A market-trader uses delta hedging for managing the exposure of an option position. On day zero, the market-maker sold 100 call options on a non-dividend paying asset, with a maturity date of 91 days and an exercise price of $102. The current price for the underlying asset is $110 and its annual volatility is 35%. The continuous annual risk-free rate is 6%.

a) Explain how dynamic hedging works. (20% weighting)

(b) Determine the appropriate number of units of the underlying asset that the marketmaker should hold on day zero for hedging the exposure. How will he fund this stock purchase? (30% weighting)

(c) On the following day, day one, the price of the underlying asset increases to $111.5, but all other factors remain unchanged except the number of days until maturity. What is the gain or loss yielded by the hedging strategy? Discuss why a gain or loss has occurred. (40% weighting)

(d) The market-maker accepts in full the gain or absorbs the loss yielded by the hedge and re-calculates the hedge ratio.

Determine the appropriate number of units of the underlying asset that the market-maker should hold on day one for hedging the exposure.  (10% weighting)