Problem 4. In plain English, dynamic delta trading is the construction of positions that do not react to small changes in the price of the underlying asset. No matter if the underlying asset goes up or down, the position maintains its value and neither increases nor decreases in price. In options trading, this is also known as Delta Neutral Hedging or Delta Neutral Trading. Delta Neutral Trading and Delta Neutral Hedging are for option traders who wants no directional risk nor bias. Why would anyone want to put on a position that does not react to movements in the price of the underlying asset? That's the magic of options trading! Bankers or market-makers who have sold options for good prices can protect their sales profits if the options position isn't reacting to changes in the price of the underlying asset. The mechanism of delta hedging can be seen clearly in a binomial model, in which the result of the hedge is perfect. However, this perfect hedge is not realistic in real world where the prices move continuously. The stock of Binomial Hedge Inc. is currently priced at $680 with volatility of 30%. The risk-free interest rate is 2%. Consider a binomial tree of this stock price with three-month time steps. Also consider a European call option that strikes at $700 and matures in six months with two-step tree below. (a) What are the stock prices and option values on the nodes of the tree? (b) What are the delta and share purchase/sale on each node of the tree? (c) What is the position in cash on each node of the tree? (d) What is the net value of the hedged portfolio on each node of the tree? (e) What is the average performance ratio of the hedging strategy? What is the standard Assignment 5: page 3 deviation of the performance ratio? Problem 4. In plain English, dynamic delta trading is the construction of positions that do not react to small changes in the price of the underlying asset. No matter if the underlying asset goes up or down, the position maintains its value and neither increases nor decreases in price. In options trading, this is also known as Delta Neutral Hedging or Delta Neutral Trading. Delta Neutral Trading and Delta Neutral Hedging are for option traders who wants no directional risk nor bias. Why would anyone want to put on a position that does not react to movements in the price of the underlying asset? That's the magic of options trading! Bankers or market-makers who have sold options for good prices can protect their sales profits if the options position isn't reacting to changes in the price of the underlying asset. The mechanism of delta hedging can be seen clearly in a binomial model, in which the result of the hedge is perfect. However, this perfect hedge is not realistic in real world where the prices move continuously. The stock of Binomial Hedge Inc. is currently priced at $680 with volatility of 30%. The risk-free interest rate is 2%. Consider a binomial tree of this stock price with three-month time steps. Also consider a European call option that strikes at $700 and matures in six months with two-step tree below. (a) What are the stock prices and option values on the nodes of the tree? (b) What are the delta and share purchase/sale on each node of the tree? (c) What is the position in cash on each node of the tree? (d) What is the net value of the hedged portfolio on each node of the tree? (e) What is the average performance ratio of the hedging strategy? What is the standard Assignment 5: page 3 deviation of the performance ratio