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All five questions are equally weighted with 20 points each.
Question 1: Structured Product (20 points)
Consider a one-year structured product issued by NOPAY BANK on an equity index consisting of one long call L and one long put H. The equity index portfolio doesn’t pay dividends. The corresponding strike and option prices are shown below.
The structure product is issued at a time when the underlying equity index level is 100.
Can you list FIVE factors that you would use to characterize this product for your investor-clients? (5 points)
Based on the five factors you have listed in (a), perform a financial analysis of the product without using the Black-Scholes formula or the greeks. (15 points)
Question 2: Airbag Contract (20 points)
Suppose today is August 2, 2021. Consider a 5-year “Airbag” security, a customized structured product offered by ABN-AMRO that is linked to the performance of the Hang Seng Index. The product is targeted at the high-net-worth individuals. The terms of the Airbag contract are as follows:
Issuance date: 02 August 2021 ()
Terminal date: 02 August 2026 (
Initial Hang Seng Index () on 02 August 2021: 26,180
Dividend yield: 2%
Payment at terminal date (per USD1,000,000) is linked to the Hang Seng Index on 02 August 2026 ():
It is believed that the Hang Seng index will fluctuate with 32.5% volatility each year for the next 5 years. The risk-free interest rate is 5%.
Draw a diagram to describe the payoffs of this Airbag product. (5 points)
Determine the fair market value of this Airbag product. (10 points)
The Hang Seng Index on August 02, 2024 has fallen to 16,946. Assume that the risk-free rate and the volatility remain the same. What is the fair value of the Airbag contract on August 02, 2024. (5 points)
Hint: The Black-Scholes formula is provided in the Excel File provided: “Q2 Black-Scholes Formula”.
Question 3: Reverse Convertible Notes (20 points)
Read the Harvard Case on Reverse Convertible Notes (RCN) and answer the following two questions.
Was the RCN fairly priced? (10 points)
Did it offer a favorable risk-return tradeoff to the high-net-worth investors? Explain. (10 points)
Question 4: Securitization of Pure Risk—Weather Derivatives (20 points)
Many businesses are in the position where their performance is adversely affected by extreme weather conditions due to global warming. Weather derivatives as an over-the-counter financial product for managing weather risk has gained popularity as a risk management tool in recent years. The weather derivative contract consists of the following terms:
HDD: Heating Degree Days
CDD: Cooling Degree Days
Suppose a day’s HDD and CDD in Hong Kong are defined respectively as follows:
Daily HDD = max{0, 24 oC – AVG} ; Daily CDD = max{0, AVG – 24 oC }
AVG is the average of the highest and lowest temperature during the day at a specified weather station measured in degrees Celsius. A typical over-the-counter product is an option contract providing a payoff determined by the cumulative HDD or CDD during a month; that is, the total of the HDDs or CDDs for every day in the month.
Suppose Nopay Bank in December 2023 sells to client a weather derivative on the cumulative CDD during August 2024 with a strike price of 130, a payment rate of USD1,000 per degree day, subject to a payment cap of USD140,000.
Draw a payoff diagram for this one-month cumulative weather option. (5 points)
Describe the payoffs in terms of options. (5 points)
Suppose the daily average temperature for the month of August is normally distributed with mean and standard deviation () equal to 30oC and 1.5 oC respectively. The risk-free rate of interest is 5% per annum. Determine the market value of the August CDD contract by doing a Monte Carlo simulation with at least 5,000 iterations in Excel. (10 points)
Hint: To generate normal random variable with mean and standard deviation () in Excel, the command to use in Excel is: “”
Step 1: Generate 31 daily random temperatures based on the mean and standard deviation.
Step 2: Determine the CDD for each simulated temperature
Step 3: Calculate the cumulative CDD and determine the corresponding terminal payoff
Step 4: Repeat Steps 1 to 3 for at least 5,000 times and obtain at least 5,000 terminal payoffs
Step 5: Take the average of the terminal payoffs simulated and discount it back to time 0 at
the risk-free rate.
Question 5: USD-HKD Callable Bonus Forward (20 points)
On July 2015, ICBC(Asia) issued a 24-month USD-HKD Callable Bonus Forward to one of its high-net-worth individual clients. The details of the product are attached in the pdf file “Q5-USD-HKD Callable Bonus Forward”.
To provide you the perspective on the macroeconomic backdrop of this product, the graph below presents the monthly USD-HKD high, low and close exchange rate from Jan 31, 2010 to Jul 31. 2024.
Based on the macroeconomic environment for the USD-HKD at the time of issuance, would the product offer a favorable risk-return tradeoff to the high-net-worth investors? Explain. (3 points)
Suppose the trade date started on Aug 03, 2015 and the first fixing date for the contract was Aug 31, 2015. Determine the maximum possible gain to the investor. (5 points)
Suppose the monthly USD-HKD exchange rates for the 24 fixing dates are as provided in the table below. Determine the profit and loss each month and the cumulative profit and loss at the end of the contract. (10 points)
Fill in the table below:
Would the same product with the same contract terms be offered by the bank after 2020? Briefly explain why or why not? (2 points)
All five questions are equally weighted with 20 points each.
Question 1: Structured Product (20 points)
Consider a one-year structured product issued by NOPAY BANK on an equity index consisting of one long call L and one long put H. The equity index portfolio doesn’t pay dividends. The corresponding strike and option prices are shown below.
The structure product is issued at a time when the underlying equity index level is 100.
Can you list FIVE factors that you would use to characterize this product for your investor-clients? (5 points)
Based on the five factors you have listed in (a), perform a financial analysis of the product without using the Black-Scholes formula or the greeks. (15 points)
Question 2: Airbag Contract (20 points)
Suppose today is August 2, 2021. Consider a 5-year “Airbag” security, a customized structured product offered by ABN-AMRO that is linked to the performance of the Hang Seng Index. The product is targeted at the high-net-worth individuals. The terms of the Airbag contract are as follows:
Issuance date: 02 August 2021 ()
Terminal date: 02 August 2026 (
Initial Hang Seng Index () on 02 August 2021: 26,180
Dividend yield: 2%
Payment at terminal date (per USD1,000,000) is linked to the Hang Seng Index on 02 August 2026 ():
It is believed that the Hang Seng index will fluctuate with 32.5% volatility each year for the next 5 years. The risk-free interest rate is 5%.
Draw a diagram to describe the payoffs of this Airbag product. (5 points)
Determine the fair market value of this Airbag product. (10 points)
The Hang Seng Index on August 02, 2024 has fallen to 16,946. Assume that the risk-free rate and the volatility remain the same. What is the fair value of the Airbag contract on August 02, 2024. (5 points)
Hint: The Black-Scholes formula is provided in the Excel File provided: “Q2 Black-Scholes Formula”.
Question 3: Reverse Convertible Notes (20 points)
Read the Harvard Case on Reverse Convertible Notes (RCN) and answer the following two questions.
Was the RCN fairly priced? (10 points)
Did it offer a favorable risk-return tradeoff to the high-net-worth investors? Explain. (10 points)
Question 4: Securitization of Pure Risk—Weather Derivatives (20 points)
Many businesses are in the position where their performance is adversely affected by extreme weather conditions due to global warming. Weather derivatives as an over-the-counter financial product for managing weather risk has gained popularity as a risk management tool in recent years. The weather derivative contract consists of the following terms:
HDD: Heating Degree Days
CDD: Cooling Degree Days
Suppose a day’s HDD and CDD in Hong Kong are defined respectively as follows:
Daily HDD = max{0, 24 oC – AVG} ; Daily CDD = max{0, AVG – 24 oC }
AVG is the average of the highest and lowest temperature during the day at a specified weather station measured in degrees Celsius. A typical over-the-counter product is an option contract providing a payoff determined by the cumulative HDD or CDD during a month; that is, the total of the HDDs or CDDs for every day in the month.
Suppose Nopay Bank in December 2023 sells to client a weather derivative on the cumulative CDD during August 2024 with a strike price of 130, a payment rate of USD1,000 per degree day, subject to a payment cap of USD140,000.
Draw a payoff diagram for this one-month cumulative weather option. (5 points)
Describe the payoffs in terms of options. (5 points)
Suppose the daily average temperature for the month of August is normally distributed with mean and standard deviation () equal to 30oC and 1.5 oC respectively. The risk-free rate of interest is 5% per annum. Determine the market value of the August CDD contract by doing a Monte Carlo simulation with at least 5,000 iterations in Excel. (10 points)
Hint: To generate normal random variable with mean and standard deviation () in Excel, the command to use in Excel is: “”
Step 1: Generate 31 daily random temperatures based on the mean and standard deviation.
Step 2: Determine the CDD for each simulated temperature
Step 3: Calculate the cumulative CDD and determine the corresponding terminal payoff
Step 4: Repeat Steps 1 to 3 for at least 5,000 times and obtain at least 5,000 terminal payoffs
Step 5: Take the average of the terminal payoffs simulated and discount it back to time 0 at
the risk-free rate.
Question 5: USD-HKD Callable Bonus Forward (20 points)
On July 2015, ICBC(Asia) issued a 24-month USD-HKD Callable Bonus Forward to one of its high-net-worth individual clients. The details of the product are attached in the pdf file “Q5-USD-HKD Callable Bonus Forward”.
To provide you the perspective on the macroeconomic backdrop of this product, the graph below presents the monthly USD-HKD high, low and close exchange rate from Jan 31, 2010 to Jul 31. 2024.
Based on the macroeconomic environment for the USD-HKD at the time of issuance, would the product offer a favorable risk-return tradeoff to the high-net-worth investors? Explain. (3 points)
Suppose the trade date started on Aug 03, 2015 and the first fixing date for the contract was Aug 31, 2015. Determine the maximum possible gain to the investor. (5 points)
Suppose the monthly USD-HKD exchange rates for the 24 fixing dates are as provided in the table below. Determine the profit and loss each month and the cumulative profit and loss at the end of the contract. (10 points)
Fill in the table below:
Would the same product with the same contract terms be offered by the bank after 2020? Briefly explain why or why not? (2 points)