(Delta-Hedge / No Rebalancing) Suppose a stock price is $50, a call option has a...
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(Delta-Hedge / No Rebalancing) Suppose a stock price is $50, a call option has a strike price of $50 and the calls market price is $4. A dealer sells 10 call option contracts (for 1000 option-shares). The original Delta is .55
(a) What does our basic hedging logic say is the Dealers real risk and what should be generally done.
(b) To start a Delta Hedge, what should the dealer do NOW, and what should it cost ? (Hint-550 shares).
(c) After (b), if there is an immediate $0.50 rise in the stock price, what is the exact delta expected change in the dealers value of her long shares + written calls, and the combined overall change.
(d) Assume the dealer hedges as indicated in (b and c), BUT, the ACTUAL change in the option price is $0.30, to $4.30, not to the $4.275 you should have computed in (c). What is the exact ACTUAL change in the dealers value of her long shares + written calls, and the combined overall change.
(e) Again assume (b, not c), but the stock price rises by $5.00 to $55. The Non-ReBalanced delta hedge has a problem. Explain with logic and perhaps graph illustration what might happen due to the Gamma problem. An exact combined overall change is not needed.
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