medium · Quantitative Finance numerical
A 'barrier' option (e.g., Up-and-Out Call) is priced via Monte Carlo.
Why might antithetic variates be less effective here than for a vanilla call?
- The barrier level B is treated as a fixed, deterministic constant known in advance
- The knock-out feature introduces a non-monotonicity in the payoff function
- Path-dependent options always require exactly 1/M convergence in every scheme
- Barrier options cannot be priced within a standard risk-neutral valuation framework
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