19) Stochastic Volatility Model

Question 1

Why do we need stochastic volatility models like Heston

Answer 1

• The Black-Scholes model often fails to price options consistently across strikes and maturities due to its constant volatility assumption
• Stochastic volatility models like Heston allow volatility to vary over time, better capturing market phenomena like the volatility smile
• These models aim to match multiple market prices with a single framework

Question 2

What are the SDEs in the Heston stochastic volatility model

Answer 2

Question 3

How do you hedge a portfolio in the Heston model to remove risk

Answer 3

Question 4

What is the general pricing PDE in the Heston model

Answer 4

Question 5

What boundary conditions are used to solve the Heston PDE for a European call

Answer 5

Question 6

How do we compute closed-form solutions in the Heston model

Answer 6