,550 per ounce. [6 marks]

Based on your results from e. and your overall knowledge about derivatives, provide a thorough and clearly arranged comparison of the three strategies A, B and C as listed above and discuss

advantages and disadvantages of each strategy. Which strategy would you recommend to Walter? [7 marks]

Assume WeTradeDerivatives has made a typo while quoting option premiums and offers to trade call options with strike price of $1,700 at a premium of $48.94 (instead of $58.94 as listed above). Does the put-call-parity hold in this case? If not, please explain in detail to Walter the arbitrage opportunity which would arise. [5 marks]

Notes:

If a hedging strategy uses options, the option premium needs to be considered as an expense (added to Cost of Goods Sold) for profit margin calculations.

For the sake of simplicity, ignore any potential exchange rate effects, transaction costs or storage costs.