Pricing Formula Black-Scholes (Underlying Price)

F

frostengine

If I have a set of historical option data with IV, option price, date etc... But I don't have the underlining price of the stock, I should be able to figure that price out correct?

Does anyone know the formula I would use to get the underlining price of the stock when all other variables are known?
 
You can reverse the BSM model for the price, or you may be able to do this easier:

Exp(-RT) * X + (C-P)

Assuming you have good Interest rate data (such as LIBOR) for R. C & P are the Call and Put prices (Mid prices may be adequate), and X= Strike, while T is time to expiration.
NOTE: This derivation is not dependent on IV, which is often incorrect! -- This uses CALL PUT parity for resolving, which is fairly good with SPX or RUT options.
Should you find issue with this for SPX options, please PM me!
 
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If you have the put and the call... and if you know if there is/was a dividend between the historical date and maturity of the options... you should be able to work it out. You don't need IV then...

If you don't have both call and put price, than you need the IV... but than that IV should be correctly modelled by whoever provided the data... and you need to know which model they used...

What do you have?
 
frostengine said:
If I have a set of historical option data with IV, option price, date etc... But I don't have the underlining price of the stock, I should be able to figure that price out correct?

Does anyone know the formula I would use to get the underlining price of the stock when all other variables are known?
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As stepandfetchit said, you can reverse the BSM formula. But there is no exact closed-form equation (I am not smart enough to work one out) for the reverse. If you know how to program in VBA and Excel, stepandfetchit was kind enough to show me how to program in VBA, then you can iterate to get the underlying price if all other parameters are known.

However, I am puzzled, historical option data with IV option price, date etc are very difficult to get whereas underlying prices of the stock are very easy, Yahoo Finance or Google Finance have them and you can download directly into your Excel spreadsheet to merge with your other data.

There must be something I am missing here. Are you another one of those that day trade options?
 
I have subscribed to a service where I am downloading the full option chain every 15 minutes. This option chain is NOT the price at that exact instant.. but delayed some amount of time, sometimes 15 minutes delayed, sometimes longer. The problem is, the option chain data does not contain the price of the underlying stock. While I have a general idea what the stock price was by pulling historical data, I can't match it 100% to the time period of the option chain.

Therefore, I was trying to figure out a way to know the price.
 
Ah! You will need slightly different formulas, depending on Dividends (discrete or continuous), and the amount of the dividends. The formula above produces a value which can be put back into the B&S formula in place of underlying price, for continuous dividends, such as SPX, without having to quantify them, by specifying the yield input to B&S as zero. However, this value is not the SPOT, but the SPOT adjusted for dividend, so another step is needed to get the SPOT price. Hopefully JackRab has this already handy, else I can dig up some papers that hopefully will shed some more light.
For accuracy, you must approximate the interest rate adequately!!! I use LIBOR rates, which are close enough for my purposes for options out to about 3 months. If you need to go out to a year or so, you will need better interest rate approximations than LIBOR. -- LIBOR rates avail from FED Reserve. "https://fred.stlouisfed.org/"
 
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ironchef said:
There must be something I am missing here. Are you another one of those that day trade options?
More...
frostengine said:
I have subscribed to a service where I am downloading the full option chain every 15 minutes. This option chain is NOT the price at that exact instant.. but delayed some amount of time, sometimes 15 minutes delayed, sometimes longer. The problem is, the option chain data does not contain the price of the underlying stock. While I have a general idea what the stock price was by pulling historical data, I can't match it 100% to the time period of the option chain.

Therefore, I was trying to figure out a way to know the price.
More...
I see, you are day trading options. I think your brokerage maybe able to provide you min by min underlying data.
 
stepandfetchit said:
Ah! You will need slightly different formulas, depending on Dividends (discrete or continuous), and the amount of the dividends. The formula above produces a value which can be put back into the B&S formula in place of underlying price, for continuous dividends, such as SPX, without having to quantify them, by specifying the yield input to B&S as zero. However, this value is not the SPOT, but the SPOT adjusted for dividend, so another step is needed to get the SPOT price. Hopefully JackRab has this already handy, else I can dig up some papers that hopefully will shed some more light.
For accuracy, you must approximate the interest rate adequately!!! I use LIBOR rates, which are close enough for my purposes for options out to about 3 months. If you need to go out to a year or so, you will need better interest rate approximations than LIBOR. -- LIBOR rates avail from FED Reserve. "https://fred.stlouisfed.org/"
More...
You and others here taught me how to program in VBA so I could iterate the BSM to obtain the risk free rate the MM used. He could do the same with stock price if all other parameters are known. It is time consuming but doable.

Also, my brokerage actually used BSM to "represent" all the parameters and I think for day trading, he/she should not have to worry about dividend/or dividend rate unless the date he/she models, etc. is very close to ex-dividend.

To the OP, may I ask why you want to day trade options?
 
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