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Local Volatility Surfaces and Vanilla Options Market Making

Article Quant Q&A · Author: Tim
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Summary

The exchange gives a brief introduction to local volatility in the context of vanilla options. It describes volatility as depending on the underlying price and time, which can be represented as a surface, and frames the model as a way to relate an assumed volatility to a future option price. The response then recommends considering stochastic-volatility models for market making in plain vanilla options.

The explanation is very limited and does not derive a local-volatility model, explain how to infer it from option prices, or compare model behavior in pricing and hedging. Its description of local volatility as both price-and-time dependent and constant is imprecise, and the recommendation is unsupported by examples or evidence. It is best read as an introductory pointer: local volatility and stochastic volatility are different modeling approaches, and the brief answer alone is insufficient guidance for choosing a market-making model.

Key ideas

  • Local volatility models represent volatility as a function of the underlying price and time.
  • A local-volatility surface relates market state variables to option valuation assumptions.
  • The response suggests stochastic-volatility models for vanilla option market making.
  • The post provides no derivation, empirical comparison, or implementation guidance.

Tags

OptionsVolatilityDerivatives pricingMarket making
Full text
# does local volatility make any sense when I only focus on vanilla option?


# does local volatility make any sense when I only focus on vanilla option?












can someone explain me the usage of local volatility? details will be appreciated. Is it of any importance when I now are doing market-making? Please do not laugh at me as I am totally new in this field.

## Answer by arodrisa (score 1)

https://quant.stackexchange.com/a/22317

Local volatility trats volatility as a function of price (St) and time (t), considering volatility constant.

It means that you are building a volatility surface depending on price and time.

What you are doing is given a certain value of volatility, what will be the price in Xdays long, or viceversa.

If you are dong market making with plain vanilla options, I will advice you to use Stochastic Volatility models.

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