Interest Rate Models, Study Notes Flashcards
For what variables should implied volatility change in an intuitive way
Change in strike and forward rates
Variation of maturities and tenors
Different types of instruments are analyzed
Compare three implied volatility models
Lognormal - objective
Displaced lognormal - stable
Absolute/Normal- stable, objective
- selected as optimal in the article because two pros
State some implications of the low interest rate environment for insurers
Value of guarantees will move when switching the implied volatility scheme
- base curve < swap curve means guarantee values will increase
Evaluating fit is easier under the normal methodology
Yield curve and implied volatility correlation becomes weakly positive (strongly negative in Black model)
Change in duration and convexity values
Easier to hedge portfolio
Alignment with what banks use
State the technical challenges of negative interest rates
Inability of spreadsheet functions to deal with negative inputs
Need to adapt mathematical models built for creating sensible sets of future scenarios
Questioning of model results
Increased difficulty in valuation and management entities
State the criteria to select interest rate models
Ability of the model to reproduce the ZCB curve
Ability to reproduce volatility surfaces and smiles
Ability to price out of calibration sample volatilities
Good balance for the number of parameters
Briefly compare risk neutral models
Normally distributed instantaneous rate models (1fHW, G2++) permit simulation of negative interest rates while exactly reproducing the ZCB curve
- 1fHW doesn’t have enough parameters, G2++ has trouble with OTM volatilities
Forward diffusion models (DD-LMM, LMM+) are often quite robust
- allow negative interest rates, fit initial ZCB curve, fit volatility smiles and surfaces
More complex CIR type models may also be used to shift instantaneous interest rates
- reproduce volatility smiles well
Real world models
- may not be as crucial for real world model to satisfy the martingale property
- may focus on time series or PCA approaches
- can have a model with low and high (2) interest rate regimes
State consequences of not modeling negative interest rates
Models that assume positive interest rates
- impossible to reproduce the actual spot rate curve
- underestimate cost of financial options and guarantees
- ESGs fail to work effectively for situations involving guaranteed rates in savings contracts
Models that have a 0% posteriori floor
- underestimate cost of financial options and guarantees
- martingality of economic scenarios will be broken
Define the physical lower bound
Opportunity cost if holding capital
Point at which the cost of keeping money in the bank is too high
Define the economic lower bound
Level below which further rate cuts cease to provide stimulus to the economy
More subjective than the physical lower bound
State explanations for low interest rates
Monetary Policy - stimulate the economy
Supply/Demand - aging demographic profiles increase the supply if savings and reduce the demand for borrowing
State impacts if low interest rates
Low Yields - monetary value of long term assets have risen
Wealth Redistribution - wealth shifts toward relatively wealthy individuals
Increase in LT Liabilities - long term guarantee values increase when interest rates decrease
Margin Squeeze - interest margin available to banks is squeezed and impacts bank profitability
Describe three desirable features of benchmark rates
Provide a robust and accurate representation of interest rates in core money markets that is not susceptible to manipulation
- should be derived from actual transactions in active and liquid markets
Offer a reference rate for financial contracts that extend beyond the money market
- will be useful for discounting and pricing cash instruments and interest rate derivatives
Serve as a benchmark for term lending and funding
- banks require a lending benchmark that behaves in a similar manner to the rates that are used for funding in order to minimize basis risk
Describe drawbacks if using LIBOR as a benchmark rate
LIBOR was constructed from a small set of banks reporting non-binding quotes rather than actual transactions
Sparse transaction activity in interbank deposit markets
- central bank policies left an abundant supply of reserves, so no need for overnight borrowing from other banks
Increased dispersion of individual bank credit risk has made it difficult for LIBOR to capture common bank risk
Banks have tilted their funding mix toward less risky sources of wholesale funding, such as repos
Describe characteristics of new RFR benchmarks
Focus on actual transactions of overnight rates on the most liquid segments of money markets
Add bank borrowing transactions from a range of non-bank wholesale counterparties
Incorporate secured transactions, such as bank repurchase agreements
Describe two methods of calculating term benchmark rates
Backward looking - constructed mechanically from past realizations of O/N rates
- computation after the realization of O/N rates is known at the end of the period
Forward looking - outcome of a market based price formation process, set at the beginning of the period to which the rate applies
- embeds market participants expectations about future interest rates and market conditions
