You are long 1000 six months ATM Put options on a non-dividend-paying asset with spot price $100, following a lognormal process with volatility 30%. Assume the interest rates are constant at 5%.
(a) Delta-hedge your option position. Explain what you have to do (including borrowing or lending money).
(b) On the next trading day, the asset opens at $102. What is the value of your hedged position (the option and shares position)?
(c) Had you not Delta-hedged, how much would you have lost?