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OMX Index Option Efficiency Test Empirical test of market efficiency of OMX options Supervisor : Professor Lennart Flood Authors : Aijun Hou Aránzazu Muñoz Luengo

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Agenda 1. Background 2. Theoretical Framework 3. Methodology and Data 4. Test of Market Efficiency 5. Conclusion and Recommendation

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1. Background 2. Theoretical Framework 3. Methodology and Data 4. Test of Market Efficiency 5. Conclusion and Recommendation

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History of Option Market Apr CBOE –First Option Traded 1983 CBOE –First Index Option Traded 1986 Stockholm Stock Exchange –OMX Index Traded Index options give market participants the ability to participate in anticipated market movements, without having to buy or sell a large number of securities, and they permit portfolio managers to limit downside risk (Ackert & Tian, 1999)

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Research Objective and Motivation Objective : Efficiency test of OMX option market Motivation : There is few paper examines OMX options Market

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Option Market Efficiency definition Or, there is capital constraints and arbitrageurs can not raise the capital necessary to form the risk-less hedging Or, there is capital constraints and arbitrageurs can not raise the capital necessary to form the risk-less hedging There is no arbitrage profit opportunities

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Three Hypothesis Lower Boundary Violation?? OMX Option Efficient Market ??? Put Call Parity Violation?? Abnormal Return on Dynamic Hedging Simulation??

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1. Background 2. Theoretical Framework 3. Methodology and Data 4. LB Test and PCP Test 5. Dynamic Hedging Simulation 6. Conclusion and Recommendation 1. Background 3. Methodology and Data 4. LB Test and PCP Test 5. Dynamic Hedging Simulation 6. Conclusion and Recommendation

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The Black Scholes Model Myron Scholes and Fischer Black, 1973 Replace Stock with Future F=Se rt Replace Stock with Future F=Se rt

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Volatility The relative rate at which the price of a security moves up and down A Measure of Risk

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Volatility Forecasting Methods –Historical Volatility (HSD) Annualized Moving Average of Daily Return –WISD (Weight Implied Volatility) Get Implied Volatility (IV) from the Market Price Weight Average IV according to its sensitivity towards price changing

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WISD Implied Volatility Smile: Solution: Weighting volatility across a number of options on the same underlying ( WISD)

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WISD (con.) Options more traded = More Market information To adjust options sensitivities to the volatility –High price sensitivity options to σ should be given more weight

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1. Background 2. Theoretical Framework 3. Methodology and Data 4. Test of Market Efficiency 5. Conclusion and Recommendation

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Methodology Lower Boundary Condition & Put Call Parity condition Dynamic Hedging Strategy Paired T-Test

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Data 1 st June th June 2004 OMX Index & Future Trading Date Time to maturity Ask Price Bid Price Close Price Volume Risk Free Interest Rate STIBOR Transaction Cost Trading and Clear fee Commission fee Bid Ask Spread Other cost Trading date Time to maturity Ask Price Bid Price Close Price Volume OMX Index Option

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Data Transformation

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1. Background 2. Theoretical Framework 3. Methodology and Data 4. Test of Market Efficiency 5. Conclusion and Recommendation 1. Background 2. Theoretical Framework 3. Methodology and Data 5. Conclusion and Recommendation 1. Background 2. Theoretical Framework 3. Methodology and Data

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Lower Boundary and Put Call Parity Tests

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Derivation of Lower Boundary Holding Equal Amount of Calls and Futures with Opposite Position Result Min. Profit (F-K)e -rt -C Holding Equal Amount of Puts and Futures with Opposite Position Result Min. Profit (K-F)e -rt -P IF (F-K)e -rt -C>0 Then Profit Ensured IF (K-F)e -rt -P>0 Then Profit Ensured C>= (F-K)e -rt P>= (K-F)e -rt

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Revised Lower Boundary Consider Transaction Cost Consider Ask Bid Spread

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Derivation of Put Call Parity It shows that the value of a EU call with a certain exercise price and exercise date can be deduced from the value of a EU put with the same exercise price and vice versa Long Hedge Short Hedge Without Bid Ask Spread With Bid Ask Spread

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Refine Data 0 or 0,01 ( Price & Volume) High Bid Ask Spread 360>T >0 Filter Data Transaction Cost Fee (Fixed) Commission (Assumption) TC0 TC1 TC2

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Empirical Results Violation Measured as : Frequency of Violation % = Number of Violations identified /Number of Observations Examined

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Dynamic Hedging Strategy Test

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Dynamic Hedging Test Design Filter Data Volati lity Forec ast Calcu late BS Modd el Price Market Price vs. Model Price Dyna mic Hedgi ng Simul ation Evalu ate NPV

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Dynamic hedging simulation Implementation Data filtration 0 ( Price & Volume) I(K-F)/K)I >10% High Bid Ask Spread T <7 or T>90 Liquidity & Non-synchronous problem

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Dynamic hedging simulation Implementation Volatility Forecasting HSD WISD u i = LN(Si/Si-1) n= 20

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Result from HSD

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Result from WISD WISD is in general higher than HSD When the underlying asset market is getting extremely volatile, the derivative market tends to moderate it.

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Standard deviation of HSD and WISD

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Result validity---Volatility Smile Left skew pattern Puts give higher volatility than calls

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Result ValidityTerm Structure Term structure shows a downward slop Consistent with Hull (2003) Short-dated volatilities are historical high

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Result validityStationarity

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Market price VS. Model price

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Result from Paired T-test

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Market Price vs. Model Price -Distribution of Price Differences

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Market Price vs. Model Price -Moneyness Composition of Price Differences

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Dynamic hedging simulation implementation Spot Mispricings Delta hedge ratio Simulate Dynamic hedging

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Spot mispricing (More than 15% difference )

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Result from Dynamic hedging

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Result from Dynamic Hedging Slight Positive NPV when little cost considered Slight Positive NPV when little cost considered Clearly Negative NPV when spread cost Considered Clearly Negative NPV when spread cost Considered

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Conclusion Little Lower Boundary Violation OMX Option Efficient Market ??? Little Put Call Parity Violation No Abnormal Return on Dynamic Hedging Simulation

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Recommendations Intraday data GARCH Commission cost

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Thank You!

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