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#1




Delta Hedging  Buying and Selling a Call Positive or Negative Sign?
I am on the delta hedging chapter and I am completely confused by the positive/negative sign convention when calculating the value of a CALL option.
When calculating the value of a portfolio of multiple CALL options, I thought BUYING a call should equate to a () sign to quantity*premium and SELLING a call option should equate to a (+) sign to quantity*premium. I am thinking about this from a cash flow perspective and this seems to be how it is calculated within PutCallParity context. When it comes to the sample problems for Delta Hedging questions, it seems that they reversed the +/ sign convention when calculating the total value of the options in a portfolio. Why is this?
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#3




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In the formula below for the value of the Call option, Abe uses a () sign for selling the 45strike Call and a (+) sign for buying the 55strike Call. Shouldn't the sign be reversed? Selling= inflow of cash and Buying=outflow of cash?
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#4




Don't quote me on this as I am actually studying for the March exam as well. But I think it depends on which side you're looking at. In this case, I think he took the view of the writer of the call. It was like that for me too when I had questions that asked about bull spreads or bear spreads. Would someone be able to verify my answer?
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#5




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However, when dealing with an ongoing position in a portfolio, it is usual to associate positive signs with long positions and negative signs with short positions. This is because a negative cash flow from the long position today will result in a positive cash flow in the future. To illustrate this point, consider an example. Suppose you buy a call option today. Recall the delta of a long call = Change in the value of the call / Change in the stock price. If the price of the stock goes up by $1 in the future, then the value of the call option in the future up would go up by $Delta. So, a negative cash flow from the long position today will result in a positive cash flow in the future. This is why we associate positive signs with long positions. 
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That makes sense. For the purpose of this exam, what is an easy way for us to remember when to use the cash flow perspective and when to use the position in a portfolio perspective? If a question involves using Put call parity, we would approach buying/selling calls from a cash flow perspective? If a question asks us to calculate the total value of a portfolio, I assume that means we approach buying/selling calls from a portfolio value perspective?
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#7




These are the 3 common cases in which I'd use the cash flow perspective (i.e., associate positive signs with cash inflows and negative signs with cash outflows):

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