Chapter 11 - The Greeks Flashcards
What are the Greeks used for?
The Greeks are a group of mathematical derivatives that can be used to help us manage or understand the risk in our portfolio.
Define the Greek “Delta”.
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.
Define the Greek “Gamma”.
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
Define the Greek “Vega”.
Vega corresponds to the rate of change of the price of the derivative w.r.t the assumed level of volatility of the underlying share St.
vega = df/dsigma
Define the Greek “Theta”.
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
Define the Greek “Rho”.
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
Define the Greek “Lambda”.
Lambda corresponds to the rate of change of the price of the derivative w.r.t the changes continuous dividend yield.
Rho= df/dq
What does it mean for a portfolio to be delta hedged?
The weighted some of the deltas of the individual assets equal 0.
What does is mean for a portfolio to be instantaneously risk free?
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 if the portfolio is delta hedged as df/ds=0
What is the purpose of rebalancing the portfolio?
To keep a portfolio delta-hedged (weighted sum of deltas equal to 0)
What is the difference between static delta hedging and dynamic delta hedging?
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
What does a Gamma indicate?
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.
What do call options allow for?
Exposure to be gained to upside movements in the price of the underlying share
What do put options allow for?
Put options allows for downside risk to be removed.
If one of the Greeks=0.5 what does this mean in reference to the price of the derivative?
If a Greek=0.5, the for every increase of 1, the derivative price will increase by 0.5
