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Quantitative Finance and Derivatives 2 > Options: Greeks > Flashcards

Options: Greeks Flashcards

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1
Q

What factors does an options’s value dpend on and what are the letters representing them?

A
  1. Price of the underlying: S/F
  2. Strike price: K
  3. Volatility: σ
  4. Time to maturity: t
  5. Interest rate: r
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2
Q

What factors affect the Intrinsic Value of an option?

A
  1. Price of the underlying
  2. Strike price
  3. Time to maturity (indirectly)
  4. interest rate (indirectly)
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3
Q

What factors affect the Time Value of an option?

A
  1. Price of the underlying
  2. Strike price
  3. Volatility
  4. Time to maturity
  5. Interest rate (indirectly)
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4
Q

What are greeks?

A

Options’ sensitivity to each risk factor can be measured through partial derivatives of the option’s value respective to each factor. The sensitivities derived in this way are referred to as greeks.

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5
Q

What risk factor does greek correspond to?

A
  1. Price of underlying: Delta and Gamma
  2. Volatility: Vega
  3. Time to maturity: Theta
  4. Interest rates: Rho
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6
Q

What is the formula for Delta?

A

Dleta is the hedge ratio for an option.
Delta = Change in the value of the option/Change in the value of the underlying asset

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7
Q

What is the formula for Gamma?

A

How sensitive our hedge is to changees in the stock price.
Gamma = Change in the value of the option’s delta/Change in the value of the underlying asset
(Second derivative to value of the option)

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8
Q

What is the formula for theta?

A

How does option value change with time decay
Theta = Change in the value of the option/Decrease in the time to expiration

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9
Q

What is the formula for Vega?

A

How does option value respond to change in asset’s volatility?
Vega = Change in the value of the option/Change in the volatility

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10
Q

What is the formula for Rho (written as RhoD)?

A

Rho represents the sensitivity of the option’s value to the change in the interest rate
RhoD = Change in the value of the option/Change in the value of the interest rate

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11
Q

What are the deltas for a call?

A
  1. Out of the money call Delta approaches 0
  2. At the money call Delta close to 0.5
  3. In the money call Delta approaches 1 the more in the money (above K) it is
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12
Q

What are the deltas for a put?

A
  1. In the money put Delta approaches -1 (the more in the money, the more lower than K, the closer to -1)
  2. At the money put delta close to -0.5
  3. Out of the money put delta approaches 0 from the negative side
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13
Q

How do we interpret delta?

A
  • Delta quantifies the impact of a change in the underlying asset price on the value
    Delta = ΔV/ΔPunderlying => ΔV = Delta * ΔPunderlying
  • Delta > 0 (+) -> bullish position
  • Delta < 0 (-) -> bearish position
  • Delta = 0 -> neutral position
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14
Q

How does one calculate the Delta for a portfolio?

A

We just take the weighted sum of Delta, weighting by the units of each option

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15
Q

Why is Gamma needed?

A

Delta is not constant but varies with the price of the underlying, as such we need the derivative of delta to see its sensitivity to changes in the price of the underlying. Gamma is the second derivative of the value of the option V with respect to Price of the underlying.

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16
Q

What is Gamma from the trader’s point of view?

A

Gamma = dDelta/dPunderlying => Gamma = ΔDelta/ΔPunderlying

A negative Gamma implies that when the underlying price grows Delta decreases, and vie versa (Delta changes in the undesired direction)

17
Q

What is the change in the Market Value of an Option with both Delta and Gamma?

A

ΔMVpf = Delta * ΔPunderlying + Gamma/2 * ΔP2underlying

18
Q

What is the interpretation of Theta?

A
  1. Theta represents the effect of the change (typically the reduction) of the option’s value as time passes (time decay)
  2. The effect of time decay on the time value of the option is clearly in favour of the seller/writer and plays against the holder/buyer
    Theta = ΔMVpf/Δt => ΔMVpf = Theta * Δt

Main convention Δt is from today to tomorrow
Generally when the option is ATM Theta increases as maturity approaches, while it decreases if the option is ITM or OTM

19
Q

What is the interpretation of Vega?

A
  1. Vega identifies the option’s sensitivity to changes in implied volatility.

Positive Vega => I earn if volatility increases => buyer’s position
Negative Vega => I earn if volatility decreases => seller’s position

20
Q

What are some general trends for Vega for options?

A
  1. Vega peaks approximately where time value is maximum (ATM option)
  2. Is roughly symmetric and decreases as time passes and maturity gets close
21
Q

What is the interpretation of Rho?

A

Rho identifies the sensitivity of the option’s value to changes in the risk-free rate r. Hard to describe general behavior.

22
Q

What are the two method when calculating the effects of a shock on a portfolio of options?

A
  1. Partial revaluation: based on combining the effects measured through the Greeks
  2. Full revaluation (repricing)
23
Q

What is the formula for approximation of the effect on the market value of options through partial revaluation?

A

ΔMVpf = Delta * ΔPunderlying + Gamma/2 * ΔP2underlying + Vega * Δσ + Theta * Δt.

Important: the total effect may differ from the sum of the effects calculated with partial derivatives.

24
Q

What are the three relevant implications of the fact that Greeks are partial derivatives of an option’s value?

A
  1. They can always be derived as weighted sums of the greeks of the options in the portfolio (weight = n of contracts)
  2. Different pricing formulas lead to different greeks
  3. They may be imprecise in assessing the effects on the option’s price in case of a joint shock of more than one factor

Quantitative Finance and Derivatives 2 (19 decks)

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