Enforcing Put-Call Parity in Monte Carlo Option Valuation

Summary

The document raises a numerical issue in Monte Carlo valuation of European calls and puts on the same stock. Under standard simulation, each option value is estimated by averaging its payoff over simulated underlying paths. With a finite sample, the simulated expected terminal stock price may differ from its forward value, so independently estimated call and put prices can fail to satisfy put-call parity even when the underlying model is appropriate.

The question asks whether path generation can enforce parity or whether estimated prices can be adjusted after simulation. It mentions models ranging from Black-Scholes to local volatility and Heston, while setting interest rates and dividends to zero for the discussion. No solution, experiment, or adjustment formula is provided. The issue is therefore posed rather than resolved, and any proposed correction would need to account for the model, the sampling scheme, and the relationship between the call, put, and simulated forward estimate.

Key ideas

• Finite Monte Carlo samples can leave the simulated expected terminal price away from its forward value.
• Separate payoff averages for calls and puts can consequently violate put-call parity numerically.
• The document asks about parity-preserving path generation or post-simulation valuation adjustments.
• It does not provide a correction method or evidence comparing alternative simulation schemes.

Tags

# Satisfying put-call parity in Monte Carlo option valuation


# Satisfying put-call parity in Monte Carlo option valuation












I am trying to price European call and put options on a stock using the Monte Carlo method, given some dynamics for the underlying that may or may not have a closed-form solution (e.g. Black-Scholes, local volatility, Heston). Interest rates, dividends, etc. can be assumed to be zero at present.

The standard approach outlined in textbooks is to simulate a large number of underlying price paths and average the option payoffs. However, put-call parity will be violated after any finite number of trials since the expected value of the stock only converges to the forward value in the limit of infinite trials.

Are there any alternative approaches to path generation that enforce put-call parity, or post-simulation adjustments to valuations that account for this error?

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