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I am developing a vertical spread trading model. Looking for a way to calculate the stop loss price on the underlying asset for a given vertical spread at an arbitrary time t.

Using Black Scholes, I can find the predicted option price given the stock price and other inputs.

But finding the stock price for a given credit spread and on two options is different because:

  1. Need to find stock price from options.
  2. There are infinite number combinations of options prices for any given credit.

Example:

Open a credit spread 940/950 on AMZN trading at 894.88 with volatility 25.415% and 40 days remaining. The credit is $260.

According to this calculator, if the price rises to 920 on the first day, the loss is $106.

How can I calculate this quickly?

Currently I am calculating the loss at each price until I find the given loss, but this is very inefficient. It takes about 100 ms per credit spread for all days. I would like to filter 250 option chains, with each having perhaps 20 spreads. So about 5,000 credit spreads.

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How can I calculate this quickly?

A quick way would be to look at 10 point spread prices with different strikes and different expirations.

For example, what is the price of the 920/930 spread for next week? This would be equivalent to AMZN moving up 20 points in 7 days. Assuming Vol does not change significantly it should give you a ballpark figure and all you have to do is pull quotes and calibrate it to your positions strike and expiry.

Of course, there are other ways but this quick due the fact that there are no calculations to make.

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    $\begingroup$ I will always remember my 1st day as a Quant at a hedge fund. Someone asked "what would the price of such-and-such S&P call option be if S&P dropped by 10 points?". I thought I could easily set up a simple model to answer this, but before I could open Excel, a colleague blurted out "16 dollars and 23 cents". I thought how did he do it, and he doesn't even have a PhD? Later I understood that (just like amdopt is suggesting) he had just looked up on Bloomberg the market price of a call option with a strike 10 above the one in the original question. (Implictly assuming unchanged vol). $\endgroup$
    – Alex C
    Apr 10, 2017 at 0:18
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    $\begingroup$ @AlexC I learned the same way! $\endgroup$
    – amdopt
    Apr 10, 2017 at 0:19

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