Quantora · Derivatives Desk
Exotic Options
Beyond vanilla calls and puts. Quantora prices two workhorses of the exotic world with exact closed-form models: Asian options that settle on an average price, and exchange options that pay the difference between two assets - each with the plain-vanilla comparison so you can see what the exotic feature is worth.
1. Geometric Asian option
Payoff on the geometric average of the price over the life (Kemna-Vorst). Averaging dampens volatility, so it's cheaper than a vanilla.
2. Exchange option (Margrabe)
The right to swap asset 2 for asset 1 at expiry - pays max(S₁ − S₂, 0). Depends on the two vols and their correlation.
An Asian option settles against the average price rather than the final price, which smooths out end-of-life spikes and manipulation - popular in commodities and FX. Because an average wobbles less than a single point, its effective volatility is lower (about σ/√3 for a geometric average), so the option costs less than the vanilla; the gap you see is the value of that averaging. An exchange option pays the outperformance of one asset over another and is the building block behind spread trades, merger arbitrage and "better-of" structures. Its only volatility that matters is the volatility of the spread - so high correlation between the two assets makes it cheap (they move together, the spread barely moves), and low or negative correlation makes it expensive.