Basic Option Terminology
Option contracts provide the buyer ( holder ) with the right but not the obligation to buy from ( calls ) or to sell to ( puts ) the seller ( writer ) the underlying asset (e.g., stocks, bonds, currencies, commodities) at a specified price or starting point (the strike price or exercise price ) for determining the intrinsic value of an option at a point in time or during a specific period of time (the term ). Prior to ( American style ) or at the end of ( European style ) the term (the expiration date ) the holder can exercise the option if it has any cash value ( intrinsic value ) or let it expire if it is worthless. The holder pays and the writer receives cash for an option (the premium ).
When puts decrease in value, the asset price on which they are based moves above the strike price, whereupon the puts are said to be trading out-of-the-money. When the underlying asset price moves below the strike price, the puts increase in value and are said to be trading in-the-money. When puts or calls trade at the strike, they are said to be trading at-the-money and have no cash intrinsic value. Calls increase in value as the underlying asset price moves above the strike price. They are then said to be in-the-money. As the asset price decreases below the strike, the calls are said to be trading out-of-the-money. If not exercised by the end of their terms (or automatically exercised by operation of rule or contract), both put and call options expire.
The market value of an option consists of two main parts: intrinsic value and time value. Intrinsic value is the dollar amount by which an option trades in-the-money (above the strike price if a call and below the strike price if a put). Time value is the amount by which an option price exceeds any intrinsic value and represents that part of the value of an option relating to the amount of time left until the instrument expires. Time value declines over the life of the instrument but also represents the option's potential to acquire more intrinsic value before it expires.
Valuing Structured Products
As mentioned in the Introduction, derivative securities and contracts are the elemental building blocks of structured products and include forward contracts and option contracts. Because of their flexibility (e.g., the ability to adjust the life span of "term," the strike price, and other components), options are an integral part of and form the basis for creating and valuing many structured derivative products.
Options are valued by analyzing the following data:
Hedging and Trading Structured Products
The management of risk associated with option price changes are quantifiable using the following mathematical constructs:
Delta (index or stock risk). The percentage amount an option's price changes in response to a change in the price of the underlying asset. It is also generally an approximate measure of the probability that an option will finish its life in-the-money. This is simply the risk of having a net long or short position in the market. The net delta position is managed by setting limits per index, country, and the firm's derivative business as a whole.
Gamma (actual volatility). The percentage amount by which an option's delta will change in price in relation to the price of the underlying security. Gamma is a function of the time remaining until expiration of the option. It is the risk due to changes in the net delta position resulting from changes in the level of the market, index, or stock.
Vega (traded volatility, also known as kappa). The dollar amount of change of an option price with a 1-point change in the volatility of the underlying security. Most option transactions are long dated and highly sensitive to changes in the level of volatility implied by the market. Vega risk can be built up very quickly on a trading desk. It does not take too many institutional-sized transactions to build a big vega position, and if the market flow is one way for an extended period of time, vega risk can grow very quickly. Fortunately, long-term volatility levels are more stable than short-term levels. It is important from a risk management perspective to prevent traders from covering long-term over-the-counter (OTC) vega by buying short-term vega because of the high probability of a volatility curve divergence. Volatility curves move just as much as yield curves. Vega risk can be managed by setting vega limits on each asset class, index, country, stock, and so on. Sublimits can be placed on individual structured products or other positions and monitored on a real-time basis by management via electronic links to trading floor computer systems and pricing models.
Theta (option time decay). The dollar amount by which an option price changes due to changes in time to expiration, often thought of as the amount of time value decay that occurs in the price of an option as it approaches expiration. (Note: time value decay is the amount of decline of an option price as it approaches expiration; it is also called erosion or evaporation of time premium.) Theta is the profit or loss in an option book due to the passage of time and therefore the decay of an option's premium. Both theta and gamma risk can be managed together by setting exposure limits based on worst-case one-day price swings given, for example, either a 3 percent up move, a 3 percent down move, or no change for a day.
Rho (interest rate risk). The dollar amount of change in an option price due to changes in interest rates. Interest rate risk is very large for long-term options. A change in market rates of interest changes the forward index price even if the spot index is unchanged. Rho risk is managed by placing currency-adjusted limits on trading positions and hedging such risk using interest rate futures, options, or swaps.
Other risks that must be managed with regard to structured product, derivative, or stock and bond positions include the following:
Currency Exchange Rate Risk. Currency exchange rate risk arises through long or short positions held on a brokerdealer's global derivative trading desk. Such positions include index options, foreign margin and bank balances, foreign index and interest rate futures contracts, foreign currency interest rate swaps, and index forwards. Exchange rate risk in U.S. dollar terms is managed by establishing a dollar equivalent limit for each currency, using such instruments as foreign exchange forward and futures contracts, currency options, and spot market cash currencies,
Yield Curve Risk. Risk due to shift in the slope of yield curves; monitored using a "slope matrix" report, extremely complex to limit and difficult to hedge.
Basis Risk. Cash market or other position risk exposure versus futures or other derivative markets.
Liquidity Risk. Level of trading volume and float (a lack of liquidity can make it difficult in setting and unwinding hedge positions).
Changes in Dividend Yields. Difficult to hedge but usually a marginal risk that is smaller than interest rate risk; in creating a two-way flow of business, dividend assumptions usually net out, otherwise the risk is hedged using OTC forward contracts.
Timing and Exercise Risk. Option contracts should expire on days (accounting for foreign holidays) and at times of day (adjusted for time zone differences) that allow traders to set or unwind hedges.
Credit Risk. Relating to counterparty creditworthiness.
Market Disruption Events. Usually covered in contract documentation that provides certain limits or cancellation of exercise rights if liquidity in certain cash and futures markets fails to exist.
Discontinuance of Index Calculation. Contract document provision that provides for an alternative method of index calculation if the primary calculator fails to update the index values or the cash securities underlying the index cease to trade.
Legal Risks. Risks associated with customer suitability for or authorization to purchase or trade certain types of investments, compliance with securities regulations, disclosure materials, copyrights, and so on.
New Product Risks. Risks arising from incorrect assumptions, computerized pricing models, or errors made in structuring a new product or about the underlying asset or market; can be partially mitigated by deferring profit realization or amortizing profits over the life of the instrument until more experience is gained.
Subsequent chapters are dedicated to reviewing the basic characteristics of a number of structured financial products presently available to individual investors, professional investment managers, and corporate clients around the world. While the product categories presented herein are extensive, they do not encompass every type of derivative product in use and available. Such a compendium is more practically the purview of a more encyclopedic financial text or series.
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