Hi,
If I want to estimate the expected price of a vanilla call or put option with strike K, tenor 3 months, in three months time what's the recommended (practical) approach?
If we assume stock price grows at expected rate x%, then a simple approximation might be to put the expected stock price in three month into Black-Scholes using the forward volatility derived from the three and six month implied vols.
Is this a reasonable approximation? Alternatively you could compute this expectation numerically by integrating the B-S formula wrt stock price or go down a stochastic vol approach etc. But it feels intuitively the approx should be reasonable.
Any thoughts appreciated.