How it is priced and built

The budget

An issuer that promises to repay 100 in T years buys a zero bond today for

price = 100 ÷ (1 + r)^T

where r is the interest rate for that maturity. The gap between 100 and that price is the option budget. At 3 % for three years the bond costs 91.51, leaving 8.49. At 0.5 % it leaves 1.49. The same note that offered 100 % participation in one year can only offer a fraction in another, and the difference is nothing but the rate.

Spending it

The budget buys options, priced by the issuer's trading desk from implied volatility, dividends and the time to maturity. A long call costs money; a sold call or put brings money in. That is the whole trade-off behind every product on this site:

• Capital protection with participation spends the budget on calls. Low rates mean a small budget and a low participation, so issuers add a cap (a sold call) or a barrier (a cheaper knock-out call) to pay for more.
• Yield enhancement sells a put. The premium is paid out as a coupon or a discount. High volatility means a high premium and a high coupon — and a higher chance that the put ends up being exercised.
• Products with additional credit risk sell protection on a reference entity. The CDS premium tops up the budget.
• Participation products hold the underlying without a bond; forgone dividends are the budget that pays for the bonus put or the extra calls.

What the chart cannot show

The payoff diagram is the picture at maturity. On every day before, the price of the product is the sum of the prices of its parts: the zero bond at current rates and the issuer's credit spread, the options at current volatility and time value. A protected note can trade at 92 two years before it repays 100; a knock-out warrant can lose its entire value in an afternoon. The diagram tells you what you will get, not what it is worth on the way there.