Using Future Paths to Bound Path-Dependent Option Values

Summary

The document describes a Monte Carlo exercise procedure sometimes called hindsight overhedge for path-dependent options. At an exercise date, it examines the simulated path through a later maturity and uses that future information to decide retrospectively whether exercising or continuing would have been better. This differs from a realizable exercise policy, which can use only information available at the exercise date.

Because the procedure has access to future path outcomes, it can choose more favorably than an investor acting in real time. The answer therefore presents its value as a presumed upper bound, rather than an attainable price or a replacement for Longstaff–Schwartz continuation-value estimation. The explanation is brief and offers no formal proof, implementation details, or numerical evidence. Its practical use is as an optimistic benchmark for Monte Carlo valuation, with the look-ahead bias kept explicit.

Key ideas

• Hindsight overhedge uses simulated future outcomes to make an exercise decision at an earlier date.
• The method compares exercise and continuation retrospectively along each simulated path.
• Looking ahead gives the procedure information unavailable to a real-time exercise policy.
• Its estimated option value is therefore presented as a presumed upper bound.
• The document gives no formal proof or implementation guidance for the bound.

Tags

# Hindsight overhedge for pricing path dependent options


# Hindsight overhedge for pricing path dependent options












I understand how to use the longstaff schwartz method in Monte Carlo to compute the continuation value of path dependent options but someone recently mentioned another technique called "Hindsight overhedge". I can't find any reference to it. Has anyone come across Hindsight overhedge in Monte Carlo simulation and can point reference to it?

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/46717

I believe this may be referring to a procedure whereby one uses the ‘future’ Monte Carlo paths to determine optimal exercise. For example, consider an exercise decision at $T_1$ within a path dependent option that expires at $T_2>T_1$. Then to determine whether to exercise at $T_1$, examine each path in [$T_1,T_2$] to decide if continuation value > exercise value, and exercise ‘retrospectively’ accordingly. This presumably gives an upper bound on the value, since you are cheating by looking into the future.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.