# Factors Affecting The Parameter Values For Fixed Index Annuities

The previous discussion makes clear that the parameters offered by an FIA (floors, participation rates, caps, spreads, and buffers) will depend in large part on the level of interest rates and the cost of financial derivatives for the associated index. Higher interest rates mean that principal can be protected with less assets, which then leaves more that can be devoted to the options budget used to purchase upside exposure. Participation rates can conceivably be higher than 100 percent if interest rates are high enough and the call options are cheap enough. On a related point, it should also be clear that if the owner is willing to accept a lower floor, it would be possible to gain more upside potential since less is needed for bonds and more is available to purchase call options.

The key factors that influence the price of call options were formulized with the Black-Scholes formula in the 1970s. The Black-Scholes formula shows the relationship and factors for determining the price of a European-style call option, which is relevant for FIAs that credit interest on a point-to-point basis. European options can only be exercised at the end date for the option and the price at that time is what matters for determining the value to the option owner. An American option can be exercised at any point before the maturity date and are even more complex to price. But even for European options, a complex mathematical relationship exists between the factors and the option price (a Nobel prize was awarded to those who figured it out) and the theorem still relies on simplifying assumptions that may not always accurately reflect market option pricing. Nonetheless it can provide a decent approximation. Generally, a call option’s price will be based on six factors.

### Implied Volatility

The implied volatility of the underlying market index may be the most important factor. Greater index volatility will increase the cost of a call option. Increased volatility creates more possibility that the index price will increase, which would require a larger payoff to the option owner. Implied volatility can be difficult to measure in practice because it depends on future beliefs about how volatile the markets will be. It is typically estimated from calculating the market’s recent volatility, with the idea that investors might expect recent volatility to continue at the same pace. For example, one might look to the annualized volatility of monthly stock market returns over the previous year as an estimate of the implied volatility for the purchase of a new option on the index. But this is only an estimate and it may not be precise. Since 1993, the VIX has been available from the Chicago Board Options Exchange as a market estimate of implied volatility for the S&P 500. It can be used as an estimate of implied volatility, but prior to its introduction any estimates of implied volatility will be less reliable. The development of low-volatility index options can be explained, in part because the lower volatility will allow for cheaper option pricing, which in turn supports more advantageous parameters with the upside growth exposure.

### Current Index Price

This current price of the index is important with regard to how it relates to the strike price for the associated option.

### Option Strike Price

Another important variable is the relationship between the strike price of the option and the current price of the index. The strike price represents the price that the index can be purchased. As the strike price increases relative to the current market price, the option is out-of-the-money and less likely to provide a payoff. Call options only make payment when the index price ends up higher than the strike price. The option will be cheaper with a higher strike price. An at-the-money call option has a strike price matching the current index price. The strike price could be less than the current price (it is in-the-money) which makes it more likely to provide a payoff and more expensive to the purchase. This also explains why an FIA that includes a spread can offer a higher participation rate than otherwise. It allows for the call options purchased with the options budget to have a higher strike price, and therefore less cost.

### Risk-Free Interest Rate

The risk-free interest rate is another relevant variable, though it has a smaller impact. It represents the return on a risk-free bond during the interval of the option. With a one-year term FIA, the call option would have a one-year maturity, and the risk-free rate could be approximated with a one-year Treasury rate. Higher interest rates will cause a slight increase in the option price, though this will usually be more than offset by allowing for a bigger options budget to support upside exposure since fewer bonds are needed to protect the principal.

### Term to Maturity

A fifth factor is the term to maturity. We mostly spoke of a one-year term, but some FIAs will have longer terms of even seven years or beyond. A longer term does increase the price of the call option, but not on a one-to-one basis. Longer terms can allow for more attractive FIA parameters. In other words, the participation rate can be higher when the terms are longer because the call option price is increasing at a less than linear rate as the term length increases.

### Dividend Rate

Finally, if the market index pays a dividend, this becomes a final input for the options price. With this input, the strike price can be entered when thinking in terms of a total return, but then it is reduced by the entered dividend to make the option cheaper in terms of an effective strike price. For example, an index priced at $100 with a strike price of $96 and a dividend yield of 4 percent would create the same call option cost as for an index priced at $100 with a strike price of $100 and no dividend yield. Because dividends could be removed and accounted for separately, it is not mandatory to include the dividend rate as an input for estimating the option price.

It is interesting to also note that the expected return for the index is not one of the factors used to price its call option.

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*This is an excerpt from Wade Pfau’s book, Safety-First Retirement Planning: An Integrated Approach for a Worry-Free Retirement. (The Retirement Researcher’s Guide Series), **available now on Amazon* AMZN .* *

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