Fixed Income Zvi Wiener 02-588-3049 Fixed Income 6.

Fixed Income Zvi Wiener 02-588-3049 http://www.tfii.org Fixed Income 6

http://www.tfii.org FI - 6 slide 2 IR derivatives Forward and Futures Options Caps, Floors Swaps Structured notes Hedging Mathematical models

http://www.tfii.org FI - 6 slide 3 Interest rate futures Legal agreement settlement, delivery date quantity and quality of deliverable asset futures price (it is NOT a price!) long and short positions margin requirements

http://www.tfii.org FI - 6 slide 4 Margin requirements Initial margin Maintenance margin - margin call trigger Variation margin - after a margin call Mark to market procedure reduces counterparty risk!

http://www.tfii.org FI - 6 slide 5 Marking to Market Your balance time Initial margin Maint. margin margin call

http://www.tfii.org FI - 6 slide 6 Futures Contract T-Bills T-Notes T-Bonds notional is typically $100,000 deliverable bond is unknown, CTD option timing option (during the delivery month) wild card option

http://www.tfii.org FI - 6 slide 7 Options This type of contract is an obligation of one side only, but it requires a payment to purchase the right to choose.

http://www.tfii.org FI - 6 slide 8 Call Value before Expiration E. Call XUnderlying

http://www.tfii.org FI - 6 slide 9 Put Value before Expiration E. Put XUnderlying premium X

http://www.tfii.org FI - 6 slide 10 IR Options Call Put European American Bermudian Exotic: Asian, Digital, Knock-In, Knock-Out, path dependent and multiple asset options.

http://www.tfii.org FI - 6 slide 11 Various IR Options Futures options Caps Floors Exchange options Swaptions

http://www.tfii.org FI - 6 slide 12 Cap Is priced as a sequence of caplets time cap

http://www.tfii.org FI - 6 slide 13 Floor time floor

http://www.tfii.org FI - 6 slide 14 Collar time floor cap

http://www.tfii.org FI - 6 slide 15 Option pricing Time value, intrinsic value underlying time to maturity interest rates strike coupons volatility

http://www.tfii.org FI - 6 slide 16 Swaps Currency swap Interest rate swap Amortizing swap Swaption

http://www.tfii.org FI - 6 slide 17 Currency swap

http://www.tfii.org FI - 6 slide 18 Currency Swap 3Y3Y3Y3Y3Y3Y 100Y $5$5$5$5$5$5 $130

http://www.tfii.org FI - 6 slide 19 IR swap

http://www.tfii.org FI - 6 slide 20 IR Swap 333333333333 100 L+1L+1L+1L+1L+1L+1 100

http://www.tfii.org FI - 6 slide 21 IR Swap L+1L+1L+1L+1L+1L+1 100 111111111111 + a regular LIBOR loan for one year!

http://www.tfii.org FI - 6 slide 22 Term Structure Models Binomial trees Short-term based analytical models LIBOR based analytical models Multi-factor models Simulations

http://www.tfii.org FI - 6 slide 23 Binomial Trees 6% 6.5% 5.5% 7% 6% 5% 7.5% 6.5% 5.5% 4.5%

http://www.tfii.org FI - 6 slide 24 6% 6.5% 5.5% 7% 6% 5% 7.5% 6.5% 5.5% 4.5% 83.97 88.2 89.8 93 94 95 100 Interest rates Bond prices

http://www.tfii.org FI - 6 slide 25 Typical yield curves time to maturity yield increasing decreasing humped

http://www.tfii.org FI - 6 slide 26 Analytic Term Structure Models

http://www.tfii.org FI - 6 slide 27 Analytic Term Structure Models Hull, White Black-Karasinsky Black-Derman-Toy Heath-Jarrow-Morton Affine TS modles Gaussian models

http://www.tfii.org FI - 6 slide 28 Arithmetic BM dX =  dt +  dW   time X

http://www.tfii.org FI - 6 slide 29 Geometric BM dX =  Xdt +  XdW time X

http://www.tfii.org FI - 6 slide 30 Mean Reverting Process dX =  (  -X)dt +  X  dW time X 

http://www.tfii.org FI - 6 slide 31 Ho and Lee Model Rates are normally distributed. All rates have the same variability. The model has an analytic solution.

http://www.tfii.org FI - 6 slide 32 Bond Prices under Ho and Lee Where

http://www.tfii.org FI - 6 slide 33 Option Prices under Ho and Lee A discount bond matures at s, a call option matures at T

http://www.tfii.org FI - 6 slide 34 Monte Carlo

http://www.tfii.org FI - 6 slide 35 Monte Carlo Simulation

http://www.tfii.org FI - 6 slide 36 Callable Bond Payoff Straight Debt Debt Callable Bond Value of the firm’s call option

http://www.tfii.org FI - 6 slide 37 Convertible Bond Payoff Stock Straight Bond Convertible Bond

http://www.tfii.org FI - 6 slide 38 Protective Put Payoff XUnderlying X Put Protective Put Stock

http://www.tfii.org FI - 6 slide 39 Covered Call Payoff X X Written Call Covered Call Stock

http://www.tfii.org FI - 6 slide 40 Straddle Payoff X X Straddle Call Put

Fixed Income Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html DAC

http://www.tfii.org FI - 6 slide 42 Life Insurance yearly contribution 10,000 NIS yearly risk premium 2,000 NIS first year agent’s commission 3,000 NIS promised accumulation rate 8,000 NIS/yr After the first payment there is a problem of insufficient funds. 8,000 NIS are promised (with all profits) and only 5,000 NIS arrived.

http://www.tfii.org FI - 6 slide 43 10,000 NIS Risk 2,000 NIS Client’s 8,000 NIS Agent 3,000 NIS insufficient funds if the client leaves insufficient profits

http://www.tfii.org FI - 6 slide 44 Risk measurement The reason to enter this transaction is because of the expected future profits. Assume that the program is for 15 years and the probability of leaving such a program is . Fees are – 0.6% of the portfolio value each year – 15% real profit participation

http://www.tfii.org FI - 6 slide 45 Obligations The most important question is what are the obligations? The Ministry of Finance should decide Transparent to a client Accounted as a loan

http://www.tfii.org FI - 6 slide 46 One year example Assume that the program is for one year only and there is no possibility to stop payments before the end. Initial payment P 0, fees lost L 0, fixed fee a% of the final value P 1, participation fee b% of real profits (we ignore real). Investment policy TA-25 (MAOF).

http://www.tfii.org FI - 6 slide 47 Liabilities (no actual loan) Assets (no actual loan)

http://www.tfii.org FI - 6 slide 48 Total=Assets-Liabilities Fair value

http://www.tfii.org FI - 6 slide 49 Liabilities (actual loan) Assets (actual loan)

http://www.tfii.org FI - 6 slide 50 Total=Assets-Liabilities (loan)

http://www.tfii.org FI - 6 slide 51 2 years liabilities (no actual loan) 2 years assets (no actual loan) In reality the situation is even better for the insurer, since profit participation fees once taken are never returned (path dependence).

http://www.tfii.org FI - 6 slide 52 2 years fair value, no loan

http://www.tfii.org FI - 6 slide 53 2 years liabilities (with a loan) 2 years assets (with a loan)

http://www.tfii.org FI - 6 slide 54 Stock index Profit No loan With a loan 10 years, L 0 =7%

http://www.tfii.org FI - 6 slide 55 Partial loan - portion q Theoretically q can be negative.

http://www.tfii.org FI - 6 slide 56 Mixed portfolio When the investment portfolio is a mix one should analyze it in a similar manner. Important: an option on a portfolio is less valuable than a portfolio of options. Another risk factor - leaving rate should be accounted for by taking actuarial tables as leaving rate.

http://www.tfii.org FI - 6 slide 57 Conclusions It is a reasonable risk management policy not to take a loan against DAC. Up to some optimal point it creates a useful hedge to other assets (call options and shares) of the firm. Intuitively DAC is good when the stock market performs badly and profit participation is valueless. DAC performs bad when the market performs well.

Fixed Income Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Risk Management

http://www.tfii.org FI - 6 slide 59 Qualitative Requirements An independent risk management unit Board of directors involvement Internal model as an integral part Internal controller and risk model Backtesting Stress test

http://www.tfii.org FI - 6 slide 60 Quantitative Requirements 99% confidence interval 10 business days horizon At least one year of historic data Data base revised at least every quarter All types of risk exposure Derivatives

http://www.tfii.org FI - 6 slide 61 Types of Assets and Risks Real projects - cashflow versus financing Fixed Income Optionality Credit exposure Legal, operational, authorities

http://www.tfii.org FI - 6 slide 62 Risk Factors There are many bonds, stocks and currencies. The idea is to choose a small set of relevant economic factors and to map everything on these factors. Exchange rates Interest rates (for each maturity and indexation) Spreads Stock indices

http://www.tfii.org FI - 6 slide 63 How to measure VaR Historical Simulations Variance-Covariance Monte Carlo Analytical Methods

http://www.tfii.org FI - 6 slide 64 Historical Simulations Fix current portfolio. Pretend that market changes are similar to those observed in the past. Calculate P&L (profit-loss). Find the lowest quantile.

http://www.tfii.org FI - 6 slide 65 Returns year 1% of worst cases

http://www.tfii.org FI - 6 slide 66 Profit/Loss VaR 1% VaR 1%

http://www.tfii.org FI - 6 slide 67

http://www.tfii.org FI - 6 slide 68

http://www.tfii.org FI - 6 slide 69 Variance Covariance Means and covariances of market factors Mean and standard deviation of the portfolio Delta or Delta-Gamma approximation VaR 1% =  P – 2.33  P Based on the normality assumption!

http://www.tfii.org FI - 6 slide 70  Variance-Covariance 2.33   -2.33  1%

http://www.tfii.org FI - 6 slide 71 Weights Since old observations can be less relevant, there is a technique that assigns decreasing weights to older observations. Typically the decrease is exponential. See RiskMetrics Technical Document for details.

http://www.tfii.org FI - 6 slide 72 Monte Carlo Distribution of market factors Simulation of a large number of events P&L for each scenario Order the results VaR = lowest quantile

http://www.tfii.org FI - 6 slide 73 Example Your portfolio consists of two positions. The first one is a zero coupon bond maturing in 1 year with current market value of $10M. The second one is a zero coupon bond maturing in 10 years with market value of $1M. Which position contributes more to the risk of the portfolio?

http://www.tfii.org FI - 6 slide 74 Real Projects Most daily returns are invisible. Proper financing should be based on risk exposure of each specific project. Note that accounting standards not always reflect financial risk properly.

http://www.tfii.org FI - 6 slide 75 Example You are going to invest in Japan. Take a loan in Yen. Financial statements will reflect your investment according to the exchange rate at the day of investment and your liability will be linked to yen. Actually there is no currency risk.

http://www.tfii.org FI - 6 slide 76 Airline company fuel - oil prices and $ purchasing airplanes - $ and Euro salaries - NIS, some $ tickets $ marketing - different currencies payments to airports for services

http://www.tfii.org FI - 6 slide 77 Airline company loans equity callable bonds

http://www.tfii.org FI - 6 slide 78 Airline company Base currency - by major stockholder. Time horizon - by time of possible price change. Earnings at risk, not value at risk, since there is too much optionality in setting prices. One can create a one year cashflow forecast and measure its sensitivity to different market events.

http://www.tfii.org FI - 6 slide 79 Reporting Division of VaR by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital).

http://www.tfii.org FI - 6 slide 80 How VaR is used Internal Risk Management Reporting Regulators

http://www.tfii.org FI - 6 slide 81 Backtesting Verification of Risk Management models. Comparison if the model’s forecast VaR with the actual outcome - P&L. Exception occurs when actual loss exceeds VaR. After exception - explanation and action.

http://www.tfii.org FI - 6 slide 82 Backtesting Green zone - up to 4 exceptions Yellow zone - 5-9 exceptions Red zone - 10 exceptions or more OK increasing k intervention

http://www.tfii.org FI - 6 slide 83 Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss?

http://www.tfii.org FI - 6 slide 84 Unifying Approach One number Based on Statistics Portfolio Theory Verification Widely Accepted Easy Comparison

http://www.tfii.org FI - 6 slide 85 Board of Directors (Basle, September 1998) periodic discussions with management concerning the effectiveness of the internal control system a timely review of evaluations of internal controls made by management, internal and external auditors periodic efforts to ensure that management has promptly followed up on recommendations and concerns expressed by auditors and supervisory authorities on internal control weaknesses a periodic review of the appropriateness of the bank’s strategy and risk limits.

http://www.tfii.org FI - 6 slide 86 pluto.mscc.huji.ac.il/~mswiener/ Useful Internet sites Regulators Insurance Companies Risk Management in SEC reports Risk Management resources

http://www.tfii.org FI - 6 slide 87 Risk Measuring Software CATS, CARMA Algorithmics, Risk Watch Infinity J.P. Morgan, FourFifteen FEA, Outlook Reuters, Sailfish Kamacura Bankers Trust, RAROC INSSINC, Orchestra

Fixed Income Zvi Wiener 02-588-3049 Fixed Income 6.

Similar presentations

Presentation on theme: "Fixed Income Zvi Wiener 02-588-3049 Fixed Income 6."— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Fixed Income Zvi Wiener 02-588-3049 Fixed Income 6.

Similar presentations

Presentation on theme: "Fixed Income Zvi Wiener 02-588-3049 Fixed Income 6."— Presentation transcript:

Similar presentations

About project

Feedback