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The University of Sydney
Discipline of Finance
FINC6010 – Derivative Securities
Assignment – 2022 Semester 1
1. Due date and time: 9 May 2022 by 18:00.
2. Please include a cover sheet containing only the student numbers of each member in your
group. Cover sheet does not contribute to the total number of pages for the assignment.
3. Assignments must be typed and submitted via Turnitin through Canvas.
4. Penalty of 5% per calendar day, or part thereof, will apply to late submissions.
5. Do not attach printouts of Excel spreadsheet to the assignment.
Background Information
The purpose of this assignment is to provide you with some insights into how financial institutions
adapt and adjust the properties of derivatives in response to the changes in the market.
A. In discounting cash flows associated with derivative contracts the so-called “risk-free” rates
(more precisely discount factors implied by risk-free rates) are commonly used.
(a) Prior to the global financial crisis (GFC), interbank borrowing and lending rates were used
as proxies for the “risk-free” rates. For example, 3-month LIBORs were used to discount
USD cash flows and 3-month BBSW rates were used to discount AUD cash flows.
(b) However, events during the GFC demonstrated that interbank borrowing and lending
rates were not suitable proxies for the “risk-free” rates and the market moved to using
central banks’ overnight cash rates to discount the cash flows. These “risk-free” rates will
be referred to as “OIS” rates in this assignment (OIS refers to overnight index swap).
B. Another consequence of the GFC was that cross currency (XCCY) swaps moved from being
based on fixed notional on both sides to the “notional resetting” where the notional on one
side is updated at the start of each interest period according to the prevailing foreign exchange
rate, and notional amounts on both legs are exchanged at the start and end of each interest
period.
In valuing XCCY swaps, it is the market convention to apply the so-called XCCY basis to the
“forecast” rates on the non-USD leg.
(a) Denote by DFUSD,OIST and DF
AUD,XCCY
T the T -year maturity OIS discount factor in
USD and the T -year XCCY basis adjusted discount factor in AUD respectively, and let
DFUSD,3mT and DF
AUD,3m
T the corresponding discount factors on the 3-month curves (that
is. implied by LIBOR and BBSW rates).
(b) Let LUSDT and LAUDT be the T -year maturity 3-month rates implied by the 3-month curves
in USD and AUD so that
LCCYT =
1
0.25 ·
(
DFCCY,3mT
DFCCY,3mT+0.25
1
)
, (1)
where CCY is USD or AUD.
2(c) Let A the notional amount on the USD leg, and denote by β the XCCY basis applicable
for a given maturity (a different basis applies to swaps of different maturities).
(d) Let T0 < T1 < T2 < . . . Tn be the swap settlement times where T0 is the swap start time. (e) The values at time t < Tn of the USD and AUD legs of XCCY swaps with fixed notional amounts are as follows: V USDt = A ·DFUSD,OIST0 · 1t≤T0 +A n∑ i=1 0.25 · LUSDTi 1 ·DFUSD,OISTi · 1t≤Ti +A ·DFUSD,OISTn 1t≤Tn (2) V AUDt = AF0 ·DFAUD,XCCYT0 · 1t≤T0 +AF0 n∑ i=1 0.25 · ( LAUDTi 1 + β ) ·DFAUD,XCCYTi · 1t≤Ti +AF0 ·DFAUD,XCCYTn 1t≤Tn , (3) where F0 is the AUD per USD foreign exchange rate at time T0, and 1t≤Ti is the “indi- cator” function that takes the value 1 if t ≤ Ti and zero otherwise. The discount factors and forecast rates are computed using the market data at time t. (f) The values at time t < Tn of the i-th “period” of the USD and AUD legs of the corre- sponding resetting notional XCCY swap are as follows: V USDt,i = A ·DFUSD,OISTi 1 · 1t≤Ti 1 +A · 0.25 · LUSDTi 1 ·DFUSD,OISTi · 1t≤Ti +A ·DFUSD,OISTi · 1t≤Ti , (4) V AUDt,i = AFi 1 ·DFAUD,XCCYTi 1 · 1t≤Ti 1 +AFi 1 · 0.25 · ( LAUDTi 1 + β ) ·DFAUD,XCCYTi · 1t≤Ti +AFi 1 ·DFAUD,XCCYTi · 1t≤Ti , (5) where Fi is the Ti-maturity AUD per USD forward foreign exchange rate at time t. The value of each leg is then the sum of the period values. (g) Note that the T -maturity AUD per USD foreign exchange rate, FT , at time t is given by the formula FT = Ft · DF USD,OIS T DFAUD,XCCYT , (6) where Ft is the spot AUD per USD exchange rate at time t. (h) The relationship between a T -maturity discount factor, D, and the corresponding T - maturity continuously compounded zero-rate, z, is given by D = e zT . (7) Macro Enabled Excel Spreadsheet To log-linearly interpolate discount factors based on a given set of discount factors, you will need an Excel function to perform the interpolation. A spreadsheet, FINC6010_assignment_2022_S1.xlsm, that contains the required function LoglinearInterpolate can be downloaded from Canvas. The spreadsheet also contains the market data you will need to answer the questions. When you open the downloaded spreadsheet for the first time, you will be asked if you trust the source and whether or not to enable macros. Please respond “yes” to both. The provided function LogLinearInterpolate 3takes as input a vertical vector of “x” values, then a vertical vector of corresponding “y” values, and finally the point at which you need the interpolated value: If you are able to download and use the interpolation function, then can skip the remainder of this section and go to the Questions section. If your PC does not allow you to download the spreadsheet FINC6010_assignment_2022_S1.xlsm, then you can create an Excel spreadsheet with the required interpolation function as follows: I. Download from Canvas the spreadsheet named FINC6010_assignment_data_2022_S1.xlsx con- taining the market data and a file named LoglinearInterpolate.bas. II. Open FINC6010_assignment_data_2022_S1.xlsx and (re)save with a name of your choice but with file type Excel Macro-Enabled Workbook (*.xlsm). III. Open a VBA code editor by hitting ALT and F11 simultaneously. IV. From the left panel of VBA editor, right click on your VBA project, then Import File. . . to open a dialogbox as follows: V. Locate the LoglinearInterpolate.bas file downloaded from Canvas and click the Open but- ton. You will now have a new Excel function with name LogLinearInterpolate. 4Questions If a question asks you compute numerical values, then you must provide a brief explanation of how you computed these values to earn full marks. If you do not provide any explanation and your values are incorrect, then you will not be awarded any marks. [55 marks] 1. Explain briefly what occurred during the GFC that specifically led to interbank lending and borrowing rates no longer being considered adequate proxies for the risk free rate. [5 marks] 2. Explain very briefly why the XCCY basis adjusted discount factors, DFAUD,XCCYT , are used in valuing the AUD leg of XCCY swaps rather than the corresponding AUD OIS discount factors, DFAUD,OIST . [3 marks] 3. Consider a fixed notional XCCY swap that started 2-years ago with 1 year remaining to ma- turity to pay USD and receive AUD. The USD notional amount is $10,000,000 and the XCCY basis spread is 0.40%. [18 marks] (a) Assuming that the AUD/USD spot rate was 0.8 at the start of the swap, compute the current value of the XCCY swap, and complete the tables below: Time DFUSD,OIS DFUSD,3m DFAUD,XCCY DFAUD,3m 0 0.25 0.5 0.75 1 Time LIBOR 3m BBSW 3m USD interest AUD interest 0 – – 0.25 0.5 0.75 1 – – Value USD leg in USD USD leg in AUD AUD leg in AUD Swap NPV in AUD Provide interest rates as percentages and round all values to 6 decimal places. [3 marks] (b) Compute the percentage change in the value of the XCCY swap if the continuously com- pounded rates in the AUD rate curves all increase by 10 basis points (0.1%), and complete the tables below: Time DFAUD,XCCY DFAUD,3m BBSW 3m AUD interest 0 – 0.25 0.5 0.75 1 – 5Value USD leg in AUD AUD leg in AUD Swap NPV in AUD % change in swap NPV Provide interest rates as percentages and round all values to 6 decimal places. [5 marks] (c) Compute the percentage change in value of the XCCY swap if the current spot AUD/USD exchange rate increases by 0.01, and complete the tables below:: Value USD leg in USD USD leg in AUD AUD leg in AUD Swap NPV in AUD % change in swap NPV Round all values to 6 decimal places. [5 marks] (d) By considering the interest rate and FX sensitivities of the XCCY swap found in parts (b) and (c) respectively, briefly explain to which risk factor the XCCY swap has greater sensitivity and why. [5 marks] 4. Consider a resetting notional XCCY swap with 1-year remaining to maturity that pays USD and receives AUD with USD notional amount of $10,000,000 and the XCCY basis spread of 0.40%. [18 marks] (a) Compute the current value of the XCCY swap by considering only the remaining periods (including the initial notionals), and complete the tables below: Time Spot AUD/USD AUD notional AUD interest Net AUD notional NPV 0 – 0.25 0.5 0.75 1 – – Value USD leg in AUD AUD leg in AUD Swap NPV in AUD Provide interest rates as percentages and round all values to 6 decimal places. [3 marks] (b) Compute the percentage change in value of the XCCY swap if the continuously compounded rates in the AUD rate curves are all increase by 10 basis points (0.1%), and complete the tables below: 6Time Spot AUD/USD AUD notional AUD interest Net AUD notional NPV 0 – 0.25 0.5 0.75 1 – – Value USD leg in AUD AUD leg in AUD Swap NPV in AUD % change in swap NPV Provide interest rates as percentages and round all values to 6 decimal places. [5 marks] (c) Compute the percentage change in value of the XCCY swap if the current spot AUD/USD exchange rate increases by 0.01, and complete the tables below:: Time Spot AUD/USD AUD notional AUD interest Net AUD notional NPV 0 – 0.25 0.5 0.75 1 – – Value USD leg in USD USD leg in AUD AUD leg in AUD Swap NPV in AUD % change in swap NPV Round all values to 6 decimal places. [6 marks] (d) Explain briefly why the sensitivity of the notional resetting XCCY swap to the spot FX is lower than the corresponding sensitivity for the fixed notional XCCY swap. [4 marks] 5. Resetting notional XCCY swaps have significantly lower risks compared to the corresponding fixed notional XCCY swaps. Identify one source of risk (other than interest rate and spot FX) that remains with notional resetting XCCY swaps and briefly explain how this risk can be mitigated. [4 marks] 6. Consider a long dated forward FX contract. That is, a forward FX contract with maturity that is far out into the future. [7 marks] (a) Identify and explain the most significant market related risk associated with long dated forward FX contracts. [4 marks] (b) Suggest how a long dated FX contract can be modified to reduce the risk identified in (a) without changing the maturity of the forward contract. You can introduce additional features to the forward contract, but you must provide an explanation as to how the risk is reduced as a result. [3 marks]