Yes, however, this requires assumptions and you would introduce a certain degree of error. This is because option prices - as all asset prices - are the result of supply and demand. Without market prices, you are missing an important piece of information, which is captured in the Black Scholes model by volatility (aka implied volatility when inferred from market prices).
In your case, where option prices are not an option ;), you need to find a replacement for implied volatility. You could look into GARCH models to forecast volatility on your underlying price (return) data. Together with the Black Scholes model this could give you an idea on the corresponding option price. Please note, from empirical data we know that this volatility forecast is usually different from the actual implied volatility, hence, you are introducing an error.
Lastly, you have to make some assumptions on your option strategy, e.g. do you roll a protective put every 3 month, etc.?
You could also have a look at option replication strategies, e.g. "delta-replicated put" (see e.g. this paper).