I have a binary option and want to calibrate it's BS pricing model. I only have a series of Strike Price vs the Option price, no knowledge on time to maturity, volatility, risk free rate or the underlying price. I have to predict option price for some out of sample set of strike prices. How would I go about calibration of such a model? Or is there some other approach?
I don't think Multi parameter optimisation makes sense here, no sense finding the optimal risk free rate.