Document Sample

Research Labs Y!RL Spot Workshop on New Markets, New Economics • Welcome! • Specific examples of new trends in economics, new types of markets • virtual currency • prediction (“idea”) markets • experimental economics • Interactive, informal • ask questions • rountable discussion wrap-up Research Labs Distinguished guests (thanks!) • Edward Castronova Prof. Economics, Cal State Fullerton • John Ledyard Prof. Econ & Social Sciences, CalTech • Justin Wolfers Prof. Economics, Stanford Research Labs Schedule 11am-noon Castronova on the Future of Cyberspace Economies noon-1pm Lunch provided 1pm-2pm Ledyard on ~ Information Markets and Experimental Economics 2pm-3pm Wolfers on ~ Prediction Markets, Play Money, & Gambling 3pm-3:30pm Pennock on Dynamic Pari-Mutuel Market for Hedging, Speculating 3:30pm-4pm Roundtable Discussion Research Labs A Dynamic Pari-Mutuel Market for Hedging, Wagering, and Information Aggregation David M. Pennock paper to appear EC’04, New York Research Labs Economic mechanisms for speculating, hedging • Financial • Continuous Double Auction (CDA) stocks, options, futures, etc • CDA with market maker (CDAwMM) • Gambling • Pari-mutuel market (PM) horse racing, jai alai • Bookmaker (essentially like CDAwMM) • Socially distinct, logically the same • Increasing crossover Research Labs Take home message • A dynamic pari-mutuel market (DPM) • New financial mech for speculating on or hedging against an uncertain event; Cross btw PM & CDA • Only mech (to my knowledge) to • involve zero risk to market institution • have infinite (buy-in) liquidity • continuously incorporate new info; allow cash-out to lock in gain, limit loss Research Labs Outline • Background • Financial “prediction” markets • Pari-mutuel markets • Comparing mechs: PM, CDA, CDAwMM, MSR • Dynamic pari-mutuel mechanism • Basic idea • Three specific variations; Aftermarkets • Open questions/problems Research Labs What is a financial “prediction market”? • Take a random variable, e.g. 2004 CA US’04Pres = =6? Earthquake? Bush? • Turn it into a financial instrument payoff = realized value of variable I am entitled to: $1 if =6 $0 if 6 Research Labs Real-time forecasts • price expectation of random variable (in theory, in lab, in practice, ...huge literature) • Dynamic information aggregation • incentive to act on info immediately • efficient market today’s price incorporates all historical information; best estimator • Can cash out before event outcome • BUT, requires bi-lateral agreement Research Labs Updating on new information Research Labs The flip-side of prediction: Hedging E.g. options, futures, insurance, ... • Allocate risk (“hedge”) • Aggregate information • insured transfers risk • price of insurance to insurer, for $$ prob of catastrophe • farmer transfers risk • OJ futures prices yield weather forecasts to futures speculators • prices of options • put option buyer encode prob dists hedges against stock over stock drop; seller assumes movements risk • market-driven lines are unbiased estimates of outcomes • IEM political forecasts Research Labs Continuous double auction CDA • k-double auction repeated continuously • buyers and sellers continually place offers • as soon as a buy offer a sell offer, a transaction occurs • At any given time, there is no overlap btw highest buy offer & lowest sell offer http://tradesports.com http://www.biz.uiowa.edu/iem http://us.newsfutures.com/ Research Labs Running comparison no risk liquidity info aggreg. CDA x x CDAwMM PM DPM Research Labs CDA with market maker • Same as CDA, but with an extremely active, high volume trader (often institutionally affiliated) who is nearly always willing to sell at some price p and buy at price q p • Market maker essentially sets prices; others take it or leave it • While standard auctioneer takes no risk of its own, market maker takes on considerable risk, has potential for considerable reward http://www.wsex.com/ http://www.hsx.com/ Research Labs Bookmaker • Common in sports betting, e.g. Las Vegas • Bookmaker is like a market maker in a CDA • Bookmaker sets “money line”, or the amount you have to risk to win $100 (favorites), or the amount you win by risking $100 (underdogs) • Bookmaker makes adjustments considering amount bet on each side &/or subjective prob’s • Alternative: bookmaker sets “game line”, or number of points the favored team has to win the game by in order for a bet on the favorite to win; line is set such that the bet is roughly a 50/50 proposition Research Labs Running comparison no risk liquidity info aggreg. CDA x x CDAwMM x x PM DPM Research Labs What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • Wagers: Research Labs What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • Wagers: Research Labs What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • Wagers: Research Labs What is a pari-mutuel market? A B • E.g. horse racetrack style wagering • Two outcomes: A B • 2 equivalent ways to consider 1+ $ on B = 1+ 8 =$3 $ on A 4 payment rule • refund + share of B total $ = 12 = $3 • share of total $ on A 4 Research Labs What is a pari-mutuel market? • Before outcome is revealed, “odds” are reported, or the amount you would win per dollar if the betting ended now • Horse A: $1.2 for $1; Horse B: $25 for $1; … etc. • Strong incentive to wait • payoff determined by final odds; every $ is same • Should wait for best info on outcome, odds • No continuous information aggregation • No notion of “buy low, sell high” ; no cash-out Research Labs Running comparison no risk liquidity info aggreg. CDA x x CDAwMM x x PM x x DPM Research Labs Dynamic pari-mutuel market Basic idea • Standard PM: Every $1 bet is the same • DPM: Value of each $1 bet varies depending on the status of wagering at the time of the bet • Encode dynamic value with a price • price is $ to buy 1 share of payoff • price of A is lower when less is bet on A • as shares are bought, price rises; price is for an infinitesimal share; cost is integral Research Labs Dynamic pari-mutuel market Example Interface A B A B • Outcomes: A B • Current payoff/shr: $5.20 $0.97 $3.27 $3.27 $3.27 $3.27 $3.27 sell 100@ $3.25 $3.27 sell 100@ $0.85 market maker sell 100@ $3.00 sell 100@ $0.75 traders sell 35@ $1.50 sell 3@ $0.50 buy 4@ $1.25 buy 200@ $0.25 buy 52@ $1.00 Research Labs Dynamic pari-mutuel market Setup & Notation A B A B • Two outcomes: A B • Price per share: pri1 pri2 • Payoff per share: Pay1 Pay2 • Money wagered: Mon1 Mon2 (Tot=Mon1+Mon2) • # shares bought: Num1 Num2 Research Labs How are prices set? • A price function pri(n) gives the instantaneous price of an infinitesimal additional share beyond nthe nth • Cost of buying n shares: pri (n)dn 0 • Different assumptions lead to different price functions, each reasonable Research Labs Redistribution rule • Two alternatives • Losing money redistributed. Winners get: original money refunded + equal share of losers’ money • All money redistributed. Winners get equal share of all money • For standard PM, they’re equivalent • For DPM, they’re significantly different Research Labs Losing money redistributed • Payoffs: Pay1=Mon2/Num1 Pay2=. • Trader’s exp pay/shr for e shares: Pr(A) E[Pay1|A] + (1-Pr(A)) (-pri1) • Assume: E[Pay1|A]=Pay1 ! Pr(A) Pay1 + (1-Pr(A)) (-pri1) Research Labs Market probability • Market probability MPr(A) • Probability at which the expected value of buying a share of A is zero • “Market’s” opinion of the probability • MPr(A) = pri1 / (pri1 + Pay1) Research Labs Price function I • Suppose: pri1 = Pay2 pri2=Pay1 natural, reasonable, reduces dimens., supports random walk hypothesis • Implies MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2 Research Labs Deriving the price function • Solve the differential equation dm/dn = pri1(n) = Pay2 = (Mon1+m)/Num2 where m is dollars spent on n shares • cost1(n) = m(n) = Mon1[en/Num2-1] • pri1(n) = dm/dn = Mon1/Num2 en/Num2 Research Labs Interface issues • In practice, traders may find costs as the sol. to an integral cumbersome • Market maker can place a series of discrete ask orders on the queue, e.g. • sell 100 @ cost(100)/100 • sell 100 @ [cost(200)-cost(100)]/100 • sell 100 @ [cost(300)-cost(200)]/100 • ... Research Labs Price function II • Suppose: pri1/pri2 = Mon1/Mon2 also natural, reasonable • Implies MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2 Research Labs Deriving the price function • First solve for instantaneous price pri1=Mon1/Num1 Num2 • Solve the differential equation dm/dn = pri1(n) = Mon1+m (Num1+n)Num2 2 N 1 n 2 N1 cost1(n) = m = Mon1e N2 N2 1 N 1 n N1 Mon1 2 2 pri1(n) = dm/dn = e N2 N2 ( Num1 n) Num2 Research Labs All money redistributed • Payoffs: Pay1=Tot/Num1 Pay2=. • Trader’s expected pay/shr for e shares: Pr(A) (Pay1-pri1) + (1-Pr(A)) (-pri1) • Market probability MPr(A) = pri1 / Pay1 Research Labs Price function III • Suppose: pri1/pri2 = Mon1/Mon2 • Implies • MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2 ( Mon1 m) Mon2 Tot • pri1(m) = (Mon1 m)Mon2Num1 (Mon2 m)Mon2Num2 Tot(Mon1 m)Num2 ln Tot(Mon1 m) Mon1(Tot m) cost1(m) = m( Num1 Num2) Num2(Tot m) Tot( Mon1 m) Mon1(Tot m) ln Tot Mon2 Research Labs Aftermarkets • A key advantage of DPM is the ability to cash out to lock gains / limit losses • Accomplished through aftermarkets • All money redistributed: A share is a share is a share. Traders simply place ask orders on the same queue as the market maker Research Labs Aftermarkets • Losing money redistributed: Each share is different. Composed of: 1. Original price refunded priI(A) where I(A) is indicator fn 2. Payoff PayI(A) Research Labs Aftermarkets • Can sell two parts in two aftermarkets • The two aftermarkets can be automatically bundled, hiding the complexity from traders • New buyer buys priI(A)+PayI(A) for pri dollars • Seller of priI(A) gets $ priMPr(A) • Seller of PayI(A) gets $ pri(1-MPr(A)) Research Labs Alternative “psuedo” aftermarket • E.g. trader bought 1 share for $5 • Suppose price moves from $5 to $10 • Trader can sell 1/2 share for $5 • Retains 1/2 share w/ non-negative value, positive expected value • Suppose price moves from $5 to $2 • Trader can sell share for $2 • Retains $3I(A) ; limits loss to $3 or $0 Research Labs Running comparison no risk liquidity info aggreg. CDA x x CDAwMM x x PM x x DPM x x x MSR x x [Hanson 2002] Research Labs Pros & cons of DPM types Losing money All money redistributed redistributed Pros Winning Aftermarket wagers never trivial, natural lose money Cons Aftermarket Winning complicated wagers can lose money! Research Labs Pros & cons of DPMs generally • Pros • No risk to mechanism • Infinite (buying) liquidity • Dynamic pricing / information aggregation Ability to cash out • Cons • Payoff vector indeterminate at time of bet • More complex interface, strategies • One sided liquidity (though can “hedge-sell”) • Untested Research Labs Open questions / problems • Is E[Pay1|A]=Pay1 reasonable? Derivable from eff market assumptions? • DPM call market • Combinatorial DPM • Empirical testing What dist rule & price fn are “best”? • >2 discrete outcomes (trivial?) Real-valued outcomes

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 2 |

posted: | 4/7/2010 |

language: | English |

pages: | 47 |

OTHER DOCS BY liuqingzhan

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.