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Estimating Vertical Spread Loss with Comparable Option Spreads

Article Quant Q&A · Author: B Seven
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Summary

The question concerns finding the underlying price at which a credit spread reaches a specified loss, using Black–Scholes option prices. The writer currently searches across underlying prices, which becomes slow when repeated across many spreads. The response proposes a quicker rough estimate: observe prices for a spread with different strikes or expiry that represents a similar underlying move over a similar time, then use that market quote to calibrate the estimate for the position being evaluated.

This is a market-based shortcut rather than an inversion formula or an exact risk calculation. Its illustration assumes implied volatility does not change substantially, and the answer describes the result as approximate. Differences in strike, expiry, volatility, and market conditions can limit how closely the comparison spread represents the target position; no measured accuracy or validation is reported.

Key ideas

  • A target spread loss can be related approximately to the price of a comparable spread after a similar underlying move.
  • Quotes from other strikes and expirations can provide a quick market-based estimate.
  • The suggested shortcut assumes volatility remains relatively stable.
  • The response gives no accuracy study and frames the estimate as approximate.

Tags

OptionsDerivatives pricingVolatility
Full text
# How to calculate vertical spread loss using Black Scholes?


# How to calculate vertical spread loss using Black Scholes?












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:

- Need to find stock price from options.

- 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.

## Answer by amdopt (score 3)

https://quant.stackexchange.com/a/33582

> 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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.