hard · Quantitative Finance numerical
An analyst is pricing a lookback option (payoff max(S_t) - S_T). He notes that antithetic variates are very effective.
Why is this conceptually consistent with the theory?
- Lookback options have a gamma of zero, making the simulation linear
- The payoff of a lookback option is always positive
- The maximum of a path and the final value are both monotonic in the increments
- Antithetic variates correct for the 'look-ahead' bias in path-dependent options
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