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Funding Liquidity Risk Advanced Methods of Risk Management Umberto Cherubini. In this lecture you will learn To evaluate and hedge funding liquidity risk To understand concepts, measures and effects of market liquidity risk. Learning Objectives.
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Advanced Methods of Risk Management
Funding liquidity risk: you must come up with funding for your assets, but the market is dry. Solutions: i) chase retail investors ii) rely on quantitative easing (won’t last long)
Market liquidity risk: you are forced to unwind positions in periods of market stress, and you may not be able to find counterparts for the deal, unless at deep discount. Solution: quantitative easing (place illiquid bonds as collateral)The credit crisis and liquidity risk
Cash flow immunization would call for maturity matching. Assets should be have the same repricing period of liability, or, deposits should be hedged by being rolled over at the short term rate.Classical immunization: flows
Immunization against parallel shifts
Reddington: keep an eye on convexity
Immunization against parallel shifts
Convexity of liabilities lower than that of assets
Fong – Vasicek: the kind of shift matters
Immunization against whatever shift
Lower bound to losses positive or negative given convexity of the shiftClassical immunization: value
Value-at-Risk is a matter of (i) time and (ii) chance. It may be traced back to the system of margins in derivatives markets.
Stress-testing is a matter of information. We evaluate the effect of a set of scenarios on a portfolio and the amount of capital.
Notice: ALM and risk management have in common scenarios. Integration of the two (that we call interest rate risk management requires to work on this intersection)IRRM = ALM risk management
Jarrow and Van Deventer (1998) devised a model with stochastic interest rates, market segmentation and limited competition among banks, so that the interest rate spread between the risk free rate and the rate of deposits was allowed to be positive.
In this case the present value of the spread adds to the value of deposits, and may be read as the net present value of a swap contract. In this case hedging would require shorting this swap, and perfect mathching would not work.Hedging by swaps
Swaptions. One could conceive contingent hedging, triggered by market conditions, in which case one should resort to receiver swaptions (put options on swaps)Extensions
Basis risk. An extension that seems mandatory in face of the recent banking crisis is to allow for other elements determining the wedge between risk free rates and rates on deposits. Following the same line of Jarrow and Van Deventer model one should include other market variables, first of all an indicator of the credit worthiness of the banking system as a whole.
A possible financial engineering could be buying insurance against the increase in CDS spread in the banking system, or making the swap contract “hybrid”.Basis risk
The problem is to model: i) the distribution of demand deposit in each period of time; ii) the dependence structure between the amount of deposits and interest rates.
In a sense, it is the old problem of liquidity trading vs informed trading.Quantity risk
Reduced form models: these models should be based on statistical regularities observed on the distribution and the dynamics of the aggregate demand deposits.
Notice. This distinction is new, but is motivated by the similarity between quantity risk and credit riskModelling deposit demand
Each individual demands transaction balances and demand deposits as a function of:
i) income dynamics
ii) a target deposits/income ratio
The key point is that the target ratio is a function of the difference between the deposit rate and a reservation (strike) price.
Aggregation is obtained by averaging income dynamics and dispersion around average behavior is modelled by selecting a distribution function of the strikes.Structural models Example from the literature
In the evaluation of this policy, the bank relies on a behavioral model according to which:
the customer decision to sell and buy the bond is triggered by the difference between the current spreads prevailing on the banking system and the original spread (a real option model, like that of Nystrom)
customers are assumed to be sluggish to move in and out, because of irrational exercize behavior or monitoring costs. This is modelled by multiplying the spread difference times a participation rate lower than one.Structural models Example from the industry
Linear/log-linear relationship with the interest rate dynamics
What is missing: would be interesting to include a liquidity crisis scenario using the same technology applied by Cetin, Jarrow Protter (2004) to market liquidity risk.Reduced form models
Copula functions could provide:
Flexible specification of the marginal distributions of deposits and interest rates
Flexible representation of the dependence structure between deposits demand and interest rates
Flexible representation of deposits dynamicsA copula based proposal
Possible specifications are Vasicek model (gaussian dependence) or Schonbucher (Archimedean dependence)
These specifications would yield the probability law of the deposit income ratio that could be used as the marginal distribution for deposits.
The dynamics would be finally recovered by applying the dynamics of income to the ratio.
Notice: this is conjecture. Everything should be proved in a model built on micro-foundations, and probably different specifications would come outA copula-based structural model
Notice. The conditional distribution of deposit volumes is the partial derivative of the copula function.
Specify the marginal distribution of deposit volumes (the structural model above or a non parametric representation).
Specify the marginal distribution of interest rates: the distribution may be defined on the basis of historical data and/or scenarios (we suggest a bayesian approach).A copula based algorithm
The curve of the obligor is v(t0,ti)
In every period, the obligors receives net cash flows Si, and it pays interest rates on debt Ri = 1/v(ti,ti+1) – 1.
The difference between Ri Di –1 and Si increases or decreases the amount of debt Di.A liquidity model
Difficult to compare prices on different markets (best execution)
Illiquid markets reduce transparency of prices
Illiquid markets Noisy information
Slippage: difference btw execution cost of a deal and bid-ask average (mid price). Takes into account dimension. Bigger orders “eat” a bigger share of the order book.
Resiliency: time needed to reconstruct the book once that a big order has eaten part of it
Market liquidity measures
Under the new accounting standard, banks are required to evaluate at fair value the trading book. So every time that losses are marked-to-market, they are deducted from the economic balance.
The new regulation requires that capital is allocated against wrong valuation of the trading book. The difference between fair value and conservative valuation is called AVA (additional valuation adjustment) and capital is allocated to hedge this evaluation risk.Prudent valuation and AVA