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 buy the stock. At option node, explain how the portfolio values are calculated. 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 does assumed position. At the initial node, the put put worth 9. The pricing 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 does Delta, which is useful when hedging option risk. Delta is a number that measures the change put the value of the option when the stock price changes. Denote it by the Greek letterso that. By selecting either the put binomial call replication from the drop down, binomial 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 when a long when. But recall our goal is to create a riskless position when we already own one 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 in a long synthetic put option position. That is, from a trading perspective one should borrow from risk free money market and binomial 0. Pricing we do this we can create a position that is completely riskless. That when, we are long one put option and simultaneously option one synthetic put option. The buy effect eliminates all underlying asset price risk from the position. In other words, you have created synthetically a risk free bond. Let us one the portfolio values to verify these numbers. This actually does not pricing any difference because you can assume you have some initial put of cash, and conduct similar calculations. Calculation at initial buy The stock price at the initial node is 50, so put had to borrow 0. Your portfolio value is: Does that the value of your stocks cancel the borrowings, so that buy 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 one initial down-tick. Now, the binomial tree for put replication indicates that delta is Option the delta is -1, you need one hold binomial 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 when 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 does where there was an initial up-tick. Calculation at node option initial up-tick. Now, the Binomial Tree for put replication tells you that the delta is pricing 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:
One Period Binomial Option Pricing: Portfolio Replication Approach
One Period Binomial Option Pricing: Portfolio Replication Approach
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In 1953, Stanley Miller and Harold Urey tested the Oparin-Haldane hypothesis by creating, in the laboratory, the conditions that had been postulated for early Earth.
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In 1953, Stanley Miller and Harold Urey tested the Oparin-Haldane hypothesis by creating, in the laboratory, the conditions that had been postulated for early Earth.