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FX Vanilla Option Pricing with Black-Scholes Implied Volatility

Article Quant Q&A · Author: Henry
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Summary

The discussion explains how Black-Scholes is used in over-the-counter FX vanilla options. Market quotes commonly express implied volatility in delta space; traders convert those quotes into prices using the relevant market inputs, such as spot, rates, and the volatility surface. Bid and ask quotes can produce prices that differ from a mid-market estimate.

For a vanilla option, the implied volatility is the Black-Scholes volatility that reproduces its quoted price. A more complex model is generally introduced for derivatives whose features require it, such as barriers or time-dependent payoffs, and is calibrated to the vanilla surface. The document cautions that different surfaces and market inputs can explain pricing discrepancies across dealers. It offers practitioner context rather than a detailed derivation or quantitative comparison of models.

Key ideas

  • FX vanilla options are commonly quoted using Black-Scholes implied volatility in delta space.
  • Implied volatility quotes can be converted into option prices using market inputs such as spot and interest rates.
  • Bid and ask quotes can differ from a price calculated from the mid-market quote.
  • Local volatility or stochastic-local-volatility models are used for more complex derivatives and calibrated to vanilla option data.
  • Dealer prices may differ because their market inputs and volatility surfaces differ.

Tags

ForexOptionsVolatilityDerivatives pricing
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# Option Pricing Question - Black Scholes


# Option Pricing Question - Black Scholes












This might be a naive question because I haven't really worked on the pricing of vanilla options before.

In particular I'm interested in FX European-style vanilla options. Let's say it's a call option with 3-month time to maturity T and converted strike K (delta quote converted into strike quote).

Once I build a volatility surface using whatever arbitrage-free techniques,

- Do we simply interpolate/extrapolate that surface using T and K to get a single number, say 9%, and plug this number into Black Scholes formula to get a price? If we use Monte Carlo to generate the paths of underlying, this also means every time step, we use the same volatility.

Or

- We use the whole surface. This means, when we use Monte Carlo, for every time step we interpolate a volatility from the surface. This means we use all points from 3M, 2M 28D, 2M 27D,...,1D. Of course, we can use Local Vol/SLV or more advanced models.

I know I certainly don't do this in exotics, but that's because I never use Black Scholes formula for exotics.

What I'm guessing is, Black Scholes formula is never used in instrument pricing as a practitioner (top buy-side firms or top investment banks), but only used in conversion between implied volatility quotes and price quotes.

Thanks for all the help!

## Answer by AKdemy (score 2)

https://quant.stackexchange.com/a/83616

FX markets are predominantly OTC.

However, it's consensus to quote in Black Scholes IV in delta space. See https://quant.stackexchange.com/a/77802/54838 for details. The referenced paper by Wystup and Reiswich is in my opinion a mist read for anyone involved with FX options.

Therefore, you have the price (quote in terms of Black Scholes IV). Bid and ask will make the actual RFQ different from mid but you can also show sided pricing.

As mentioned, https://quant.stackexchange.com/a/70296/54838 shows how IV translates into price.

The discrepancies in pricing that you observe is due to the nature of OTC. A different vol surface, different spot, different interests rates etc will give you a different price. You can check if you have access to the vol surface of the MM on OVDV. You can also ask the bank to explain a difference but in my experience it's very similar for liquid pairs.

For digitals, see https://quant.stackexchange.com/a/74544/54838 and https://quant.stackexchange.com/a/68264/54838.

If you add more complex models, you just add a modelling error (with regards to price). The vanilla IV is the IV that yields the price. If you use more complex models, it's because of the nature of the derivative (time dependent, barriers etc). However, you still rely on the vanilla surface to calibrate your LV or SLV model.

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.