Equity Index Options Valuation

How do we price equity options? 

Assume we want to calculate the value of options expiring in 3.5 months time. We first need to calculate the 3.5 month forward on the same stock. We first need to calculate the interest to finance a long position in one of the shares. This is calculated by interest x stock price x time. To this, we need to deduct any benefits to owning the stock, i.e. dividends. Therefore forward price is determined as: Spot + Costs of holding - Benefits. 

Now we have calculated the forward price, we can calculate the prices of the 3.5 month options using the same options valuation model Lindsey has outlined in other videos. 

Again, we need the volatility of the underlying to calculate the width of the bars, calculated by the forward price x volatility x square root of time. Once the bar sizes have been calculated, we can determine which are in the money, the expected payoffs and then the respective values at maturity. 

What are equity index futures? 

Equity index futures allow the trading of the level of an equity index such as the S&P 500 or the FTSE 100. 

Determining the value of the equity index futures is the same as determining the future price of an individual stock. We need to know the risk-free rate, how long to expiry and whether there are any benefits to holding the index. The fair value for the futures price is therefore the spot price + Costs - Benefits. 

What are equity index options?

Equity index options exist as both options on futures and options on the underlying index. Equity index options can be valued using the simple valuation model outlined by lindsey, alternatively the prices of options on indices should be available online.