Pricing a contract on a sports star's future value
Question
How would you go about valuing an option written on a celebrated professional athlete (for example, a right to sign them or share in their future earnings)?
Short answer
Model the athlete's value as the underlying and price the payoff, but recognise the market is incomplete. Define the underlying (future earnings, contract value or performance metric), choose a process with drift, volatility and jump risk for injury or retirement, and value the payoff with a binomial tree or Monte Carlo. Because the athlete cannot be traded or hedged, there is no replication argument, so you need a risk-adjusted discount rate or market price of risk, and comparables (similar contracts) for calibration.
Adapted from Crack, Heard on the Street, Q5.5.9, p.55; question and answer rewritten by SelfMadeQuant.com.
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