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2

A good reference book for FX conventions can be found from the book Foreign Exchange Option Pricing by Iain Clark. The 25% delta risk-reversal quote $\sigma_{25-RR}$ satisfies the system of equations \begin{align*} \begin{cases} \Delta_{call}(k_{25-call}, \sigma_{25-call}) &\!\!\!= 0.25\\ \Delta_{put}(k_{25-put}, \sigma_{25-put}) &\!\!\!= -0.25\\ \...

1

The values of implied volatility are deduced from option prices on the market. It is a market view of how the Black-Scholes prices should be modified due to various factors like fat tails in the probability distribution, supply and demand etc. If the prices are higher than those from BS, then sure the prices include a premium. The implied volatility ...

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You are an investment bank. You trade a multitude of vanilla and exotic options. You want to make sure the option prices you quote as a client are arbitrage-free with respect to liquid option prices quoted in the market $-$ and also consistent between the different trading desks within your bank. Basically you want to avoid other market participants taking ...

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The answer in Implied Vol vs. Calibrated Vol as suggested by noob2 is more complete. But it may be slightly misleading in your last example. I've been a vanilla option market maker for ten years, so I'll chime in on what I would mean by that. If a market maker says he's calibrating his vols to the market it means exactly what you're saying: getting prices ...

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