Managing Risks in Multiple Online Auctions: An Options Approach Ram Gopal Steven Thompson Y. Alex Tung Department of Operations and Information Management University of Connecticut Andrew B. Whinston Department of Management Science and Information Systems University of Texas at Austin

Presentation Outline Introduction Risks (buyer and seller) Overview of Options –In Financial Markets –In Auction Markets A framework for Auction Options Heuristic and Illustration Concluding Remarks

Introduction Online Auctions are becoming increasingly popular as a sales channel for new items. –eBay Stores opened to rave review with 18,000 stores signing up. –ebay.com/storesebay.com/stores Repeat Seller’s sponsor a significant proportion of auctions (data from 8 week period Nov. 02 – Jan. 03) We are concerned with sellers that move a number of new, identical items through single unit auctions over a sustained period of time. ItemTotal # of auctionsRepeat Seller Percentage Bose Radio % Grand Theft Auto % Palm % Palm Tungsten % Philips MP3 player % Play Station % Windows XP %

Seller Risks: We Sold It For What!? Primarily an issue of revenue uncertainty. Allocative Efficiency –Individual auctions are efficient, but sets of auctions do not reliably allocate items to the top bidders ItemNumber of auctions by most active seller Number of top M bidders that did not win an item Bose Radio29 8 Grand Theft Auto5113 Palm Palm Tungsten263 Philips MP3 player1110 Play Station Windows XP16167

Buyer Risks: Time, Money, and Loser’s Lament Wasted Time: “Time is money” Uncertainty of Acquisition: A firm time constraint exists Price Uncertainty: Will the time spent at auction result in a price that is “worth it”? Loser’s Lament: A “loser” places a bid that would have made her a winner at a different auction. ItemNumber of items (M) Total number of bidders# of bidders who left empty-handed who bid higher than: 0 th percentile50 th percentile 75 th percentile Bose Radio Grand Theft Auto Palm Palm Tungsten Philips MP3 player Play Station Windows XP

Options: What Are They? An option is a contract : The seller agrees to buy or sell the underlying at an agreed upon price by or on a pre- determined date. –Many types of options: Calls, Puts, American, European, Real –Example: A covered call option on shares of GE common stock Options are risk management tools: The seller of an option assumes the risk. –Risk is defined in terms of price fluctuations of the underlying asset. –The magnitude of the risk largely determines the price of the option.

Options in Auction Markets: Some Issues How Options work in online auctions: Example-A call option on a Bose Radio Would anyone want to buy one? –Data on “Buy-it-now” usage suggests an interest in risk managementData Can Sellers profit from issuing options? How would they be priced? –There are a number of option-pricing models (real and financial), most famous is the Black-Scholes model –All share some common fundamentals. No arbitrage Redundant Security Law of one price

“Traditional” Option Pricing Scenario: A sells a call option to B. Current asset price = $30, Strike price = $35, A single time period The price of the asset will either go up (to $50) or down (to $20). A’s net benefit is: P option = P option -15 A’s net benefit is: P option Case 1: A sells an “uncovered” option to B So long as P option > $15, A can achieve risk-free profits

“Traditional” Option Pricing Scenario: A sells a call option to B. Current asset price = $30, Strike price = $35, A single time period The price of the asset will either go up (to $50) or down (to $20). A’s net benefit is: P option = P option + 5 A’s net benefit is: P option = P option - 10 Case 2: A sells a “covered” option to B So long as P option > $10, A can achieve risk-free profits

“Traditional” Option Pricing In general, A could purchase x units of the underlying asset to cover the risk associated with selling a single option. x Option Price x Option Price Stock price is high: B will exercise the option. A will have to buy the stock at $50 and then give this stock to B. B will then give A $35 (the strike price) for it. A can sell his x units of stock at $50. A’s net benefit is: -30x P option +50x = P option +20x -15 P option +20x -15 Make Money Lose Money

“Traditional” Option Pricing In general, A would purchase x units of the underlying asset to cover the risk associated with selling a single option. x Option Price x Option Price Stock price is low: In this case B will not exercise the option. A will have to sell his stock at $20 and get his money back. A’s net benefit is: -30x + 20x+ P option = P option -10x P option +20x -15 P option -10x Feasible Region For Arbitrage At this point there is no arbitrage but also no risk of losing money, regardless of what the price does! That is the price the market will give to the option. For 1 time period this is a simple LP. Black- Scholes generalizes this to a generic asset price and across multiple time periods.

“Traditional” Option Pricing Solving the LP gives us the option price and the “hedge ratio” The decision variables are P option and x. In this case P option and x are $5 and.5 respectively.

Pricing Options: Traditional vs. Auction Markets Fundamental assumptions of extant option-pricing models do not apply in auction markets. –Arbitrage is possible (Gopal, et al) Due largely to limited information processing A seller could win some other auction for less than the current top bid at his auction, make a quick risk-free buck –Options impact price movements of underlying asset Auction markets are comparatively illiquid Behavioral differences between bidders and option holders impact auction ending price. –At any given moment multiple prices exist Posted price, other auctions, etc. –This creates a problem from the standpoint of pricing auction options.

An Alternative Framework Based simply on supply and demand Three fundamental components –Demand for Options –Option holder behavior –Impact of option holder behavior on auction outcomes Standard notation : = Option contract price = Option strike price = Number of options issued = Number sold at time t = Number exercised at time t Index the M auctions = Number of option holders participating in auction i

Demand for options

Option Holder Behavior Could be anything –Active deal seeking Option holders participate in all auctions conducted during life of option –Passive deal taking Option holders buy the option and exercise it immediately –Semi-active deal seeking Any extreme between active deal seeking and passive deal taking

Impact of Option Holders on Auction Outcome Unsold Options Proposition P strike + P option Time Auction ending price

Impact of Option Holders on Auction Outcome Variance Reduction Proposition

Impact of Option Holders on Auction Outcome Variance Reduction Proposition

Impact of Option Holders on Auction Outcome Option Holder Competition Proposition

Impact of Option Holders on Auction Outcome Option Holder Competition Proposition

A Heuristic For The Initial Foray A learning algorithm Uses bid-by-bid data from previous M auctions –Determines option holders Probability of purchase First-come, first served –User selects an option holder behavior patters Active deal seeking Passive deal taking A version of semi-active deal seeking –Determines auction ending price

Example: The Impact of Options

Closing Remarks and Future Research A first step into an unexplored facet of e- business risk management Additional research –Option holder behavior –Impact of options on auction outcome –Formal option-pricing models

Questions

Windows XP Prevalence of ‘Buy-it-now’