Estimating Option Value After an Underlying Price Move
Summary
The document asks how to estimate the value of a put option if its underlying reaches the strike within a chosen future interval. It distinguishes the premium recorded as cost basis when the option is sold from the later market value relevant to buying the position back. The proposed inputs include the underlying price, volatility, and time remaining, with the goal of planning a hedge around a price-based exit condition.
The answer identifies Black–Scholes as a theoretical framework for estimating value, while stressing that traded option prices also reflect supply and demand. It suggests that fitting a model to observed market data could address the practical pricing question, but describes that route as substantially more complex and costly. The discussion offers no worked calculation, broker-specific cost-basis details, data comparison, or assessment of model accuracy. A theoretical estimate therefore should not be treated as a guaranteed executable price or as a forecast that the underlying will reach the strike on schedule.
Key ideas
- Black–Scholes can provide a theoretical estimate of an option’s value under specified inputs.
- Observed option prices are also shaped by supply and demand.
- A modeled future value can help frame a hedge, but it does not guarantee the price available to close the trade.
- Fitting a pricing model to market observations is possible but may require substantial complexity and cost.
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# Calculation of market price for option at underlying strike price at some point in future # Calculation of market price for option at underlying strike price at some point in future Would appreciate clarification on the below scenario. If a put option was sold at the start of the week, when the broker (Interactive Brokers) calculates the cost basis (the premium collected) are the option greeks fixed at that point of writing the option and used for this cost basis (along with commission)? I need to be able to calculate for any specific time of the day, from the current underlying price and its current volatility and time to expiration, what the option value would be should it move to the strike within the next hour or so (to define this time movement would be a amazing, but for sake of example 60 minutes would suffice). I am using the strike price of the underlying as the exit condition as opposed to the stop loss on the contract itself - knowing what the option value would become should it hit the strike in the near future I can put additional hedging in place to offset the cost when buying to close the option position. Would this be along the lines of Black-Scholes Merton (BSM), or would I need to subscribe to live option market data (as that's only giving current price of options) or a combination thereof? As a side note any recommendations for paid commercial options data would be appreciated. ## Answer by justasking (score 1, accepted) https://quant.stackexchange.com/a/61295 A theoretical answer to your question is provided by Black-Scholes but remember that actual option prices are set by supply and demand (with guidance from models for different market participants.) You could also try to fit a model to the actual data to solve this problem, though that would be a much more complex (and costly) solution.
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