[944] About HW6 Q2

[Gautam Iyer]

I'm not sure I follow everything you ask. But let me clarify that you
hedge using the delta hedging rule with the implied volatility (as
written in the problem).

My understanding of your question is that you got

    dX = (something) dt + 0 dW

and are worried you have a portfolio with arbitrage?

This is no contradiction. The setup of the problem assumes call options
are priced "wrong"! (Explicitly call options are priced assuming the stock
price is a GBM with volatility sigma_1; however the stock price is
modeled as a GBM with volatility sigma_2.)

If call options are priced "wrong", there will necessarily be arbitrage
in the market.

Best,

Gautam

-- 
Thanks to Disney I am going to have to listen to Star Wars fans complain
for another decade.