Chapter 11 - The Greeks

Question 1

What are the Greeks used for?

Answer 1

The Greeks are a group of mathematical derivatives that can be used to help us manage or understand the risk in our portfolio.

Question 2

Define the Greek “Delta”.

Answer 2

Delta corresponds to the rate of change of the derivative price w.r.t the price of the underlying asset.

delta = df/dSt

where f(t,St) is the value of the dericatie at time t, with price of St at time t.

Question 3

Define the Greek “Gamma”.

Answer 3

Gamma corresponds to the rate of change of delta w.r.t the price of the underlying asset. i.e. it gives you an idea of how much delta will change for each $1 shift in the underlying asset.

gamma = df^2/d^2St = d[delta]/dSt

Question 4

Define the Greek “Vega”.

Answer 4

Vega corresponds to the rate of change of the price of the derivative w.r.t the assumed level of volatility of St.

vega = df/dsigma

Question 5

Define the Greek “Theta”.

Answer 5

Vega corresponds to the rate of change of the price of the derivative w.r.t the time since the start of the contract i.e. how far in the contract you are.

theta = df/dt

Question 6

Define the Greek “Rho”.

Answer 6

Rho corresponds to the rate of change of the price of the derivative w.r.t the changes in the risk-free rate.

Rho= df/dr

Question 7

Define the Greek “Lambda”.

Answer 7

Lambda corresponds to the rate of change of the price of the derivative w.r.t the changes continuous dividend yield.

Rho= df/dq

Question 8

What does it mean for a portfolio to be delta hedged?

Answer 8

The weighted some of the deltas equal 0.

Question 9

What does is mean for a portfolio to be instantaneously risk free?

Answer 9

Instantaneously risk-free means that if we know the value of the portfolio at time t, then we can predict its value at time t + dt with complete certainty.

I.e. in a diffusion process there is no stochastic term

Question 10

What is the purpose of rebalancing the portfolio?

Answer 10

To keep a portfolio delta-hedged (weighted sum of deltas equal to 0)

Question 11

What is the difference between static delta hedging and dynamic delta hedging?

Answer 11

Static - start with a delta hedged portfolio and do not rebalance

Dynamic - start with a delta hedged portfolio and continuously rebalance the portfolio to ensure delta=0

Question 12

What does a Gamma indicate?

Answer 12

If gamma is low you will not need to rebalance your portfolio to keep it delta hedged as much as you would if gamma was high.