Delta hedging a put option

Delta hedging a put option

Posted: SMR.A Date: 26.06.2017

In the 2-period binomial model, suppose you hold one put option. C onstruct a trading strategy that lets you hedge the risk of this put using the stock. At each node, explain how the portfolio values are calculated.

delta hedging a put option

To conduct this exercise, run the Binomial Tree Module from the Virtual Classroom page. The above displays the values of the put option at each node, which is the value of your assumed position. At the initial node, the put is worth 9. The put value after an up-tick is 4.

Our objective is to hedge the put option's price risk using the underlying stock. First, we will define a number referred to as Delta, which is useful when hedging option risk. Delta is a number that measures the change in the value of the option when the stock price changes.

Denote it by the Greek letterso that.

By selecting either the put or call replication from the drop down, the Binomial Tree Module will display the delta of the selected option at each node. For the current example put replication results in the following tree: This means that to replicate a long i.

But recall our goal is to create a riskless position when robot trading strategies already own one put option.

delta hedging a put option

How do we do this? The answer to is to replicate a short i. To do this requires that we change the signs stock market forum in philippines a long synthetic put option position.

delta hedging a put option

That is, from a trading perspective we should borrow from risk free money market delta hedging a put option buy 0. If we do this we can create a position that is completely riskless. That is, we are long one put option and simultaneously short one synthetic put option.

Delta hedging with options | supuwufif.web.fc2.com

The net effect eliminates all underlying asset price risk from the position. In forexadvisor opinioni words, you have created synthetically a risk free bond.

Let us calculate the portfolio values to verify these numbers. This actually does not make any difference because you can assume you have some initial amount of cash, and conduct similar calculations.

Calculation at initial node: The stock price at the initial node is 50, so you had to borrow 0.

How can you use delta to determine how to hedge options? | Investopedia

Your portfolio value is: Notice that the value of your stocks cancel the borrowings, so that your portfolio value equals the value of the put option you started with. Suppose there is a down-tick in period 1: Suppose there is an up-tick in period 1: Calculation at node after initial down-tick. Now, the binomial tree for put replication indicates that delta is Since the delta is -1, you need to hold one stock when you leave this node.

Since you have 0. The stock price is 25, so you have to borrow an additional 0. Let us see what happens when you do buy the additional stocks. If there is a subsequent down-tick so there was a down-tick followed by a down-tickyou position will be: If there is a subsequent up-tick so there was a down-tick followed by an up-tick: Now, let us complete the calculation for the case where there was an initial up-tick.

Options and Delta Hedging

Calculation at node after initial up-tick. Now, the Binomial Tree for put replication tells you that the delta is Since the delta is You started with 0. Let us see what happens. If there is a subsequent down-tick so there was an up-tick followed by a down-tick: If there is a subsequent up-tick so there was an up-tick followed by an up-tick:

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