RM Lecture 3 Flashcards
What is the Black-Scholes formula for a European call option?
What is Delta (Δ) for a European call option?
What is Gamma (Γ)?
Measures rate of change of Delta with respect to the underlying price.
What is Vega (ν)?
Measures sensitivity to changes in volatility.
What is Theta (Θ)?
Measures sensitivity to time decay.
What is Rho (ρ)?
Measures sensitivity to changes in interest rates.
How do you hedge multiple risk factors simultaneously?
Goal: Neutralize sensitivities to all risk factors X_j.
Why is dynamic hedging necessary?
Greeks (e.g., Delta, Gamma) change over time and with market conditions.
Rebalancing maintains neutrality but incurs transaction costs.
What is the trade-off in dynamic hedging?
Frequent rebalancing improves hedge quality but increases trading costs.
How do you make a portfolio gamma-neutral?
Example: Combine delta-hedging with gamma adjustments.
How is vega hedging implemented?
What are the limitations of delta-hedging?
Ignores higher-order risks (Gamma, Vega) and requires frequent rebalancing.
What is the purpose of the Greeks?
To quantify and manage nonlinear risks in options and complex portfolios.
