Notes

Primary provider documentation accessed Sep7 2026: indicative quotes are derivatives, not actual OPRA quotes; option-chain reference says trades delayed and quotes modified. This is one provider origin, not independent corroboration. Historical OPRA403 is prior journal evidence, not newly retried this run. No current executable-price claim. https://docs.alpaca.markets/us/docs/historical-option-data

A calculation was done on September 7 for the September 4 indicative price of P42 on September 18. The bid price was $0.58 and the ask price was $0.73. The fair price, using a stock-GBM FD model, which is a type of financial model, was $0.78105845. Assuming the stock will be sold at this fair price minus half of the current spread, which is $0.075, and including round-trip fees of $0.20, the result is a loss of $2.59. Without considering the exit-spread allowance, the result would be a gain of $4.90. These numbers are diagnostics from the model and do not reflect actual payoffs or quotes that can be executed. The premium of $73 is higher than the full-risk ceiling of $8.51. The exact fees and future spread are unknown. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

On September 7, a model showed that the base return was 40.818% and the high return was 58.927%, which is 1.2 times the 60-day adjusted realized volatility, using inputs from independent financial data records. All bids were zero. The JSON values were: for FRO260918P00025000, the financial data value was 3.4896e-11 and the high value was 0.000003499251788, with an alpha of 0.07; for FRO260918P00029000, the financial data value was 6.61965807e-7 and the high value was 0.000578235730393, with an alpha of 0.08; for FRO260918P00030000, the financial data value was 0.000004456422241 and the high value was 0.001576383729013, with an alpha of 0.08; and for FRO260918P00031000, the financial data value was 0.00002511936869 and the high value was 0.003927209820749, with an alpha of 0.08. A correction was made to observation 7769, which initially displayed a K25 tail as 0 due to pandas 10 decimal rounding, but the actual financial data value was 2.820563e-11, not mathematical zero. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the stock FRO261016P00060000. On September 7, a calculation was done to estimate the value of the stock using a method called finite-difference American revaluation. This method uses a formula to estimate the stock's value, which was $46.15. The calculation also used the following numbers: sigma, which measures volatility, was 0.408179926, the interest rate was 0.04, and the dividend yield was 2.61. This was done on September 18 when the market opened, and it was 14 out of 42 days on the calendar. The calculation used 2400 spaces and 1800 time steps, and it took into account the exact dividend jump interpolation. The prices used were the ask and bid prices from September 4, which were indicative. The net value was calculated as 100 times the difference between the fair value and the ask price, minus $0.20, which is the assumed cost of buying or selling the stock before the spread. The calculation does not claim to show the actual probability of the stock's price or the physical probability of execution. The numbers may be rounded, which could make very small positive values appear as zero. The calculation resulted in the following values: the strike price was $0.00, the bid price was $15, the ask price was $18.37, the fair dividend value was $16.378572907933826, and the net fair dividend value was -$199.34270920661749. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00060000 option. On September 7, a finite-difference American revaluation was done. This means a method was used to estimate the option's value. The stock price was 46.15 dollars, the volatility, or sigma, was 0.408179926, the risk-free interest rate, or r, was 0.04, and the time to expiration, or D, was 2.61 days at the September 18 open. The calendar had 14 out of 42 days left. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation. This means the calculation tried to accurately account for dividend payments. The ask and bid prices were from September 4 and were indicative, or estimated. The net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which was assumed to be the cost of exiting the trade. The calculation did not claim to predict the actual execution or physical probability of the trade. The results were: the stock symbol is FRO261016C00060000, the bid price is 0 dollars, the ask price is 0.27 dollars, the fair dividend value is 0.031521282303014, and the net fair dividend value is -24.047871769698588. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00055000. This is about a stock option, which is a contract to buy or sell a stock at a set price. The option is for the stock with the ticker FRO. On September 7, a calculation was done to estimate the value of this option. The calculation used a method called finite-difference to estimate the value of an American option, which can be exercised at any time. The stock price was $46.15, the volatility, which is a measure of how much the stock price changes, was 0.408179926, the risk-free interest rate, which is the rate at which an investor can borrow or lend money without risk, was 0.04, and the dividend yield, which is the ratio of the annual dividend payment to the stock price, was 2.61. This calculation was done for the opening of the stock market on September 18, which is 14 out of 42 days on the calendar. The calculation used 2400 steps and 1800 time intervals, and it took into account the exact dividend payment and the jump in the stock price when the dividend is paid. The ask price, which is the price at which an investor can buy the option, and the bid price, which is the price at which an investor can sell the option, were used to estimate the value of the option on September 4. The net value of the option was calculated as 100 times the difference between the estimated value and the ask price, minus $0.20. The result of the calculation is: the strike price of the option is $55.00, the bid price is $10.65, the ask price is $12.56, the estimated value of the option is $11.47, and the net value of the option is -$108.89. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00055000 option. On September 7, a finite-difference American revaluation, which is a method to calculate the value of an option, was done. The values used were a stock price of 46.15, a volatility, or sigma, of 0.408179926, an interest rate, or r, of 0.04, and a dividend yield, or D, of 2.61, as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 spaces and 1800 timesteps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices from September 4 were used as a guide. The net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed 0.20. The result was a fair value of 0.153286355069853 and a net value of -16.87136449301466. The option had a bid price of 0.13 and an ask price of 0.32. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00050000 independent stock-GBM value. On September 7, a finite-difference American revaluation, which is a method to estimate the value of a stock option, was done. The values used were: stock price of 46.15, sigma of 0.408179926, which is a measure of volatility, r of 0.04, which is the interest rate, and D of 2.61 at the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 spaces and 1800 timesteps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices from September 4 were used as an indication. The net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed 0.20 dollars, before the exit spread, which is the difference between the prices at which you can buy and sell. This calculation does not claim to represent the actual execution or physical probability. The float display may round tiny positive values. The result was: the stock symbol is FRO261016P00050000, the bid price is 5.98, the ask price is 7.69, the fair dividend value is 6.891470420564403, and the fair dividend net value is -80.05295794355976. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00050000 option. This is a piece of information about a specific stock option, which is a contract to buy or sell a stock at a certain price. The option's value was calculated on September 7 using a method called finite-difference American revaluation, which takes into account the stock's current price, volatility, interest rate, and time to expiration. The stock's current price is $46.15, its volatility is 0.408179926, and the interest rate is 0.04. The time to expiration is 2.61 days, as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 spaces and 1800 timesteps, with exact dividend jump interpolation. The ask and bid prices on September 4 were used as indicators, with a net value calculated as 100 times the difference between the fair value and the ask price, minus $0.20, which is the assumed exit spread. The calculation does not claim to represent the actual probability of execution or physical probability. The values are displayed as floating point numbers, which may round very small positive values. The results of the calculation are: the stock option symbol is FRO261016C00050000, the bid price is $0.52, the ask price is $0.77, the fair value is $0.649639421634445, and the net fair value is -$12.236057836555537. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00049000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to calculate the value of a stock option. The result was a stock price of 46.15 dollars, a volatility of 0.408179926, an interest rate of 0.04, and a dividend yield of 2.61, all as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices on September 4 were used as a guide, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which is the assumed cost of buying or selling the stock, before the exit spread, which is the difference between the prices at which the stock can be bought and sold. The result was a fair value of 6.057680070043313 dollars, and a net value of -69.43199299566872 dollars, with a bid price of 5.43 dollars and an ask price of 6.75 dollars. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016C00049000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to calculate the value of an option, with the following values: stock price at 46.15, volatility at 0.408179926, interest rate at 0.04, and dividend yield at 2.61, as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices were from September 4, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, before the exit spread, which is the difference between the prices at which you can buy and sell. The calculation does not claim to predict the probability of execution or physical probability. The float display may round tiny positive values. The result was: the stock symbol is FRO261016C00049000, the bid price is 0.37, the ask price is 1.53, the fair dividend is 0.855519916848315, and the fair dividend net is -67.64800831516852. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00048000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to estimate the value of a stock option, and it showed the following results: the stock price was $46.15, the volatility, or sigma, was 0.408179926, the risk-free interest rate, or r, was 0.04, and the dividend yield, or D, was 2.61, all as of the September 18 open, with 14 out of 42 days on the calendar. The revaluation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to estimate the effect of dividend payments on the stock price. The ask and bid prices on September 4 were used as an indication, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed $0.20, before the exit spread, which is the difference between the prices at which you can buy and sell a stock. The results were: the strike price, or s, was FRO261016P00048000, the bid price, or b, was $3.53, the ask price, or a, was $5.76, the fair dividend, or fd, was $5.264036979277707, and the net fair dividend, or fd_net, was -$49.796302072229295. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00048000 option. The option's value was calculated on September 7 using a finite-difference method, which is a way to approximate the value of an option. The calculation used the following numbers: stock price of 46.15, volatility of 0.408179926, interest rate of 0.04, and dividend yield of 2.61. This calculation was done for the opening price on September 18, with 14 out of 42 days left on the calendar. The calculation used 2400 space steps and 1800 time steps, and it took into account the exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices were based on indicative prices from September 4. The net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which is the assumed cost of exiting the trade. The calculation does not claim to predict the actual execution or physical probability of the trade. The display of the results may round very small positive values. The results of the calculation are: strike price symbol is FRO261016C00048000, bid price is 0.88, ask price is 1.18, fair dividend value is 1.120694334752694, and net fair dividend value is -6.130566524730607. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00047000. On September 7, a finite-difference American revaluation, which is a method to estimate the value of a stock option, was done. The stock price was 46.15 dollars, the volatility, or sigma, was 0.408179926, the risk-free interest rate, or r, was 0.04, and the dividend yield, or D, was 2.61. This was calculated at the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices were from September 4. The net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which is the assumed exit spread. This calculation does not claim to predict the probability of execution or physical probability. The float display may round very small positive values. The data line shows the following values: the stock symbol is FRO261016P00047000, the bid price is 4.28 dollars, the ask price is 4.94 dollars, the fair dividend value is 4.516394671002216 dollars, and the net fair dividend value is -42.56053289977848 dollars. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00047000 option. The option's value was calculated on September 7 using a finite-difference method, which is a way to approximate the value of an option. The calculation used the following numbers: stock price of 46.15, volatility of 0.408179926, interest rate of 0.04, and time to expiration of 2.61 days as of the September 18 open. The calculation also used 2400 space steps and 1800 time steps, and took into account the exact dividend and jump interpolation, which is a method to estimate the effect of dividends on the option price. The ask and bid prices were based on indicative prices from September 4. The net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed exit spread of 0.20 dollars. The calculation does not claim to represent the actual probability of execution or physical probability. The display of floating point numbers may round very small positive values. The result of the calculation is: the option symbol is FRO261016C00047000, the bid price is 1.18, the ask price is 1.73, the finite-difference value is 1.457846039338404, and the net finite-difference value is -27.41539606615961. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00046000. The calculation used a finite-difference method, which is a way to approximate values, to revalue an American option, a type of contract that can be exercised at any time before expiration, on September 7. The values used were a stock price of 46.15, a volatility, which is a measure of how much the price changes, of 0.408179926, an interest rate of 0.04, and a dividend yield, which is a ratio of the annual dividend payment to the stock price, of 2.61, all as of the opening on September 18, with 14 out of 42 days left on the calendar. The calculation used 2400 spaces and 1800 time steps, with exact dividend jump interpolation, which is a method to account for dividend payments. The ask and bid prices, which are the prices at which someone is willing to sell or buy, were from September 4. The net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed 0.20 dollars, before the exit spread, which is the difference between the bid and ask prices. The calculation does not claim to represent the probability of physical execution. The float display may round very small positive values. The result was a sell price of 3.32, a buy price of 4.14, a fair dividend value of 3.820362753071128, and a net fair dividend value of -32.16372469288718. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00046000 option. On September 7, a finite-difference American revaluation was done, which is a method to estimate the value of an option, using the following numbers: stock price of 46.15, volatility of 0.408179926, interest rate of 0.04, and time to expiration of 2.61 days, as of the September 18 open. This calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices on September 4 were used as a guide. The net value is calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which is the assumed cost of buying or selling the option. The result is: the option's fair value is 1.878711624245778, and the net value is -13.228837575422125, with a bid price of 1.47 and an ask price of 2.009. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00045000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to estimate the value of a stock option. The results were: stock price of 46.15, volatility of 0.408179926, risk-free interest rate of 0.04, and dividend yield of 2.61, all as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices were from September 4, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed 0.20. The results are: strike price of FRO261016P00045000, bid price of 2.72, ask price of 4.019, fair dividend value of 3.180969516363222, and net fair dividend value of -84.0030483636778. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00045000 option. This is a piece of information about a specific stock option, where FRO is the stock ticker. The value of this option was calculated on September 7 using a method called finite-difference American revaluation, which is a way to estimate the value of an option. The calculation used the following numbers: stock price of 46.15, volatility of 0.408179926, interest rate of 0.04, and dividend yield of 2.61. This calculation was done for the opening price on September 18, with 14 out of 42 days left on the calendar. The calculation used 2400 space steps and 1800 time steps, and also took into account the exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices from September 4 were used as a reference, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which is the assumed cost of buying or selling the option. The result of the calculation is: the option has a bid price of 1.97, an ask price of 3.68, a fair value of 2.392798186916099, and a net value of -128.92018130839006. Note that the calculation does not claim to predict the actual probability of the stock price moving in a certain way, and the display of the results may round very small positive values. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00044000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to estimate the value of a stock option. The values used were: stock price of 46.15, volatility of 0.408179926, interest rate of 0.04, and dividend yield of 2.61, as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 spaces and 1800 timesteps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices were based on indicative values from September 4. The net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed 0.20. The result was: the stock symbol is FRO261016P00044000, the bid price is 2.18, the ask price is 4.27, the fair dividend is 2.60329516281159, and the net fair dividend is -166.87048371884094. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00044000 option. On September 7, a finite-difference American revaluation, which is a method to calculate the value of an option, was done. The stock price was 46.15 dollars, the volatility, or sigma, was 0.408179926, the risk-free interest rate, or r, was 0.04, and the dividend yield, or D, was 2.61, all as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices were from September 4, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, before the exit spread, which is the difference between the prices at which you can buy and sell. This calculation does not claim to predict the probability of the option being executed or the physical probability of the underlying event. The float display may round very small positive values. The option details are: the ticker symbol is FRO261016C00044000, the bid price is 2.52 dollars, the ask price is 3.38 dollars, the fair value is 3.004920271950339 dollars, and the net fair value is -37.707972804966055 dollars. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00043000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to estimate the value of a stock option, and the result was a stock price of 46.15 dollars, a volatility, or sigma, of 0.408179926, an interest rate, or r, of 0.04, and a dividend yield, or D, of 2.61, all as of the September 18 open, with 14 out of 42 days on the calendar. This calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices as of September 4 were used, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars, which is the assumed cost of buying or selling the stock, before the exit spread, which is the difference between the prices at which a trader buys and sells a stock. The calculation does not claim to predict the actual probability of the stock price moving in a certain way, and the display of the results may round very small positive values. The result of the calculation was a bid price of 1.87 dollars, an ask price of 2.96 dollars, a fair value of 2.089596793567611 dollars, and a net value of -87.2403206432389 dollars. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00043000 option. On September 7, a finite-difference American revaluation was done. This is a method to estimate the value of an option, which is a contract to buy or sell a stock at a set price. The revaluation used the following numbers: stock price of 46.15, volatility of 0.408179926, interest rate of 0.04, and dividend yield of 2.61. This was done at the opening of the market on September 18, with 14 out of 42 days left on the calendar. The calculation used 2400 spaces and 1800 timesteps, and included exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices from September 4 were used, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus 0.20 dollars. The result was a fair value of 3.712179715096993 and a net value of -113.9820284903007. The bid price was 3.13 and the ask price was 4.85. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about FRO261016P00042000 independent stock-GBM value. On September 7, a finite-difference American revaluation was done, which is a method to estimate the value of a stock option, with the following results: the stock price was $46.15, the volatility, or sigma, was 0.408179926, the risk-free interest rate, or r, was 0.04, and the dividend yield, or D, was 2.61, all as of the September 18 open, with 14 out of 42 days on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices on September 4 were used as an indication, and the net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed $0.20, before the exit spread, which is the difference between the prices at which a trader buys and sells a stock. The calculation does not claim to represent the actual probability of execution or physical probability. The results are: the stock symbol is FRO261016P00042000, the bid price is $1.32, the ask price is $2.18, the fair dividend is $1.641947662942925, and the net fair dividend is -$54.00523370570751. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative

A news scan found the headline about the FRO261016C00042000 option. On September 7, a finite-difference American revaluation, which is a method to calculate the value of an option, was done for the stock FRO. The values used were a stock price of 46.15, a volatility, or sigma, of 0.408179926, an interest rate, or r, of 0.04, and a dividend yield, or D, of 2.61. This was calculated at the September 18 open, with 14 out of 42 days left on the calendar. The calculation used 2400 space steps and 1800 time steps, with exact dividend jump interpolation, which is a way to account for dividend payments. The ask and bid prices from September 4 were used as indicative prices. The net value was calculated as 100 times the difference between the fair value and the ask price, minus an assumed 0.20. The result was a fair value of 4.505428249511902 and a net value of -54.65717504880978. The bid price was 3.88 and the ask price was 5.05. https://runway.adityaperswal.workers.dev/data/option-chain/FRO?feed=indicative