I know there is a lot of content about this topic, but I have not seen a post which gives a satisfying answer to my problem.

I am trying to hedge a European call option with real market data under the Black-Scholes model (or Bachelier model - it does not matter right now).

I have for every trading day a discount curve and a forward rate curve. Since my option runs only for 60 days ($T$=60), I decided to not distinguish between the both curves. I have the requirement to fix all parameters (and they should be constant for now) at the first trading day.

However, I need to calibrate my model to the market data. I think it is clear for the volatility, I look in the vol. surface and pick the exact vol. value (with maturity) for my option. Regarding the risk-free rate I wanted to do the same, look in the forward rate curve and get the rate $B(T)$ for the option maturity. Then I could draw $r$ by $$r = \frac{\log(B(T))}{T}$$.

But, would it be smarter to take $B(t)$ for $t$ being the first trading day after $0$? The "bank account" grows within the sort-rate, doesn't it? So I would take the first value of the forward curve to calibrate the risk-free rate. My intuition is, that the bank account would have maximal liquidity, since money in the bank account should be ready for transfers all the time.

My question is, which of the both approaches makes more sense? Have I forgotten something important?

Thanks for taking your time.


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