« Massachusetts goes it alone on hedge funds | Main | Delta hedging »
Basic options terms
By Martin | October 18, 2011
ome of this is necessary to express the basic operation of options contracts (such as ‘premium’ or ‘exercise price’)
and some of it is the result of the mathematical complexity of option pricing.
In particular, it is impossible for any potential user of options to avoid contact with the ‘Greeks’
a set of Greek letters used to denote variables used in option valuation.
However, although the underlying mathematics used in today’s option pricing models can be complicated
and well beyond the grasp of non-mathematicians, it is not necessary to understand advanced calculus
nor even the key variables such as delta and gamma respectively the first and second derivatives of the option premium
with respect to the price of the underlying.
For an end-user who needs to hedge an underlying cash position, or an investor who wishes to take a directional view on a market,
the concepts that the ‘Greeks’ represent and their impact on the price of any particular option are intuitive and easy to grasp.
This page explains all the terms an end-user of options (as opposed to a professional trader) is likely to encounter in putting together an options trade.
For easy reference, ‘Greeks’ are listed below with a brief explanation.
| Delta (δ) | The change in option value for a given change in the value of the underlying. |
| Gamma (γ) | The change in the delta of an option for a one-unit change in the price of the underlying. |
| Rho (ρ) | The change in option value for a one percentage point change in interest or discount rates. |
| Sigma (σ) | The standard deviation or volatility of the instrument underlying an option. |
| Theta (θ) | The change in option value over (usually) one day keeping strike, volatility and discount rate the same. |
| Vega: (V) | The change in option value for a small movement in volatility. |
| Lambda (L) | The change in option value for a small change in the dividend rate (equity options) or foreign interest rate (foreign exchange options) |
| American-style | An American-style option can be exercised at any point during its life. In cases where early exercise is beneficial (for example, deep in-the-money calls {puts} on underlying stocks with large {small} dividends), American-style options are more expensive than European-style options. However for options on non-dividend-paying stocks the American-style call option is the same price as the European-style. See Bermudan-style, European-style, option. |
| Assignment | Notice to an option writer that an option has been exercised. In the swap market, assignment zis the transfer of a swap obligation to another counterparty. |
| Asymmetric payoff | The skewed profit pattern associated with options that gives profit sharing on the upside (appreciation of the underlying for a call, depreciation for a put) while limiting liability on the downside. Contrast with the symmetrical payoff associated with forwards and futures. |
| At-the-money | An option is at-the-money forward if its strike price option is equal to the current implied forward price of the underlying. A useful rule of thumb for the approximate price of an at-the-money forward option is Price = 0.4 * volatility * time * discount factor. For example, a three-month EUR Call/USD Put with a strike of 1.0370 and with a forward rate at 1.0370 and volatility of 10% would cost approximately 0.4*0.1*sqrt(0.25)*0.992 = 1.90%. The Black-Scholes price is 1.92%. Options are often struck at-the-money forward but can also be struck at-the-money spot. This is the point at which the strike is equal to the prevailing spot price of the underlying. An interest rate cap struck at the current Libor level is at-the-money spot; one struck at the current swap rate for the period of the cap (or the FRA rate for a caplet) is at-the-money forward. An option is in-the-money if it has positive intrinsic value because the market price of the underlying is above {below} the strike price of a call {put}. The reference rate to determine whether an option is in-the-money can be either the spot (in which case the option is said to be in-the-money spot) or the forward (in which case the option is said to be in-the-money forward). If an option is not in-the-money and is not at-the-money then it is said to be out-of-the-money. |
| Bermudan-style | An option that can be exercised on a number of predetermined occasions. So, for example, a bermudan receiver swaption would allow the buyer to enter into an interest rate swap as fixed-rate receiver on a number of pre-determined occasions as a hedge for a step-up fixed-rate callable bond in which the bond coupon stepped up annually and the bond was cancellable at each annual coupon payment. Also known as limited-exercise or quasi-American. |
| Buy-Write | A covered call position created by simultaneously buying the underlying asset and selling a call option on it. This synthetically creates a short put position – see put-call parity. |
| Call option | An option that grants the holder the right but not the obligation to buy the underlying at a predetermined price at or by a predetermined time. The buyer of a call is expressing a bullish view of the underlying and also implicitly, since he is long an option, believes either that volatility will rise or at least that it will not fall. |
| Delta (³) | Delta is defined in three, interrelated ways:
For European-style options delta increases in a non-linear fashion from zero to one as an option moves from far out-of-the-money to deep in-the-money. |
For interest rate options delta can be calculated with respect to the underlying bond price,
with respect to each underlying forward interest rate (as sometimes with cap deltas),
or with respect to a small parallel shift in the zero coupon yield curve so that delta is the change in the option price for a small change in all zero-coupon rates.
See delta hedging, dynamic hedging, static replication, replication.
Topics: Derivate | No Comments »
Comments
You must be logged in to post a comment.