Replication Desk - Row Reduction and Pricing Practice
Setting up the desk…
About the Replication Desk
Replicate a payoff from the assets on the desk by row reduction, then price it. Each round gives you a system of equations: the columns are traded assets, the target is the payoff you need. Reduce it and read the answer off the pivot rows.
What the reduced form tells you
An inconsistent system means no replicating portfolio exists. One free variable left over means infinitely many portfolios replicate the payoff. A pivot in every column means a unique portfolio, and its weights are the holdings.
The portfolio costs its holdings times today's prices, and a short counts as money in. When the replicating portfolio and the quoted price disagree, you sell the expensive side and buy the cheap one, and the edge per lot is the difference between the two prices.
Why quant interviews test this
Replication is how derivatives are priced, and row reduction is the mechanical way to do it. Trading interviews use it to check that you can go from a payoff to a hedge to an arbitrage without losing the signs.
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