Your firm makes market in options and you are responsible for managing a profitable options book. The problem you face is that if the order flow is continuous and regular your job is simple. A continuous and regular order flow ensures you can run a balanced book, lock in the spread and receive nice bonuses! Unfortunately, in reality you face a very irregular order flow and so success at your job relies upon your personal skill at managing the risk generated by your option's book.

For this exercise suppose your option trader has written 1000 at-the-money (approximately) call contracts, but it will take about 5-days before you can close out this contract as a market maker. For the purpose of the assignment you can assume that these options are written on any stock of your choice at the prevailing ask when you start this assignment. Thus you must hold this position for at least 5 days before you can unwind it as a market maker (i.e., at the prevailing bid at this time). In the mean time your task is to try and lock in the bid/ask spread by minimizing your position's exposure to risk.

In this assignment you can assume that for any hedging strategy that you use, you can always buy and sell all securities as a market maker. That is you get to sell at the ask and buy from your bid to your clients. For all calculations of implied volatility, and delta you should use the mid point of the prevailing bid ask spread as your estimate for price. Finally, for calculations of profit/loss again assume that you trade as a market maker.

Relevant background information for completing this task is provided at the end of this project.

1. Compute the option's delta at the time of writing the options using the midpoint between the bid/ask spread for the option price and similarly for the underlying's price. You can then compute the implied volatility, and other Greeks at the time of writing these contracts using Option Tutor.

In a spreadsheet maintain the following positions by adjusting your hedge as frequently as you want to. Note, assume that you can always adjust your position in the underlying asset as a market maker.

1. Delta neutral using the original implied volatility estimate.
2. Delta neutral using the implied volatility that you re-estimate at the time of adjusting your hedge.
3. Run this hedge for at least 5 trading days and then compute the following:

• Realized return from each hedged position i. and ii.

• Realized volatility (standard deviation) from fluctuations in the market value of each hedged position

• Plot the relationship between delta in part i. and deltas in part ii. over time.

• Plot the relationship between implied volatility in part ii., the underlying stock price and time.

• Compute the realized delta over the day as change in option price divided by change in stock price and plot delta in part ii. against realized delta over time.

In not more than three pages plus whatever appendices you want to include (e.g., the above data, plus any other strategy you deem to be relevant), answer the following: Under the market making assumptions above can you make a profit from this trade with minimal risk? Discuss this question including what exposures you face. Your report should commence with a short Executive Summary that gets straight to the bottom line.

• How do I compute delta and implied volatility using Option Tutor?

Answer: Complete the following online exercises:

Launch Option Tutor and select the subject Option Calculator. Click on the menu item Help. From the online Help select Applications Guide and then click on Quick Examples:

You should work through the following examples provided in the Quick Examples section, titled:

A good alternative practice lesson is in the Detailed Examples. From the detailed examples select (by clicking) the example titled: Option Calculator and Implied Volatility, and work through this example.

• Where can I get the Bid/Ask option prices?