What is continuous compounding? How is it done?
What are equivalent rates?
Two rates are equivalent if applied to the same capital, for the same period of time, they give the same interest.
What is a spot rate?
Spot rate (=zero rate): rate of interest earned on an investment that provides payoff only at T
—> expressed using continuous compounding
What is a yield curve?
Yield curve: representation of relationship between zero rates and remaining time to T of zero-coupon debt securities
How are bonds priced?
Discount each cashflow (earned coupons, face value at T,…) at corresponding zero rate. = fair price of financial instruments
What is the bond yield?
Discount rate that, when applied to all cashflows, gives bond price equal to market price (search for a single discount rate equal to several zero rates) (=solve for r)
What is the par yield?
Coupon rate that causes the bond price to equal its face value (use initial zero rates, not bond yield)(=solve for c)
e.g.: with 4 semi-annual coupons:
What is bootstrapping?
Method for estimating the yield curve:
Compute each point of the yield curve as yield (zero rate) of a ZCB with corresponding T.
What are forward rates? how are they calculated?
What are criteria for calibration models for the yield curve (ECB)
Set by Nymand-Andersen (2018):
- Flexibility & goodness of fit
- Robustness
- Smoothness
—> Best method: Parsimonious functional forms, i.e. Svensson-Nelson-Siegel
(alternatives: Spline based or bootstrapping, both have risk to overfit)
Explain the SNS model
Svensson-Nelson-Siegel
Zero rates:
—> fit by minimizing quadratic difference between yields computed from curve and yields measured in the market
what rate should we use as risk-free rate for derivative pricing?
Treasury rate (considered artificially low)
Repo rates (based on repurchase agreements) (agreement where a financial institution that owns securities agrees to sell them for X and buy them back in the future (usually the next day) for a slightly higher price, Y)
EURIBOR (rate at which AA-Bank estimates it can borrow money on unsecured basis from other bank at 11am) (LIBOR discontinued Dec. 2021)
Overnight rates (unsecured borrowing & lending between banks, computed on previous day activity)
What are derivatives? What are they used for?
Instrument whose value depends on, or is derived from value of another asset.
Uses: Hedging risk, speculation, lock in arbitrage, change nature of investment/liability
How are derivatives traded?
Exchanges, OTC markets
before 2008 largely unregulated, since then regulated to reduce systemic risk, increase transparancy
What are interest rate contracts?
= majority of global derivative market; mostly interest rate swaps & forward rate agreements
What are forward rate agreements?
Exchange at time T the difference between a fixed rate defined in T (forward rate) and a variable rate (settlement rate) given at time T, based on notional value (fictional value, never actually exchanged
Seller makes payment based on variable rate, earns fixed rate
Buyer other way round
—> Buyers will always realize forward rate
How are FRAs valuated?
Present value of difference between forward rate agreed on in FRA and current EURIBOR rate calculated today (assuming that EURIBOR rate is certain to be realized)
What are interest rate swaps?
= “Portfolio of FRAs” with different maturities à fixed & floating reference rates, regular interest exchange
How are interest rate swaps valuated?
Initially worth close to zero
Later, valuated as portfolio of FRAs
Procedure: calculate floating forward rates; based on this, calculate cash flows; discount swaps
Last changeda year ago
