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Old 01-31-2018, 07:22 PM
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Default 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 Put-Call-Parity 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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Old 02-01-2018, 12:25 AM
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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 Put-Call-Parity 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?
Delta measures the change in the option's value corresponding to an increase in the stock price. As the stock price increases, the call option's payoff increases, thus the option's value will increase, making the call's delta positive. On the other hand, as the stock price increases, a put option's payoff decreases, thus the put option must decrease in value, making the put's delta negative.
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Old 02-01-2018, 11:12 AM
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Delta measures the change in the option's value corresponding to an increase in the stock price. As the stock price increases, the call option's payoff increases, thus the option's value will increase, making the call's delta positive. On the other hand, as the stock price increases, a put option's payoff decreases, thus the put option must decrease in value, making the put's delta negative.
I am looking at Exercises 12.37-38 from the Market-making and Delta-Hedging video lecture.

In the formula below for the value of the Call option, Abe uses a (-) sign for selling the 45-strike Call and a (+) sign for buying the 55-strike Call.

Shouldn't the sign be reversed? Selling= inflow of cash and Buying=outflow of cash?
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Old 02-01-2018, 12:20 PM
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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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Old 02-01-2018, 12:56 PM
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Originally Posted by Ren_St View Post
I am looking at Exercises 12.37-38 from the Market-making and Delta-Hedging video lecture.

In the formula below for the value of the Call option, Abe uses a (-) sign for selling the 45-strike Call and a (+) sign for buying the 55-strike Call.

Shouldn't the sign be reversed? Selling= inflow of cash and Buying=outflow of cash?
You are correct that selling results in a cash inflow and buying results in cash outflow. If you sell a call, you receive a call premium, so that's a cash inflow; if you buy a call, you have to pay a call premium, so that's a cash outflow. From a cash flow perspective, it's easy to keep things straight by associating positive signs with short positions and negative signs with long positions.

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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Old 02-01-2018, 02:33 PM
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You are correct that selling results in a cash inflow and buying results in cash outflow. If you sell a call, you receive a call premium, so that's a cash inflow; if you buy a call, you have to pay a call premium, so that's a cash outflow. From a cash flow perspective, it's easy to keep things straight by associating positive signs with short positions and negative signs with long positions.

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.

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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Old 02-02-2018, 04:59 PM
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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):
  • Whenever a problem deals with cashflow-related items such as net cash flow or profit/payoff.
  • To synthetically create an asset. For example, to synthetically create a long call option using the cash flow perspective, let -C be the variable of interest and move all other variables to the other side of the equation. Knowing that I'm using the cash flow perspective, it is easy to identify the cash flows needed to replicate the desired position.
  • To exploit arbitrage using the trick of moving everything to the greater than side of the inequality.
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