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

Agenda 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 4. Test of Market Efficiency 5. Conclusion and Recommendation

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)

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

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

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

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

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

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

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

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

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

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

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

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

Data Transformation

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

Lower Boundary and Put Call Parity Tests

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

Revised Lower Boundary Consider Transaction Cost Consider Ask Bid Spread

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

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

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

Dynamic Hedging Strategy Test

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

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

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

Result from HSD

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.

Standard deviation of HSD and WISD

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

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

Result validityStationarity

Market price VS. Model price

Result from Paired T-test

Market Price vs. Model Price -Distribution of Price Differences

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

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

Spot mispricing (More than 15% difference )

Result from Dynamic hedging

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

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

Recommendations Intraday data GARCH Commission cost

Thank You!