Using Market-Implied Inputs for Risk-Neutral Monte Carlo Option Pricing

Summary

The document asks how to set geometric Brownian motion inputs when simulating asset paths to price exotic options under a risk-neutral measure. It distinguishes pricing inputs from estimates drawn directly from historical price data. Its central guidance is to use parameters implied by current market prices, including implied volatility and implied dividend yield, rather than treating realized historical variance as the pricing volatility.

The answer notes that implied inputs can vary with option moneyness and maturity, so a single volatility or yield may not represent the market across all contracts. It gives no derivation, calibration procedure, numerical example, or comparison of pricing errors, and it does not elaborate on rates, model choice, or exotic payoff specifics. The note is therefore a concise principle for market-consistent calibration, not a complete Monte Carlo implementation guide.

Key ideas

• Risk-neutral option pricing should use market-implied inputs rather than relying only on historical estimates.
• Implied volatility and dividend yield can vary across option strikes and maturities.
• The document offers a high-level calibration principle but no detailed procedure or empirical evidence.

Tags

# Asset price simulation under Monte Carlo for option pricing using market data


# Asset price simulation under Monte Carlo for option pricing using market data












I am trying to use Monte Carlo to price some exotic options. I have in mind to simulate asset prices under GBM (say S&P prices) using Monte Carlo and price the option accordingly from the payoffs of the paths.

However, I am slightly confused on how to obtain the parameters of the GBM equation from market data to ensure that I can correctly price the options under the risk neutral framework? Is it simply finding the dividend yields and subtracting from a risk free rate for risk neutral drift? Is it simply computing variance of the time series data to obtain the volatility?

Hoping for someone to enlighten me. Many thanks in advance.

## Answer by Magic is in the chain (score 1)

https://quant.stackexchange.com/a/41604

For pricing, you should use parameters implied by the market prices, not historical data. i.e., vol and dividend yields would be the implied vol and implied dividend yield, which could vary by the moneyness and maturity, for example.

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