Interpolating Inputs for Vanna–Volga Option Pricing

Summary

The document asks how to apply the Vanna–Volga method when market inputs are quoted for discrete maturities. The desired outputs are an option premium and delta for a specified spot, strike, and expiry, using domestic and foreign rate curves and implied volatilities for delta-defined options and at-the-money options. The central choice is whether to interpolate the inputs to the target expiry before calculating the price, or calculate prices across a grid and interpolate the resulting smile or surface.

No answer or comparison of the two workflows is provided, so the document offers no evidence that one method is more accurate. It highlights a practical modeling question: input interpolation and price interpolation need not produce identical results. Any implementation would need consistent rate and volatility conventions and validation against market quotes; the post raises these considerations but does not resolve them.

Key ideas

• The question concerns Vanna–Volga pricing from discrete maturity and volatility quotes.
• The requested outputs are an option premium and delta for a chosen spot, strike, and expiry.
• One approach interpolates rates and volatilities before calculating the option value.
• Another approach calculates a grid of option values and interpolates the resulting surface.
• The document provides no answer or evidence comparing these approaches.

Tags

# Should I interpolate before or after to find option price using Vanna-Volga method?


# Should I interpolate before or after to find option price using Vanna-Volga method?












I am trying to calculate the implied option premium $C(K)$ and $\Delta$ using the procedure outlined by Castagna and Mercurio in this paper - http://www.fabiomercurio.it/consistentfxsmile.pdf

My question is if I am given a range of option premiums for different maturities, and a swap curve for domestic and foreign rates, should I build the Vanna Volga option premium smile for a range of maturities $T$s and strikes $K$s and then interpolate to find the Vanna Volga option premium from this smile/surface or is it better to interpolate each item of my inputs to find the inputs at the correct maturity $T$ and then calculate the option premium without building a matric for a range of $T$s and $K$s.

### Given

- risk-free rates for specific Ts from 0, 1wk, 2wk, ..., 2y etc.

- $\sigma$ for $ \sigma_{\Delta25p} $, $ \sigma_{\Delta25c} $, $ \sigma_{\Delta_{ATM}} $

### Input

$S_0$, $K$, and $T$

### Output

$C(K)$ and $\Delta$

So, to clarify I want to kow whether I should interpolate to find a specific risk-free rate and $\sigma$ for a specifc $S_0$, $K$, and $T$ first or to interpolate the smile once I have calculated the above for a range of $T$s and $K$s.

Thanks

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