Consider a commercial property loan of amount V with a total duration of n3 years and m compounding payments per year at annual interest rate r1.
In the first n1 years, payments only cover interest (the interest-only grace period, with no principal amortization).
In the next n3 − n1 years, equal periodic amortizing payments repay the loan.
After a duration of n2 years from loan inception (where n1 < n2 < n3),
immediately after making the year-end payment,
the borrower has an option to refinance the remaining loan balance B into a new loan at annual interest rate r2 for the remaining
n3 − n2 years again with m payments per year.
Refinancing incurs a fixed upfront fee F and a prepayment penalty fraction α on the remaining balance B,
both paid out-of-pocket in cash by the borrower at year n2.
Write a program to calculate:
- Regular periodic payment amount after the grace period;
- Remaining loan balance B;
- Total interest saved by refinancing over the n3 − n2 years;
- Annualized net internal rate of return (IRR) of the refinancing decision.
The annualized net IRR is defined as m × y, where the periodic IRR y is the unique rate satisfying:
C0 = ∑t=1K (ΔPMT) / (1 + y)t = (ΔPMT) × [1 − (1 + y)−K] / y
where:
- C0 = F + α × B is the upfront cash outflow (refinancing fee plus the prepayment penalty on B);
- K = (n3 − n2) × m is the total number of payments;
- ΔPMT = PMTold − PMTnew is the periodic cash savings from refinancing.
Inputs:
- V: original loan amount in dollars, a float or integer;
- m: number of payments per annum, a positive integer;
- n1: duration of the initial interest-only grace period in years, a positive integer;
- n2: duration from loan inception to refinancing in years (n1 < n2 < n3), an integer;
- n3: duration of the original loan in years, a positive integer;
- r1: annual interest rate of the original loan (compounded m times per annum), a float;
- r2: annual interest rate of the refinanced loan (compounded m times per annum), a float;
- F: upfront closing fee for the new loan in dollars, a float;
- α: prepayment penalty rate on the remaining loan balance (a fraction between 0 and 1, e.g., 0.01 for 1%), a float.
Outputs:
- regular payment amount after grace period;
- remaining balance after duration n2;
- total interest saved over the remaining term;
- annualized net IRR.
Example:
If V = 10000000, m = 12, n1 = 3, n2 = 5, n3 = 20, r1 = 0.025, r2 = 0.018, F = 50000, and α = 0.01:
- Input Format (for Python, replace with your student ID in uppercase):
python3 D13922016_HW_1.py 10000000 12 3 5 20 0.025 0.018 50000 0.01
- Output Format (comma-separated):
60222.193744, 9031668.918858, 527518.711395, 0.243936
Please submit your source (and executable) code and a brief explanation text file (if the code is not written in Python, describe how to compile and run it) via Gradescope in NTU COOL before 08:00 AM (GMT+8) 2026 Oct 8. No late submissions will be accepted. Compress all files into a single zip file named ID_HW_i.zip, where ID is your student ID in uppercase and i is the homework number (e.g., D13922016_HW_1.zip). If the code is not written in Python, you may be asked to demonstrate your code to the TA.
Write a program to price a structured note and calculate its key financial metrics. Consider an investor who deposits a domestic principal amount D into a structured note that pays an enhanced coupon rate c (annualized) at maturity T. Let St denote the FX spot rate at time t, expressed as domestic currency per unit of foreign currency. At maturity T, the investor receives the guaranteed coupon payment D × c × T in the domestic currency. If the terminal FX spot rate ST ≥ X, the investor receives their full principal D back in domestic currency. If ST < X, the principal D is converted into foreign currency at the conversion strike rate X (yielding D / X units of foreign currency, worth (D / X) · ST in domestic terms). Your goal is to compute the fair value of the note at t = 0 (in domestic currency), the delta of the note with respect to the initial FX spot rate S0, the breakeven spot rate at maturity (ST* such that total terminal payout equals initial principal D).
Inputs:
- D: domestic principal amount, a float;
- T: time to maturity in years, a float;
- c: enhanced annual coupon rate, a float;
- S0: initial FX spot rate at t = 0, domestic per unit of foreign, a float;
- X: conversion strike exchange rate, a float;
- rd: domestic risk-free interest rate, a float;
- rf: foreign risk-free interest rate, a float;
- σ: FX spot volatility, a float.
Outputs:
- Fair value of the note in domestic currency;
- Delta with respect to S0;
- Breakeven spot rate ST* at maturity.
For Example, if D = 1000000, T = 1.0, c = 0.06, S0 = 32.0,
X = 31.5, rd = 0.015, rf = 0.005, σ = 0.12, the outputs are 1006065.998257, 13119.408633, 29.716981. Input Format (for Python codes, replace the student ID with uppercase): "python3 D13922016_HW_2.py 1000000 1.0 0.06 32.0 31.5 0.015 0.005 0.12". Output Format: "1006065.998257, 13119.408633, 29.716981". Please submit your source (and executable) code and a brief explanation text file (if the code is not written in Python, describe how to compile and run it) via Gradescope in NTU COOL before 08:00 AM (GMT+8) 2026 Nov 5. No late submissions will be accepted. Compress all files into a single zip file named ID_HW_i.zip, where ID is your student ID in uppercase and i is the homework number (e.g., D13922016_HW_2.zip). If the code is not written in Python, you may be asked to demonstrate your code to the TA.
