# Change in Option Price given Change in Implied Volatliity, Moneyness, and Maturity

I have an implied volatility surface parametrized into moneyless-maturity coordinates. At each period of time, I only have access to an option's moneyness (K/S), maturity, and change in implied volatility (defined as $$\Delta I_t(\xi,\tau)=I_{t+1}(\xi,\tau)-I_t(\xi,\tau)$$), where $$\xi$$ is the moneyness, $$\tau$$ is maturity. I want to find the change in an option's price (from period t going to t+1) via the Black-scholes formula. I know that the Vega of the formula times the change in implied vol gives the change in price, but to calculate Vega you need the actual volatility, in this setting we only have access to the changes in implied volatility. How can I find the change in price under this setting?

• You mentioned the vega times the change in implied vol gives the change in price. This is the price change due to changes in IV, not the change in price from the change in time (which is what you are looking for). It seems like what you require is the theta (the change in option price due to time passing). Does this help? Commented Aug 1 at 6:15
• How do you only have access to the change in IV. A vol surface is never defined in terms of changes over time. To get to $\Delta I_t$< you need the inputs on the right hand side. If you really don't have that, I would invest in a system that has that. Commented Aug 1 at 7:40
• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
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Commented Aug 8 at 20:04