Financial Derivatives: A hedging tool 6/21/12

Transcription

1 Financial Derivatives: A hedging tool 6/21/12

2 Agenda We will explore 4 types of OTC and Exchange trades Point-to-point / Call Spread Digital / Binary Long-dated put Variance Swap / Variance Future For each trade, we will examine the following components OTC vs. CBOE terminology Notional vs. Contract size OTC vs. CBOE Trading Processes Execution Costs Collateral / Margin Valuations The Options Clearing Corp.

3 Point-to-Point / Call Spread

4 Point-to-Point / Call Spread Terms CBOE refers to a point-to-point trade as a call spread In both OTC and at CBOE: Strikes can be expressed as either a percentage of the underlying or as a fixed dollar amount European or American style exercise Any strike price going out two decimal places Any expiration date going out 15 years CBOE trades options on all major U.S. indices, ETFs, and individual equities 1/1/01

5 Point-to-Point / Call Spread Size OTC Size: notional amount (e.g. $25 million SPX) CBOE Size: contracts $25 million SPX notional is contracts $25,000,000 / 1300 (index level) / 100 (contract multiplier) Cannot trade fractional contracts Mini-SPX (1/10 th size) can be used for the residual 0.3 ($39,000) $39,000 / 130 (index level) / 100 (contract multiplier) = 3 mini contracts 192 big options + 3 mini options = $25 million notional

6 Point-to-Point / Call Spread Trading Process OTC Insurer asks various dealers for a market CBOE LP1 LP2 LP3 OTC DEALER A OTC DEALER B OTC DEALER C FLEX BROKER LP4 LP5 LP6 CBOE has conducted several OTC vs. FLEX price tests. FLEX has consistently shown significantly better markets. LP8 LP7 LP9 LP10

7 Point-to-Point / Call Spread Trading Process (CFLEX)

8 Point-to-Point / Call Spread Execution Costs OTC Broker commissions embedded in dealer s offer Ticket charges may accompany smaller trades E.g. $25 million notional 1-year SPX 100% / 106% call spread offered at 2.88% Dealer commission ~2 bps $5,000 execution cost Paid $37.44 for the spread (SPX = 1300) Listed Effective Spread Price [(spread $ price)x100x # of spreads] + execution costs (contracts x 100) Savings (OTC $ spread price effective listed $ spread price) x 100 x # of spreads traded CBOE Broker commissions are explicit No ticket charges E.g. $25 million notional 1-year SPX 100% / 106% call spread offered at 2.85% 192 contracts per side (384 total) Executing broker charges ~$2.00 per contract $768 execution costs CBOE exchange fees included (CBOE SPX customer exchange fees = $0.44 per contract) Effective price = $37.09 for the spread (including exchange fees and broker commissions) Savings of $6,720 p.1

9 Point-to-Point / Call Spread Collateral / Margin OTC Traded with ISDA agreements Collateral terms vary Negotiated CBOE Traded in an optionsapproved securities account Example if transacted in portfolio margin account (not Reg T) 100% / 106% 1-yr. call spread ($78 spread /1378) Requirement is ~$1,300 per spread ~17% of the maximum gain of the spread ~1% of the notional value of the contract Government securities can be posted at OCC to satisfy this requirement

10 Point-to-Point / Call Spread Valuations OTC Daily marks generally provided by executing dealer FASB 157 Level 2 CBOE Daily marks provided by Options Clearing Corporation FASB 157 Level 2 OCC marks: pps/flex-reports OCC valuation methodology (interpolation from the listed vol surface): onal/pdf/occflexvolatility methodology.pdf

11 Point-to-Point / Call Spread The Options Clearing Corp. OCC is AA-rated They act as the buyer to every seller and the seller to every buyer OCC manages the cash flows from trade date until expiration Netting effect allows market participants to exit trades with any willing counterparty April 2011: Insurer A +500 Call Spreads from Market Maker B OCC stands in between Insurer A and Market Maker B (manages all cash flows) July 2011: Insurer A sells 500 Call Spreads to Market Maker C OCC stands in between Insurer A and Market Maker C Open interest: Insurer A has closed. Market Maker B faces Market Maker C, with OCC in the middle

12 Digital / Binary Option

13 Digital / Binary Terms OTC OTC market participants refer to an option with a fixed payout as Digital CBOE CBOE refers to an option with a fixed payout as Binary CBOE lists binary options on SPX and VIX Both are eligible for FLEX trading

14 Digital / Binary Size Size: notional OTC E.g. insurer guarantees to pay 3% if SPX settles 3% or higher one year from today s close Exposure = $10 million SPX = 1300 Digital strike = 1339, i.e. a 103% digital call option Size: contracts CBOE Same example as OTC (pay 3% if equal to or above 1339) Buy 3,000 call contracts of CBOE SPX binaries struck at (or 103%) expiring 1-year from today CBOE binaries pay $100 if ITM

15 Digital / Binary Trading Process

16 Digital / Binary Execution Costs OTC Broker commissions embedded in dealer s offer Ticket charges may accompany smaller trades SPX today = 1300; strike = 1339; payout = 3%; notional = $10 million Dealer offers digital call at 1.58% of notional ($158,000) 5 bps embedded broker commission ($5,000) Equivalent listed execution price is $ (1.58%/3.0%) Listed Effective Binary Price [(binary $ price) x 100 x contracts] + execution costs (contracts x 100) Savings (OTC $ digital price effective listed binary price) x 100 x # of contracts traded CBOE Broker commissions are explicit No ticket charges Same trade details as OTC CBOE FLEX liquidity providers offer the option at $0.50 per contract Buy 3,000 contracts Pay $150,000 ($0.50 x 100 contract multiplier x 3,000 contracts) Position will pay $300,000 (3% of notional) if SPX settles equal to or higher than 1339 Executing broker charges $2.00 per contract ($6,000) Effective execution price is $0.52 (broker and exchange fees included) Savings = $1,980 p.1

17 Digital / Binary Collateral / Margin OTC Traded with ISDA agreements Collateral terms vary Not uncommon for insurers to pay the entire premium ($158,000) CBOE Traded in an options-approved securities account Transacted in portfolio margin account (not Reg T) Portfolio margin requirement ~$105,000 (70% of premium) OCC handles all of the cash flows during the life of the contract OCC provides daily valuations OCC accepts government securities to fulfill margin requirement

18 Long-dated Put Option

19 Long-dated Put Size OTC Size: notional amount (e.g. $25 million SPX) CBOE Size: contracts $25 million SPX notional is contracts $25,000,000 / 1300 (index level) / 100 (contract multiplier) Cannot trade fractional contracts Mini-SPX(XSP, 1/10 th size) can be used for the residual 0.3 ($39,000) $39,000 / 130 (index level) / 100 (contract multiplier) = 3 mini contracts 192 big options + 3 mini options = $25 million notional

20 Long-dated Put Trading Process OTC CBOE Insurer asks various dealers for a market LP1 LP2 LP3 OTC DEALER A OTC DEALER B OTC DEALER C FLEX BROKER LP4 LP5 LP6 LP7 LP8 LP9 LP10

21 Long-dated Put Trading Process (CFLEX)

22 Long-dated Put Execution Costs OTC Broker commissions embedded in dealer s offer Ticket charges may accompany smaller trades E.g. $10 million notional 5-year SPX 100% put offered at 18.00% Dealer commission ~2 bps $2,000 execution cost Paid $ for the put (SPX = 1300) Listed Effective Put Price [(outright put price) x 100] + total execution costs Savings 100 (OTC put $ price effective listed put $ price) x 100 x # of contracts traded CBOE Broker commissions are explicit No ticket charges E.g. $10 million notional 5-year SPX 100% put offered at 17.80% 77 contracts Executing broker charges ~$2.00 per contract $154 execution costs CBOE exchange fees included (CBOE SPX customer exchange fees = $0.44 per contract) Effective price for the put is $ (including exchange fees and broker commissions) Savings of $8,162

23 Long-dated Put Collateral / Margin OTC Traded with ISDA agreements Collateral terms vary Negotiated CBOE Traded in an optionsapproved securities account Example if transacted in portfolio margin account (not Reg T) 5-yr. SPX put Requirement is ~$2,500 per contract ~2% of the notional value of the contract Government securities can be posted at OCC to satisfy this requirement

24 Long-dated Put Valuations OTC Daily marks generally provided by executing dealer FASB 157 Level 2 CBOE Daily marks provided by Options Clearing Corporation FASB 157 Level 2 OCC marks: pps/flex-reports OCC valuation methodology (interpolation from the listed vol surface): onal/pdf/occflexvolatility methodology.pdf

25 Variance Swaps / Variance Futures σ²

26 Variance Swaps/Variance Futures Terms OTC CBOE Futures Exchange RealizedVariance = RealizedVariance = 252 * S Ln(P i /P i-1 ) 2 /(N-1) 252 * S Ln(P i /P i-1 ) 2 /(N-1) There may be slight variations in the definitions between a typical OTC Variance Swap and the exchange traded Variance Future, such as disruption event definitions, but the instruments are virtually the same in payout and vega exposure

27 Variance Swaps/Variance Futures Terms OTC OTC variance swaps are quoted in volatility. E.g % CBOE Futures Exchange 3-month Variance Futures Quoted in variance points: e.g Front-month and forward starting contracts can be stripped together to create longer dated spot or forward starting exposures. Using the quoted price in variance points and the realized variance accrued-to-date (disseminated on Bloomberg as RUG), one can back out implied variance and convert to implied volatility. (Quoted Price * Expected days) (Realized Accrued * Realized days) = Implied Volatility Remaining days ( * 64) ( * 39) = 19.46% 25

28 Variance Swaps/Variance Futures Size OTC OTC variance swaps are sized in vega notional. E.g. $250,000 per point CBOE Futures Exchange 3-month Variance Futures Sized in number of contracts Contract multiplier is $50. No. Expected Days 64 No. Realized Days 39 No. Remaining Days 25 Variance Notional of one contract = $50 * (25/64) = $19.53 Vega Notional of one contract = 2 * * $19.53 = $ For $250,000 Vega exposure: 250,000 / = = ~329 contracts CFE website provides a calculator to make the conversions:

29 Calculation Variance Futures are cleared in Variance Points 20^2 = 400 Variance is quoted in Volatility 20 Size is often quoted in Vega Notional $50 * 2 * 20 = 2000

30 Variance Swaps/Variance Futures Collateral / Margin OTC Traded with ISDA agreements Collateral terms vary Between 2 and 5 times vega notional. CBOE Traded in a futures account Margin telescopes through time and varies depending on the prevailing level of volatility. OCC handles all of the cash flows during the life of the contract OCC provides daily valuations OCC accepts government securities to fulfill margin requirement

31 Other Instruments to consider Et Cetera

32 Other FLEX options CBOE One tenth SPX = XSP One tenth NDX = MNX 1/100 of DJIA = DJX FLEX All are eligible for FLEX All are centrally cleared All are priced daily S&P500 dividends = DVX

33 John Wiesner CBOE Risk Management Strategist (312) Matt McFarland CBOE Business Development (312) Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of Characteristics and Risks of Standardized Options. Copies are available from your broker, by calling OPTIONS, or from The Options Clearing Corporation, One North Wacker Drive, Suite 500, Chicago, Illinois The information in this presentation is provided solely for general education and information purposes and therefore should not be considered complete, precise, or current. Many of the matters discussed are subject to detailed rules, regulations, and statutory provisions which should be referred to for additional detail and are subject to changes that may not be reflected in the information. In order to simplify the computations, commissions, fees, margin interest and taxes have not been included. These costs will impact the outcome of all transactions and must be considered prior to entering into any transactions. Multiple leg strategies involve multiple commission charges. Investors should consult their tax advisor about any potential tax consequences. The information in this presentation, including any strategies discussed, is strictly for illustrative and educational purposes only and is not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities. Supporting documentation for any claims, comparisons, recommendations, statistics, or other technical data, will be supplied upon request. Trading FLEX options may not be suitable for all optionsqualified investors; the strategies discussed in this presentation should only be considered by investors with extensive prior options trading experience. CBOE, Chicago Board Options Exchange, CFE, CFLEX, FLEX, Flexible Exchange and VIX are registered trademarks and CBOE Futures Exchange, DJX, DVX, SPX and XSP are service marks of Chicago Board Options Exchange, Incorporated (CBOE). S&P and S&P 500 are registered trademarks of Standard & Poor s Financial Services, LLC and are licensed for use by CBOE. Copyright 2011 CBOE. All rights reserved.

34 De-risking VAs using Variance John Wiesner

35 What is Variance Variance, put simply, is the square of volatility Variance contracts are used by some insurers as a hedge against Gamma This presentation will include pricing of variance, and a simple example of its practical use For a detailed, technical explanation of Variance Futures, please see:

36 A formula Variance = s 2 A Variance contract pays out the annualized one day volatility, squared for each trading day that the contract exists. Annualized Volatility is (252 x x Ln(P i+1 /P i ) 2 ) 0.5 (where P is index or stock closing price, and assuming 252 trading days in one year, also the ln result is multiplied by 100, so that a 2% move is simply 2 rather than 0.02 ) From this we can see that a 1% move in the market is roughly a 15.8 Volatility sqrt(252) And the Annualized Variance of a 1% move would be 252

37 1 year Variance Future pays $50 The 1 year Variance future accrues, daily: $50 for ~ 1% move; (50 x 1 2 ) = $50 $200 for ~ 2% move; (50 x 2 2 ) = $200 $450 for ~ 3% move; (50 x 3 2 ) = $450 The move in the market can be either positive or negative. Up 2% or down 2%, the owner still accrues $200 (This is NOT necessarily your daily PnL. Much like bonds with accrued interested, the yield or price of the bond may change more or less than the accrued interest, so also the Variance contract can change independently of that day s realized volatility, based on changes in the expected future volatility)

38 The Sum of all the days The Variance contract will be worth all the days of payments simply added up VariancePayout = S Ln(P i+1 /P i ) 2 /(N-1) We start with i+1 because the first realized variance starts a day after i N i+1 VariancePayout is then multiplied by the Notional amount. One CFE contract has $50 notional.

39 The Sum of all the days So for the same expected volatility, a Variance future with twice as much time will have twice the value; four times the time, four times the value This is very useful for spreading, for building forward starting volatility, and for understanding theta The theoretical daily theta is exactly the same regardless of how much time there is to expiry (for the same implied volatility)

40 Vega Vega is generally considered the sensitivity of any instrument (such as an option or a VA product) to the change in future implied volatility. Variance contracts are no exception. Quite the opposite in fact. At the beginning, the whole value of a Variance contract comes from future expected volatility Unlike theta though, Vega is NOT constant in Variance contracts. The more Volatility, all the more Vega

41 Vega VarianceVega = dvp/ds This is a very simple derivative VP = Notional x (daysremaining/252) x s 2 VP = $50 x (daysremaining/252) x s 2 So dvp/ds = 2 x 50 x (daysremaining/252) x s So at the beginning of a one year contract Vega = 2 x 50 x (252/252) x s = 100 x s e.g., s = yields 1579 Vega

42 Implied Forward Volatility Implied Forward Starting Volatility can be inferred from over lapping Variance contracts. Since Variance is additive the difference between two contracts would give the no arbitrage price of the remaining period Realized today Expiry Expiry Unrealized Value----- Realized Unrealized Value Unknown Value-

43 Implied Forward Volatility Solving for forward starting Volatility in this method, is solving for the implied Value of a forward starting variance contract, and then solving for the implied volatility. Let A = Unrealized Value of the first contract; T A = remaining time of contract A Let C = Unrealized Value of the second contract; T C = remaining time of contract C Let B = Unknown Value of the forward starting period; T B = time period in question of contract B Realized today Expiry Expiry Unrealized Value----- Realized Unrealized Value Unknown Value-

44 Implied Forward Volatility 252(C A) notional x T B Let A = Unrealized Value of the first contract; T A = remaining time of contract A Let C = Unrealized Value of the second contract; T C = remaining time of contract C Let B = Unknown Value of the forward starting period; T B = remaining time of contract B T B = T C - T A Realized today Expiry Expiry Unrealized Value----- Realized Unrealized Value Unknown Value-

45 Another method Solving for forward starting Volatility is essentially the same as solving for one side of a right triangle using the Pythagorean Theorem. Let s A = Implied Volatility of the first contract; T A = remaining time of contract A Let s C = Implied Volatility of the second contract; T C = remaining time of contract C Let s B = Implied Volatility of the forward starting period; T B = remaining time of contract B Realized today Expiry Expiry Unrealized Value----- Realized Unrealized Value Unknown Value-

46 Another method T A (s A ) 2 + T B (s B ) 2 = T C (s C ) 2 Let s A = Implied Volatility of the first contract; T A = remaining time of contract A s B = T C (s C ) 2 - T A (s A ) 2 T B Let s C = Implied Volatility of the second contract; T C = remaining time of contract C Let s B = Implied Volatility of the forward starting period; T B = remaining time of contract B Realized today Expiry Expiry Unrealized Value----- Realized Unrealized Value Unknown Value-

47 Using Variance for Gamma One huge advantage of Variance is the fact that the Gamma coverage is constant, day in, day out, across the life of the contract. There is no decay of the coverage There is no stock based price strike This is very useful if the portfolio being replicated has homogenous Gamma exposure along many different price points, and if the Gamma of the portfolio does not display considerable decay of Gamma over time

48 Using Variance for Gamma A good example of this may be a large block of Variable Annuities For VA s the strike is not exactly known, as the ratchets and longevity in the future make the determination of the strike more difficult Stochastic processes that generate the greeks for the portfolio may very well generate a Gamma for the portfolio without indentifying optimal strikes for a hedge

49 Using Variance for Gamma If the long-dated Liability model generates a gamma for the portfolio that is fairly constant across both time (say the next year) and across price shocks, then a Variance contract may be a suitable tool to mitigate risk. How would you use it?

50 Delta replication and Variance An example: For this study we took the sum of the gamma from each of the following options year Puts, struck equally spaced from 20% OTM to 20%ITM 41 15year Puts with the same strikes 41 20year Puts again with the same strikes; all with the same 18.5 volatility. The notional amounts for each of those years is, $10BB for the 10 year $7BB for the 15year $3BB for the 20year to provide some flavor of mortality The result was 1,188,149 negative Gamma (in percentage terms) for this VA block proxy

51 Delta replication and Variance How much Variance do we need to buy to cover 1.2 million Gamma? Delta will change by 1.2 million for a 1% move in the market, so a Delta neutral position should lose circa 1/2 of $1.2 million, as the average Delta will be about 600,000 across the move So we need Variance that will accrue $600,000 for a 1% move.

52 Delta replication and Variance Variance futures accrue $50 per 1% move, so for $600,000 coverage we need 12,000 contracts. What if the market moves 3.5% one day? 1.2 million Gamma would change Delta by 3.5 x 1.2 million or 4.2 million, so the average Delta across the move would be 2.1 Million. 2.1MM Deltas x 3.5 move = $7.35 million loss What do 12,000 Variance Futures pay on that day? 12,000 x $50 x (3.5) 2 = $7.35 million gain

53 Delta replication and Variance Next, we did 1000 scenarios of possible market outcomes a year later, took an 3% lapse assumption and re-evaluated the Gamma of the proxy portfolio as 9year, 14year, and 19year options. The resulting total was 1,249,653 negative Gamma The Gamma increased a little over the year, as we expect with time decay of near-the-money options, but not a lot. Partly due to the long tenor of the options, but also due to the decrements The main point is that 12,000 Variance Futures would cover the expected Gamma across one whole year fairly well. It is rare that replicating portfolios do NOT need adjustment, but the less adjustment needed, the less basis risk and transaction cost there will be

54 When to adjust the Delta If the Variance contract (OTC or exchange traded) is predicated on daily variance payments, the Delta rebalancing should likewise be daily. More frequent or less frequent rebalancing exposes the portfolio to undue basis risk.

55 When to adjust the Delta Gamma; constant -10 emini, $50 per point Daily Rebalance Mkt Cls Prc Delta Liability CumFutures OneGreek Variance CumVar Portfolio Friday 1000 Future action 0 PnL PnL PnL Payout Payout PnL Monday Tuesday (500.00) 0.00 (500.00) Wednesday (1,280.00) (680.00) Thursday (500.00) (300.00) (800.00) Friday (12,500.00) 3, (8,800.00) 8, , Monday (10,125.00) 1, (8,925.00) , Tuesday (8,000.00) (1,050.00) (9,050.00) , Wednesday (6,125.00) (3,050.00) (9,175.00) , Thursday (4,500.00) (4,800.00) (9,300.00) , Friday (1,805.00) (8,100.00) (9,905.00) , Weekly Rebalance Mkt Cls Prc Liability Futures OneGreek Variance CumVar Portfolio Friday 1000 Future action PnL PnL PnL Payout Payout PnL Monday Tuesday (500.00) 0.00 (500.00) Wednesday (1,280.00) 0.00 (1,280.00) (590.18) Thursday (500.00) 0.00 (500.00) Friday (12,500.00) 0.00 (12,500.00) 8, , (3,120.50) Monday (10,125.00) (2,500.00) (12,625.00) , (3,107.72) Tuesday (8,000.00) (5,000.00) (13,000.00) , (3,346.38) Wednesday (6,125.00) (7,500.00) (13,625.00) , (3,836.44) Thursday (4,500.00) (10,000.00) (14,500.00) , (4,577.91) Friday (1,805.00) (15,500.00) (17,305.00) , (6,747.12)

56 Another example, quiet market Gamma; constant -10 emini, $50 per point Daily Rebalance Mkt Cls Prc Delta Liability CumFutures OneGreek Variance CumVar Portfolio Friday 1000 Future action 0 PnL PnL PnL Payout Payout PnL Monday Tuesday (500.00) 0.00 (500.00) Wednesday (1,280.00) (680.00) Thursday (500.00) (300.00) (800.00) Friday (125.00) (800.00) (925.00) , Monday (125.00) (1,300.00) (1,425.00) , Tuesday (500.00) (1,050.00) (1,550.00) , Wednesday (1,125.00) (550.00) (1,675.00) , Thursday (80.00) (2,200.00) (2,280.00) , Friday (2,400.00) (2,400.00) , Weekly Rebalance Mkt Cls Prc Liability Futures OneGreek Variance CumVar Portfolio Friday 1000 Future action PnL PnL PnL Payout Payout PnL Monday Tuesday (500.00) 0.00 (500.00) Wednesday (1,280.00) 0.00 (1,280.00) (590.18) Thursday (500.00) 0.00 (500.00) Friday (125.00) 0.00 (125.00) , Monday (125.00) (500.00) (625.00) , Tuesday (500.00) (750.00) (1,250.00) , Wednesday (1,125.00) (1,000.00) (2,125.00) , (378.42) Thursday (80.00) (450.00) (530.00) , , Friday (250.00) (250.00) , ,169.94

57 Conclusion Variance contract pricing can be used to infer implied forward starting volatility Long dated Insurance Liabilities may benefit from using variance over actual puts if the Strikes are harder to determine than gamma If a liability is being dynamically replicated by futures and variance, the rebalancing period should be equal to the variance time sub-period

58 John Wiesner CBOE Risk Management Strategist (312) Michael Mollet CBOE Futures Exchange (312) Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of Characteristics and Risks of Standardized Options (ODD). Copies of the ODD are available from your broker, by calling OPTIONS, or from The Options Clearing Corporation, One North Wacker Drive, Suite 500, Chicago, Illinois The information in this presentation is provided solely for general education and information purposes and therefore should not be considered complete, precise, or current. Many of the matters discussed are subject to detailed rules, regulations, and statutory provisions which should be referred to for additional detail and are subject to changes that may not be reflected in the information. In order to simplify the computations, commissions, fees, margin interest and taxes have not been included. These costs will impact the outcome of all transactions and must be considered prior to entering into any transactions. Multiple leg strategies involve multiple commission charges. Investors should consult their tax advisor about any potential tax consequences. The information in this presentation, including any strategies discussed, is strictly for illustrative and educational purposes only and is not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities. Trading FLEX options may not be suitable for all options-qualified investors; the strategies discussed in this presentations should only be considered by investors with extensive prior options trading experience. CBOE, Chicago Board Options Exchange, FLEX and Flexible Exchange are registered trademarks and SPX and XSP are servicemarks of Chicago Board Options Exchange, Incorporated (CBOE). Copyright 2011 CBOE. All rights reserved.