VRM16 - Option Sensitivity Measures: The "Greeks"

Question 1

Describe and assess the risks associated with naked and covered option positions

Answer 1

Naked positions can lead to big loss if shorting, but big profit since no additional costs

Covered positions work if option is exercised, potential for big loss if strike not met

Question 2

Describe the use of a stop loss hedging strategy, including its advantages and disadvantages, and explain how the strategy can generate naked and covered option positions

Answer 2

Stop-loss hedging is having naked position when in the money, covered when out of the money

Good when share price exceeds or never meets strike, gets very expensive if fluctuates around strike

Question 3

Describe delta hedging for options as well as for forwards and futures contracts

Answer 3

Position is partially covered, extent to which depends on delta which is interpreted as the probability of the option being exercised

Question 4

Compute the delta of an option

Answer 4

Long call d = N(d1)
Long put d = N(d1) - 1

d1 = (ln(S0 / K) + (r + sigma^2/2) ^T) / (sigma * sqrt(T))

Question 5

Describe the dynamics of delta hedging and distinguish between dynamic hedging and hedge-and-forget strategies

Answer 5

Delta does not remain constant so has to be constantly rebalanced with share price changes, can be a bit buy-high and sell-low so gets expensive

Hedge and forget is where you hedge and leave alone

Question 6

Define and calculate the delta of a portfolio

Answer 6

Weighted average of deltas depending on how many shares of each option

Question 7

Define and describe theta, gamma, vega, and rho for option positions, and calculate gamma and vega for a portfolio

Answer 7

Vega v measures the exposure of an option to volatility
v = S0 * sqrt(T) * N’(d1) where N’(x) is normal pdf at x
v largest when S0 close to K, goes to zero as gets further away

Gamma measures sensitivity of delta to stock price changes
gamma = N’(d1) / (Ssigmasqrt(T))

Theta measures rate of change of value over time

Rho measures an options sensitivity to interest rates

Question 8

Explain how to implement and maintain a delta and gamma neutral position

Answer 8

Gamma has to be hedged by taking position in another derivative dependent on the same underlying asset

Question 9

Describe how to implement portfolio insurance, and how this strategy compares with delta hedging

Answer 9

Can use deltas by matching deltas in opposite direction to portfolio to provide insurance instead of neutralising delta, didn’t work as well as expected in 1987 so stopped implementing it