Price Discovery Under Different Market Conditions and Moneyness

7/31/2019 Price Discovery Under Different Market Conditions and Moneyness

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Price Discovery under Different Market

Conditions and Factors: A Study on IndianMarket

Rajesh Pathak

IBS, Hyderabad

Deepak AgrawalDenuoSource Knowledge Center, Hyderabad


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Introduction

This study is an attempt to find out whether informedtraders prefer derivatives (options) market and if yes,to what extent the trading activity from this market

affects the price of underlying

We account for various factor and market conditionse.g. bull vs. bear phase, moneyness, expiration weekeffect, which may affect the choice of a trader to

place his trade and subsequently can result theaberration in price discovery process.

We follow option trading value ratio model of Chen,Lung and Tay (2004) to examine the relationship

between options and underlying market.


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Analytical Framework

Let us say that for a trader at time 0, the cash outflowfor buying a call or put option will be as follows

For call option: Qc * Pc and for put option Qp * Pp

Where Qc (Qp) are call(put) trading volumes and Pc (Pp)are call (put) premiums. At expiry T, the intrinsic valueof these options will be Qc* (Su Xc) and Qp* (Xp Sd)

respectively, where S represents underlyings price andX represents stike price. Subscripts c and p differentiatecall and put options, whereas u and d indicate upwardand downward movements of prices with probabilities uand d


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With his or her expected utility and limited wealth W0,the objective and constraint function will be as follows

Maximize: u U (Qc* (Su Xc)) + d U (Qp* (Xp Sd))

Subject to: Qc * Pc + Qp * Pp = W0

Where U is the log utility function.

The Lagrange representation of this optimizationproblem will be

L = u log {U (Qc* (Su Xc))} + d log {U (Qp* (Xp

Sd))} (Qc * Pc + Qp * Pp - W0)Where is the Lagrange multiplier

Solution of the first order condition of equation (C) w.r.tto Qc and Qp suggests that market participant can inferthe relative magnitude of unobservable probabilities of

price changes by observing the ratio of options tradingvalues hereafter VR.


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To identify the cycles we plot daily index value againsttime and then based on the graph (figure 1) wesegregated it into three periods namely bull phase(January 2006-December 2007), bear phase (January2008- December 2008) and recovery phase (January

2009 to December 2009).


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To examine the place of information based trading westudied the lead lag relationship between indexreturns and VR for entire period, sub periods, andcondition based samples

We estimate the coefficients with the following model:


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VAR Results (entireperiod)


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VAR Results(Bear Phase)


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VAR Results(RecoveryPhase)


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VAR Results(expiry and exexpiry)


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Findings and Future Scope

Results support the theoretical framework of Chen etal (2005), that the stock returns are related to call puttrading value ratios.

Results of OTM options show feedback relationship

suggesting traders preference for OTM options andalso consistent with liquidity and leverage hypothesis.

Other factors are not found influential. Results aresubject to market wide information as index data is

employed.

Study can be extended using stocks data and alsotesting for industry effect to find if the relationshipchanges in case of marketwide information and stock

specific information.

Documents

Price Discovery Under Different Market Conditions and Moneyness