# INDEX OPTIONS

INDEX OPTIONS

STEP 1

Choice of Options for Analysis

Consider pairs of put and call options with each pair having the same strike price and maturity. You need pairs of American-style (OEX) and of European-style (XEO) options. For each style choose a pair that are at-the-money, and another that are out-of-the-money, so that American and European pairs that are at-the-money have the same (or close) time to maturity and exercise price. Do the same for in-the-money and out-of-the-money options. You should end up with a choice of options that fit the description of the table below.

American (OEX) European (XEO) Same or close

ATM call ATM call Exercise price and time to maturity All options should be active (i.e., showing some volume and/or open interest, but preferably both)

OTM call OTM call Exercise price and time to maturity

ITM call ITM call Exercise price and time to maturity

ATM put ATM put Exercise price and time to maturity

OTM put OTM put Exercise price and time to maturity

ITM put ITM put Exercise price and time to maturity

For ATM options choose options that are closest at-the-money (i.e., with a strike price closest to the level of the S&P100 index at the time of downloading the data). Then choose options with exercise price on either side of that of the ATM options such that a pair is ITM and a pair is OTM Choose a particular maturity between 1 week and 1 year for all options that you will use. In all your choices of strike price and maturity be guided by the table above (flexible) and by options that are most active (i.e., ones that are showing some volume of trade and/or open interest, but preferably both). If you do not see price, volume and open interest data next to an option it is either you are accessing the website when CBOE is not open or the options are not heavily traded. In this case choose other options and access the website during Chicago opening times. Take a note of the exact time and date of your data download, or simply copy the screen information.

Downloading Option Data

Login to the CBOE website www.cboe.com. Choose the ‘delayed quotes classic’ tool under the ‘Quotes&Data’ tab. Download prices for the selected puts and calls, by entering the symbol codes OEX or XEO while checking (clicking) the choice ‘List all options, LEAPS, Credit Options & Weeklys if avail.’

Interest Rate Data

You need an annualised risk-free rate for pricing the options. Use the ‘interest rates’ market data provided by Bloomberg (http://www.bloomberg.com/markets/rates/index.html). Select an appropriate yield for the risk free interest rate. This usually is the yield of a Treasury Bill (or zero curve) that has a maturity closest to that of the option(s). Note that if you download options with different maturities you may need more than one interest rate to match.

Alternative sources of interest rate data (the first is more official) are:

1. http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-LongTerm-Rate-Data-Visualization.aspx

2. If you have access to Datastream use the following mnemonics (instrument code): FRTB3M, FRTB6M.

Enriching Your Analysis?

You can do the analysis using mid prices = (bid+ask)/2. Or you can enrich your analysis by performing calculations on bid and on ask prices separately. The difference should be a reflection of the effect of ‘transaction costs’.

Step 1 Coursework Requirements

The requirements are:

a. Investigate (calculating and checking) whether the put-call parity holds for the actual market prices of both the European and the American options. Interpret the results (more emphasis and marks will be given to interpretation).

b. Calculate the difference between the prices of the American and European options that have the same exercise price and maturity. Interpret the results (more emphasis and marks will be given to interpretation).

STEP 2

Binomial Model Setup Features

Using the ‘binomial model’, build a binomial tree for the index level with three time steps, so that the overall time horizon is equal to the maturity of the options selected (i.e., divide the maturity into three equal intervals).

With regard to calculations of the maturity dates of the options, bear in mind that the XEO and OEX option contracts at CBOE mature on the Saturday following the third Friday of the maturity month of each contract (full contract specifications are available under the ‘Products’ tab in the CBOE website).

With regard to the binomial calculations choose the upward and downward size of price movement as a function of the volatility of the index level (i.e., function of sigma of the index). You can use the equations provided by Chance and Brooks for up (u) and down (d) parameter movements as functions of sigma, also provided in the lecture material.

Estimating Volatility of the Index

An estimate of sigma (volatility) for the index can be obtained by reading the value of the volatility index that has a symbol VXO. (Enter VXO on the right hand side box that appears when you click the ‘Quotes&Data’ tab and choose ‘Delayed Quotes Classic’ in the CBOE website).

Estimating Annualised Dividend Yield

To calculate prices you also need an estimate of the annualised dividend yield of the S&P100 index at the time of downloading the price data. Search for a reasonable value, and although this can be difficult, try http://etfdb.com/index/sp-100-index/dividends/ which gives the dividend yield on a fund that tracks the S&P100.

If you can’t find 15-minute dividend try:

http://markets.on.nytimes.com/research/markets/mutualfunds/snapshot.asp?symbol=OEF

Binomial Pricing

Using the VXO estimate of volatility evaluate the call and put options using the three-step binomial tree previously constructed for the index level (here you need to have your tree calculations automated so you can evaluate all options). Compare these values with the observed prices in the market and discuss the reasons why you may or may not observe differences. (More emphasis and marks will be given to discussion.)

Black and Scholes versus Binomial

Use the VXO estimate of volatility to calculate the Black-Scholes prices of the put and call options. Compare these values with market prices and with those obtained by the Binomial tree. Discuss possible reasons for any differences (Black-Scholes versus Binomial, American versus European, puts versus calls, ATM versus OTM). (More emphasis and marks will be given to discussion.)

Implied volatility

By trial and error, find the value of the volatility parameter at which the Black and Scholes price equals the observed actual market price for each option (here you need to have your tree calculations automated so that it will give you a price every time you vary the volatility value). The value of volatility at which the observed actual market price equals the model price is known as ‘implied volatility’. Compare these values of implied volatility with each other and with that obtained from the VXO index and discuss the reasons for any differences from each other and from the VXO value. (More emphasis and marks will be given to discussion.)

**10 %**discount on an order above

**$ 100**

Use the following coupon code :

WIZARDS35