5. The next question deals with a different type range option, called a range accrual option. Range accrual options can be used to take a view on volatility directly. When a trader is short volatility, the trader expects the actual volatility to be less than the implied volatility. Yet, within the bounds of classical volatility analysis, if this view is expressed using a vanilla option, it may require dynamic hedging, otherwise expensive straddles and must be bought. Small shops may not be able to allocate the necessary resources for such dynamic hedging activities. Instead, range accrual options can be used. Here, the seller of the option receives a payout that depends on how many days the underlying price has remained within a range during the life of the option. First read the following comments then answer the questions. The Ontario Teachers’ Pension Plan Board, with CAD72 billion (USD48.42 billion) under management, is looking at ramping up its use of equity derivatives as it tests programs for range accrual options and options overwriting on equity portfolios. The equity derivatives group is looking to step up its use now because it has recently been awarded additional staff as a result of notching up solid returns, said a portfolio manager for Canadian equity derivatives. . . . With a staff of four, two more than previously, the group has time to explore more sophisticated derivatives strategies, a trader explained. Ontario Teachers’is one of the biggest and most sophisticated end users in Canada and is seen as an industry leader among pension funds, according to market officials. A long position in a range accrual option on a single stock would entail setting a range for the value of the stock. For every day during the life of the option that the stock trades within the range, Ontario Teachers would receive a payout. It is, hence, similar to a short vol position, but the range accrual options do not require dynamic hedging, and losses are capped at the initial premium outlay. (Based on an article in Derivatives Week).

(a) How is a range accrual option similar to a strangle or straddle position?

(b) Is the position taken with this option static? Is it dynamic?

(c) In what sense does the range accrual option accomplish what dynamic hedging strategies accomplish?

(d) How would you synthetically create a range accrual option for other “vanilla” exotics?