希腊值详细整理

The directional risk of an option in terms of an equivalent position in the underlying contract.

• For each purchased (sold) option you have a directional risk equivalent to being long (short) 50% of an underlying contract
• Being long delta means that the price of the option increases as the spot goes up.

Approximately the probability that an option will finish in-the-money. (from Black-Scholes formular)

With the approaching of expiration date:

• ATM stays the same
• ITM becomes more in the money
• OTM becomes more out of the money

The delta increases as the price of the underlying increases for both call and put.

• When the option is deep in the money, its value changes at a rate almost identical to that of the underlying. When the option is deep out of money, its value only slightly changed.

The rate of change in an option’s delta with respect to movement in the price of the underlying contract

Both calls and puts must have positive gamma

When Gamma is negative, if market goes up, the delta decrease which is bad for my position. So when Gamma is negative, we want the market to be quite.

• if the market sits still, profits come from theta
• Gamma and theta are always opposite sign

So for long Gamma, we want the market to make big move.

With the approaching of expiration date:

• the gamma of ATM increases dramatically
• the gamma of ITM and OTM decreases to zero

Gamma increases as the option moves from being in-the-money reaching its peak when the option is at-the-money. Then as the option moves out-of-the-money the Gamma then decreases. Gamma increases as time to maturity decreases.

The sensitivity of an option’s value to the passage of time

• Usually expressed as the change in value per one day’s passage of time

Depends on two factors:

• decay in volatility value
• decay in interest value

An option which loses value as time passes will have a negative theta. the great majority of options lose value as time passes.

A positive theta: when present value of the expected value of the underlying asset is equal to the value today.

• If there are no changes in other market conditions, as time passes, the value of the option will rise to intrinsic value. (negative time value)
• must be deep in-the-money, so that time value is negative
• must be European and subject to stock-type settlement
• Intuitively: the value of the option is known, so it needs to be compounded to today –> negative time value.

• A long-term option always has a greater vega value than an equivalent short-term option.

For stock type settlement:

• options on futures have negative rho values
  • future contracts have no carrying cost but options have
  • the effect is small since the value of the option is small
• calls have positive, puts are negative

In stock option markets, interest and dividends always have the opposite effect on option values.

The amount of money and the length of the investment determine how sensitive an investment is to a change in interest rates

• An in-the-money option has a greater rho value than an equivalent at-the-money or out-of-the-money option
• A long-term option has a greater rho value than equivalent short-term option.