As a hypothetical example, heating degree days (HDD), an index used in weather derivatives, are counted with a base temperature of 18°C. The daily average temperatures over 4 days were 12°C, 16°C, 20°C, and 15°C. What is the HDD for these 4 days?
Quiz: Other Derivatives
Last reviewed: September 25, 2026
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8 questions to check your understanding of the chapter “Other Derivatives”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: C
HDD adds up the differences on days when the daily average temperature is below the base. The difference is 6 on the 12°C day, 2 on the 16°C day, and 3 on the 15°C day. The 20°C day, which is above the base, counts as 0. 6 + 2 + 0 + 3 = 11, so the HDD is 11°C days.
2°C days is the value of cooling degree days (CDD), which add up the differences on days when the daily average temperature is above the base. Over these 4 days, only the 2°C days from the 20°C day count toward CDD. 13°C days also adds the difference of 2 on the 20°C day to the HDD. 9°C days subtracts that difference of 2 from the HDD. In HDD, days above the base are neither added nor subtracted.
Learn more: Weather Derivatives
Question 2
Which of the following correctly describes how weather derivatives differ from insurance?
Answer and explanation
Answer: D
A weather derivative does not assess whether there was a loss or how large it was. It pays a set amount when observations such as temperature meet the conditions. With no assessment process, payment arrives quickly.
Because weather derivatives resemble insurance in that both prepare for losses from the weather, it is easy to assume they decide payment the same way as insurance and to pick the choice that assesses the loss.
Assessing the actual loss and covering it up to a limit is what insurance does. A weather derivative is not limited to damage from natural disasters. It can also cover lower sales or higher costs caused by heat or cold.
On the other hand, because payment depends only on the observations, the amount received does not always equal the actual loss, and the two can differ. The risk of this gap is called basis risk. A company may have a loss but receive nothing because the index does not meet the conditions, or it may receive a payout because the index meets the conditions even though it had no loss.
Learn more: Weather Derivatives
Question 3
The Cboe Volatility Index (VIX) is calculated from what, and what does it show?
Answer and explanation
Answer: A
The VIX is an index calculated from the prices of S&P 500 Index options. It measures how much the market expects the US stock market to move over the next 30 days. Option prices carry the market's view of volatility, the size of price moves. The VIX condenses the view priced into many options into a single number.
The choice saying the VIX measures volatility actually observed in past moves is an easy mistake if the word "volatility" makes you think of how widely past prices varied. The VIX uses option prices, not past price moves. VIX futures are futures on the VIX. The VIX is not calculated from VIX futures prices. Instead, VIX futures are settled using the value of the VIX.
The VIX is an annualized volatility expressed in percent, but the period it looks at is the next 30 days. For example, a VIX of 20 means the market expects prices to move over the next 30 days at an annual rate of about 20%.
Learn more: Volatility Products such as VIX Futures
Question 4
As a hypothetical example, the VIX today is 16.00, VIX futures expiring in 1 month are at 18.00, and VIX futures expiring in 2 months are at 19.50. Suppose you buy 2 contracts of the futures expiring in 2 months at 19.50, and a month later the VIX is unchanged and the term structure has exactly the same shape. Taking the VIX futures contract size as USD 1,000 per point, what is the profit or loss on the futures after 1 month?
Answer and explanation
Answer: C
The result is a loss of USD 3,000. After a month, the contracts you bought are now the futures expiring in 1 month, so their price falls to 18.00. The profit or loss per contract is (18.00 − 19.50) × USD 1,000 = −USD 1,500. For 2 contracts, it is −USD 1,500 × 2 = −USD 3,000. The shape in this example, where prices are higher the later the expiry, is called contango. If the term structure does not change, simply holding the futures makes their price fall.
A loss of USD 1,500 is the figure for only 1 contract. A loss of USD 7,000 assumes the futures price falls to 16.00, the same as the VIX, after a month, and calculates (16.00 − 19.50) × USD 1,000 × 2. After a month, the futures still have 1 month left to expiry. A profit of USD 3,000 reverses the direction of the profit or loss.
Conversely, suppose stocks fall sharply during the month and these futures rise to 24.00. The profit or loss per contract is (24.00 − 19.50) × USD 1,000 = USD 4,500. For 2 contracts, the profit is USD 9,000.
Learn more: Volatility Products such as VIX Futures
Question 5
As a hypothetical example, a property and casualty insurer, Company Y, issues a 10 billion yen catastrophe bond. The term is 3 years, and the trigger reduces the principal by the amount by which Company Y's typhoon claims exceed 300 billion yen, with the reduction capped at 10 billion yen. The investor receives 1.8 billion yen in coupons over the 3 years. If the principal reduction is fixed at the end of year 3 and Company Y's typhoon claims are 304 billion yen, what is the investor's profit or loss?
Answer and explanation
Answer: C
The investor has a loss of 2.2 billion yen. The claims exceed 300 billion yen by 304 − 300 = 4 billion yen, so the principal falls by 4 billion yen. Subtracting that reduction from the 3 years of coupons of 1.8 billion yen gives 1.8 − 4 = −2.2, a loss of 2.2 billion yen.
A profit of 1.8 billion yen is the result when the principal is not reduced, which is the case when claims are 300 billion yen or less. A loss of 4 billion yen looks only at the principal reduction and forgets to add the coupons received. A loss of 3.4 billion yen adds only 1 year of coupons, 600 million yen, instead of the 3 years.
In the opposite case, if claims are 300 billion yen or less, the principal is not reduced and the investor's result is the coupons of 1.8 billion yen. The profit is capped at the coupon amount. The loss grows with the principal reduction and stays constant at 8.2 billion yen once claims reach 310 billion yen or more.
Learn more: Insurance-Linked Securities and Cat Bonds
Question 6
As a hypothetical example, a pension fund has entered into a longevity swap covering pensions paid to its members, and the two sides settle by netting. In one year, the fixed payment (fund to taker) is 900 million yen, the amount equal to the actual pension payments is 960 million yen, and the pensions the fund paid to members were also 960 million yen. In this year, when members lived longer than expected, what happens to the payments and to the fund's net burden?
Answer and explanation
Answer: A
The amount equal to the actual pension payments is larger than the fixed payment, so the difference is 960 − 900 = 60 million yen, and the taker pays it to the fund. The fund pays members 960 million yen in pensions and receives 60 million yen from the taker, so its net burden is 960 − 60 = 900 million yen, which stays at the fixed payment.
The choice saying the net burden rises to 960 million yen assumes the swap does not transfer the cost of longer lives. The choice saying the burden does not change even though the taker pays 60 million yen forgets to subtract the difference received. The choice with 1,020 million yen reverses the direction of the difference. That direction applies in a year when members die sooner than expected and the amount equal to the actual pension payments is less than the fixed payment.
From the taker's side, gains and losses are the reverse of the fund's. If members die sooner than expected, the fund pays the difference to the taker, and the fund is spared the extra cost it would otherwise have borne.
Learn more: Longevity Swaps
Question 7
As a hypothetical example, Company A owns a rental office building with a market value of 10 billion yen and has entered into a swap on a real estate index with a notional amount of 10 billion yen. Company A pays an amount based on the index total return, and the dealer pays 300 million yen, which is 3% a year on the notional amount. In a year when both the index and the property have a total return of +8%, what is Company A's total, combining the net swap payment and the property's total return?
Answer and explanation
Answer: D
The total is a profit of 300 million yen. In a year when the index is +8%, Company A pays 10 billion yen × 8% = 800 million yen and receives 300 million yen, so the net swap payment is −500 million yen. The property's total return is +800 million yen, so −500 + 800 = +300, and the total is 300 million yen.
A loss of 500 million yen looks only at the net swap payment and forgets to add the property's return. A profit of 800 million yen looks only at the property's return and forgets to subtract the swap payment. A profit of 1.1 billion yen adds only the 300 million yen interest received to the property's 800 million yen return, and forgets to subtract the 800 million yen index payment. In a year when the index total return is positive, Company A is the payer.
If the property's total return always equals the index, the total is 300 million yen every year regardless of the index. For example, in a year when the index is −4%, the net swap payment is +700 million yen and the property's total return is −400 million yen, so the total is again 300 million yen. In exchange, even if the index rises, Company A cannot receive the property's gain in value.
Learn more: Property Derivatives
Question 8
As a hypothetical example, a shipping operator, Company B, buys a forward freight agreement (FFA) on a Capesize freight index, with a contract rate of USD 20,000 per day for 30 days (1 day counted as 1 lot). The arithmetic average of the freight index published during the settlement period is USD 17,000 per day. There is no delivery of ships or cargo, and the difference is settled in cash. What happens to Company B's payments on the FFA?
Answer and explanation
Answer: B
Company B pays USD 90,000. The buyer's profit or loss on an FFA is the average of the index minus the contract rate, multiplied by the number of days. (17,000 − 20,000) × 30 = −90,000, so Company B pays USD 90,000.
The choice of paying USD 600,000 is the contract rate of USD 20,000 per day multiplied by 30 days, assuming the buyer pays the full contract rate instead of the difference. The choice of paying USD 3,000 is the difference per day and does not multiply by the 30 days. USD 510,000 is the average index of USD 17,000 per day multiplied by 30 days, which corresponds to the cost of chartering the ship. FFA settlement is the difference from the contract rate, not the cost of chartering the ship.
In the opposite case, if the average of the index is USD 23,000 per day, then (23,000 − 20,000) × 30 = USD 90,000, which Company B receives. If Company B's cost of chartering a ship equals the index, then once the FFA payments are included, the cost is fixed at USD 600,000, the contract rate of USD 20,000 per day multiplied by 30 days, whether freight rises or falls.
Learn more: Freight Derivatives (FFA)