Stress Testing Option Prices with Underlying and Implied Volatility Changes

Summary

The exchange discusses estimating an option’s future price after a specified move in its underlying when future implied volatility is unknown. One approach is to make explicit assumptions about both the underlying price change and the change in implied volatility, then reprice the option with the Black–Scholes formula using those stressed inputs. The model does not determine the volatility change; that assumption needs its own basis.

A simpler approximation uses the option’s current delta and vega, multiplying each by the assumed change in underlying price and implied volatility to estimate the price change. This linear method assumes the option price changes approximately linearly around today’s spot and implied volatility. The answer suggests treating rho and theta as negligible relative to delta and vega for the scenario, an assumption that may not hold for every option or horizon. The discussion does not establish a volatility forecasting model or provide evidence favoring local volatility.

Key ideas

• Black–Scholes repricing requires an assumed future implied volatility as well as an underlying price scenario.
• A scenario can estimate option value by repricing with stressed underlying and volatility inputs.
• Delta and vega provide a linear approximation to price change around current market conditions.
• The approximation assumes other Greeks, including theta and rho, are negligible for the scenario.

Tags

# Modelling option price change in N days


# Modelling option price change in N days












I need to understand how will my option price change if the price of underlying asset changes by, for example, 15% in 30 days. I would like to use BS formula, but in this case I know all parameters except implied volatility. The problem is that IV today will differ from IV in 30 days. How can I model that? Should I use local volatility model?

## Answer by JejeBelfort (score 1)

https://quant.stackexchange.com/a/32600

First you have to assume that the main drivers of your option price are its underlying value and implied volatility, meaning that greeks like rho and theta are negligible with reference to delta and vega.

Then, could you enlighten us on how you determine the underlying change? If your approach is sound for the underlying, and the one used to find the implied vol changes is sound as well, you can find the change in the option price by plugging these "stress" parameters into BS formula.

Otherwise just compute the delta and vega of your option today and deduce the new option price my multiplying the greeks with the variations of the underlying and implied vol of your choice (this assumes a linearization of the option price around the spot and the current implied vol).

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