Suppose a stock price is $51, a call option has a strike price of $50 and the calls market price is $ 3. A dealer sells one call option contract (for 100 option-shares). The original Delta is .50. Assume the dealer immediately sets up a Delta Hedge, using shares of stock. There is NO rebalancing in this problem. We examine what if the stock price changes, and there is no re-hedging.

(a) How many shares should the dealer buy or sell (say which) to begin? (100*0.50)

NOTE - for (b) and (c), there is NO rebalancing the dealer stays hedged as in (a).

(b) What is the Delta-Expected change in the value of the dealers option position, stock, and overall value , if the stock price immediately FALLS by $ 1 from $51 to $50 ?

(c) (Ignore part b) If the stock price quickly rises to 60, explain what is likely to happen to the value of the dealer's stock, option, and overall position / and why / mentioning Gamma.