Q. Assume a call option’s strike price is initially equal to the price of its underlying asset. Based on the binomial model, if the volatility of the underlying decreases, the lower of the two potential payoff values of the hedge portfolio:
- decreases.
- remains the same.
- increases.
Answer- option (2)
Please explain.
If volatility decreases, then the two possible stock price in .aturity would be less extreme..
I mean if So was 500 and the possible.prices were , say, 20% up or down, they were 600 and 400
But due to decrease in volatility, two prices would be say 10% up or down say 550 and 450.
Due to a higher price on the downside ie 450 instead of 400, payoff of the hedged portfolio ( C- and delta S+ will increase.
Incase the last part is not clear…
Let me explain elaborately…
Option was ATM( given in the sum)
So in case of down move, call will lapse..and payoff would by selling delta shares…so delta × 400 earlier but delta × 450 now.
So u see how payoff will increase…
It’s a superb question…thanks for asking the same.