Risk Mitigation Services for Ads
Hubert Jin, Jinsong Tan
Motivation
• Hedge against the fluctuation of bids for
sponsored ads.
• Risk sharing and budget control on future
sponsored ads cost.
• Opportunity for speculation - win or lose.
• Secondary market for sponsored ads.
Risk Sharing Models
• Guaranteed slot (premium, deductible)
– Is it possible ?
• Number of slots is limited.
• Insurance (premium, deductible, limit)
– Customers may be fooled.
• Two policies with limits of $5.00 and $5.01.
• Co-pay (premium, deductible, co-pay rate)
– Risk is shared, not 100% mitigated.
Advantages of Co-pay Model
• It prevents irrational bidding of those who
purchase policies (risk mitigation service).
• Those who purchase policies are more likely
to win the bids, which forces the rest to
participate in risk mitigation.
• Unlimited policies can be sold on limited
ads slots.
• Policies can be trade at exchange market.
Valuation
• Borrow ideas from Black-Scholes of the
stock option market.
• Historical data provides trends and the
variability of the bids.
• Speculation activities on the exchange
market will ‘likely’ to bring the valuation
right.
• Equilibrium of bids with risk mitigation.
When Risk Mitigation Wins
• Suppose that
– We have some advertisers buy risk mitigation
product (co-pay model).
– Bid goes up in a future time.
with risk mitigation
Make Even
• (premium, deductible, co-pay, duration)
– (p, d, r, t)
– bid ~ N(u(t), s(t))

p   (1  r )( x  d ) f N ( u ( t ),s ( t )) ( x)dx
d
Equilibrium With Risk Mitigation
• No risk mitigation.
– Google/Yahoo take all the money on the table.
• Bidders escalate the bids.
• Except for those bidder whose limits are too low to compete.
• With risk mitigation (assume it is offered by
the auctioneer)
– The risk mitigation mechanism could force bidders to buy risk
mitigation service which also drives up bids.
– Auctioneer also collects money from bidders who purchase risk
mitigation contracts but withdraw when bids are too high.
Black-Scholes
• The price of the underlying instrument S_t
follows a geometric Brownian motion with
constant drift and volatility:
–
–
–
–
–
–
dS_t = \mu S_t dt + \sigma S_t dW_t
It is possible to short sell the underlying stock.
There are no arbitrage opportunities.
Trading in the stock is continuous.
There are no transaction costs or taxes.
All securities are perfectly divisible (e.g. it is possible to buy 1/100th of a
share).
– It is possible to borrow and lend cash at a constant risk-free interest rate.
Black-Scholes (continue)