Delta hedging of put option. Delta hedging means trading something somewhere such that the portfolio's overall delta is zero (or neutral). This would be desirable if we did not want any exposure to changes in the price of the underlying security. So if we own a put option, typically we might expect its value to rise and fall with falls and rises (respectively).

Delta hedging of put option

Buying Puts to Protect Profits and Hedge Risk

Delta hedging of put option. I understand Delta Hedging of a call option, but when it comes to puts, I seem to get confused. More specifically how the Market Makers profit is different between calls and puts? Initial investment for call = S*Delta-C(S) Is the initial investment for puts the same? ie) S*Delta-P(S). I've been trying to think this.

Delta hedging of put option


Hedging is a term used in finance to describe the process of eliminating or minimizing at best the risk of a position. For example, take Vodafone stock. Your price risk would be reduced but you would now have exposure to currency and dividend risk. As mentioned, Option Delta represents the relative price movement that an option will experience given a one point move in the underlying.

Delta hedging this option position with shares means you would sell MSFT stock to offset the "deltas" of call options. As you are short deltas, your hedge would involve buying 4, shares of AAPL stock. The tricky part when using the delta of an option to determine the hedge volume is that the actual delta value is always changing. You might sell shares to hedge a delta value 0.

Now, your total position delta has increased to meaning you will need to sell another shares to square off the delta to zero. This changing of the delta can be measured and estimated by an other option Greek called option gamma. Let's go through an example showing the gamma effect on delta and the resulting hedging that is needed.

The delta of the call option is now 0. Your long 10 calls is now worth deltas. Your short ABC stock is worth - deltas. Total deltas of ABC Call option delta now 0. You are short shares of ABC. Total position delta Buy 10 calls 4. As the delta changes, the total position also changes resulting in the need to re-hedge.

In the example above the only input to the delta that changed was the underlying price. There are, however, keep in mind that there are four variables that will effect the delta of an option and hence change your hedge position; underlying price, volatility, time and interest rates. Increasing underlying price, vol and interest rates all increase the value of delta. The effect of Time value depends on the options moneyness.

If you;ve read the section on Option Charm you'll be aware that for in-the-money call options a decrease in time will increase the value of the option's delta; with less time to expiration, the already in-the-money option becomes even more likely to remain in-the-money. Conversely, a call option already out-of-the-money becomes less certain with each day that passes all other factors staying the same.

So, for ITM call options decreasing time increases delta your position becomes "longer" while your OTM call becomes shorter. For an ITM put option the delta is already negative, so as expiration approaches and the option becomes more likely to expire ITM the delta moves closer to As the stock price fluctuates, the implied volatility changing and the time to expiration ticks away, the delta is constantly changing, which raises the important question of how often and on what criteria do you hedge?

In theory, the idea is that you should hedge whenever the position delta is non-zero, so you transact with the underlying to bring the delta back to zero. However, the transaction costs involved in this level of trading prohibit its use in practice. Managing Vanilla and Exotic Options.

Hedging Options Using Option Delta As mentioned, Option Delta represents the relative price movement that an option will experience given a one point move in the underlying. The Gamma and the Delta The tricky part when using the delta of an option to determine the hedge volume is that the actual delta value is always changing. Factors Affecting Delta In the example above the only input to the delta that changed was the underlying price. Options What are Options? Where are Options Traded?

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