Home and Mortgage

Financial options exist for many financial instruments. The most common form of exchange traded options are stock options. These are usually restricted to the largest stocks in a market. They have highly standardized terms. They usually have a common expiry date, in other words on a particular day each month a number of contracts will all expire. It is usually possible to trade options across a range of exercise dates.
Options can be issued in a number of different forms:
American versus European. An option may be written that can be exercised on any date until the expir y of the option contract or can only be exercised on its expir y date. The former is referred to as American style and the latter as European style.
Asian. Asian-style options are a relatively recent innovation and differ from traditional options in that they use an average price of the underlying instrument over a specified period rather than a single spot price.
Warrants. Warrants are simply a form of long-dated call option contract. While exchange traded options are highly standardized, exist for a range of expiry dates and have a common expiry date warrants are issued in a particular form and for a specific expiry date. They may be issued in a “covered” form, where the issuer owns the underlying instrument, or uncovered where in the result of their exercise the issuer will have to buy the stock in the market.
Rights issues. Companies may look to raise more capital from their shareholders by having a rights issue whereby shareholders are “invited” to subscribe for additional, new shares. These new shares are usually priced at a significant discount to the current market price. These rights are a form of European-style call option. Rights for larger companies may be listed and traded on an exchange.
Convertible bonds. Conver tible bonds comprise a straight bond plus a stock call option. When companies issue conver tible bonds these options are usually implicit but investment banks may buy these bonds and break them up into their constituent par ts and sell on the straight bond equivalent and option separately.
Exchange traded versus over-the-counter. Option contracts may be traded on an exchange or be “over-the-counter” (OTC), that is a private agreement reached between two par ties. Exchange traded options are issued in a highly standardized form. OTC contracts may take many forms giving greater flexibility than exchange traded options. They are, however, inherently illiquid, and bid–offer spreads given by the (usually) single market-maker may be very wide.
Black–Scholes. Various models have been developed to value traded options based on a framework derived by Fischer Black and Myron Scholes. These models require a relatively high level of mathematical skills to understand well. My first degree was in theoretical physics and I struggle with them. For all save option specialists it is probably sufficient to treat Black-Scholes as a fairly reliable black-box model. Give it these four inputs (price of underlying instrument, volatility of price of the underlying instrument, time and interest rate) and it will give a plausible value for an option’s premium.
Three of these four factors are well defined and can be measured with a high degree of certainty. The exception is the volatility of the price of the underlying instrument. The historic level of volatility varies over time and its measured value depends on the frequency (hourly, daily, weekly etc) and time period selected. Valuation models need the future (rather than past) volatility and there is no guarantee that the historic level of volatility will be maintained. The value these models put on an option is therefore an estimate and two traders are likely to arrive at different (but close) estimates for an option’s premium.
It is helpful to remember the following relationships. Both call and put options become more valuable as they move deeper into the money. Their value increases with the time to expiry and volatility of the price of the underlying instrument. Rising interest rates result in higher stock call option prices but lower stock put option prices.
Embedded options. Many financial instruments, including loans and deposits, contain embedded options. These differ from traded and OTC options in that they are not defined in explicit terms. Someone who has taken out a 30-year mor tgage has effectively bought a prepayment option allowing them to pay off the loan before it comes to term.