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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.

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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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  • $\begingroup$ Hi, thank you for the reply. Is there a way I can obtain the required parameters from historical time series of the asset price itself? Or do you mean that I should find implied dividend yield and implied vol from historical option prices? And would that then mean i just need the market price of an option on the underlying asset to do so? $\endgroup$
    – user8465900
    Sep 7, 2018 at 16:37
  • $\begingroup$ Hello, for pricing you will need to use current market data. If you are pricing under physical measure (say for potential future exposure), then you can use historical data. Your model won’t reproduce the current market prices if you don’t use the parameters implied by the current quoted prices. $\endgroup$
    – Magic is in the chain
    Sep 7, 2018 at 17:09
  • $\begingroup$ Thank you for your reply. For my purposes and from your answers, I believe that using implied vol from option prices is the way I should go. I am however quite new to calibrating the gbm parameters to implied vol and have not found any clear description online. Will you kindly show me the right direction on how to calibrate the gbm drift and vol to implied vol from option prices? Is it simply choosing the implied vol of the option that has the same strike and time to maturity? Any good reading that you recommend for this? $\endgroup$
    – user8465900
    Sep 10, 2018 at 14:04

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