Read the article "When Stocks Dither, 'Buy Write' and 'Covered Call' Funds May Deliver". When Stocks Dither, 'Buy Write' and 'Covered Call' Funds May Deliver Stocks are off to a bumpy start in 2014, but there is one group of stock-fund managers who see a sideways market as their time to shine: managers who layer on options strategies as a way to earn extra investment income. For the past couple of years, so-called buy-write and covered-call funds have been left in the dust by the big stock-market rally. That is because those options strategies limit potential gains in exchange for the income they generate. But with the S&P 500 up just 1.3% in the first quarter, and with many investors expecting a more volatile market going forward, options strategies could be coming back into favor. Taking the market outlook into account, "we're hitting a sweet spot," says Kevin Amell, a portfolio manager for Eaton Vance Corp. funds that use option strategies, such as its $38 million Eaton Vance Risk-Managed Equity Option. The fund was down 0.25% for the year through March 31. These types of funds employ different variations on the strategy, but the basics are the same. They start by building a portfolio out of individual stocks or a basket of stocks meant to outperform a benchmark such as the S&P 500. The fund then sells "call" options against those stocks. If those stocks rise in value beyond a specified "strike" price, the fund pays the option buyer the difference between the equity price and the strike price. If the stock falls or doesn't rise enough to hit the exercise price, the fund keeps the income paid by the option buyer. The idea is that over the long term, an investor will earn stock- like returns with fewer ups and downs. The chief drawback is that this strategy caps gains in the kind of big stock rally seen during 2013, when the S&P 500 rose 30%. Since early 2013, volatility as measured by the Chicago Board Options Exchange Volatility Index, or VIX, has generally been below its long-term average. Volatility is a key variable in options pricing. In a market with bigger price swings, options sellers can demand higher premium payments. With the drag of the options positions, "it's been very difficult to keep up," says Mr. Amell at Eaton Vance, which manages a number of closed-end mutual funds using options strategies, the open-end Risk-Managed Equity Option rose 15.5% in 2013. In 2012, when the S&P 500 was up 16%, the fund rose 3.3%. Some funds in the space have had a hard time attracting investors. The six-year-old PowerShares S&P 500 BuxWrite exchange-traded fund has $241 million in assets, and the nearly seven-year-old iPath CBOE S&P 500 BuyWrite Index exchange-traded note has just $10 million. The granddaddy among these funds is the $8.1 billion Gateway Fund, which launched in 1977 and returned 8.4% last year, Michael Buckius, a portfolio manager of the fund, feels confident that the stock market will be more prone to back-and- forth swings in coming years than it has been for the past two years. In large part, he says, that is because the Federal Reserve's aggressive efforts to pump easy money into the financial markets have helped cushion stock-market declines. Gateway is up 0.5% this year, through March 31. Now, as the Fed begins to pull back on its easing efforts, "volatility should tick back up," he says. In that environment, he adds, options strategies should provide the kind of performance "that always gets lost in a big bull market." Answer the following questions. Michael Buckius said that 'volatility should tick back up. Discuss which option trading strategy is the most profitable if you expect that there will be a significant upward price movement. (7 marks) Question 2 | Suppose you are an option trader and are now considering the options on the shares of Tencent Holdings Limited. The current stock price of Tencent Holdings Limited is $120. It is expected that the stock price of Tencent Holdings Limited will go up by 20% or down by 20% over each of the next two six-month periods. The risk-free interest rate is 8% per annum with continuous compounding. a Determine the value of a one-year European put option on the shares of Tencent Holdings Limited with a strike price of $100 using a binomial option pricing model. (15 marks) b If the put option on the shares of Tencent Holdings Limited was American style, discuss whether you will exercise it early at any of the nodes on the tree. (10 marks) Using the put-call parity, determine the European call price of Tencent Holdings Limited if the European call option has the same strike price and expiration date as that of the European put option. (5 marks)