Define the term correct delta with an example

Question

Define the term correct delta with an example?

Answer 1

The implied volatility is 20% but you think that is cheap and volatility is nearer 40%. Do you put 20% or 40% into the delta calculation? The stock then moves, should you rebalance, incurring some inevitable transactions costs, or waits a bit longer while taking the risks of being un-hedged?

Let’s implied volatility is as of a call option 20% but you believe volatility will be 40 percent. Does 0.2 or 0.4 go into the Black–Scholes delta computation or perhaps something extra? Firstly reassure that you would not theoretically lose money in either case (or even though you hedge using volatility somewhere in the 20 to 40 ranges) so long as you are right regarding the 40% and you hedge incessantly. However there will be a big impact on your P and L depending on such volatility you input.

If you utilize the actual volatility of 40 percent then you are guaranteed to make a profit that is the difference among the Black–Scholes formula using 40 percent and the Black–Scholes formula using 20 percent.

V(S, t; σ) − V(S, t;˜ σ),

Here V(S, t; σ) is the Black–Scholes formula for the call option and σ shows actual volatility and ˜ σ shows implied volatility.