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Paper Review: “On the Pricing and Hedging of Volatility Derivatives” by S. Howison, A. Rafailidis and H. Rasmussen (Applied Mathematical Finance J., 2004). Anatoliy Swishchuk Math & Comp Finance Lab Dept of Math & Stat, U of C “Lunch at the Lab” Talk February 10, 2006. Variance Swap. - PowerPoint PPT Presentation
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Paper Review:“On the Pricing and Hedging of
Volatility Derivatives”by S. Howison, A. Rafailidis and H. Rasmussen
(Applied Mathematical Finance J., 2004)
Anatoliy SwishchukMath & Comp Finance LabDept of Math & Stat, U of C
“Lunch at the Lab” TalkFebruary 10, 2006
Variance Swap
Realized Variance in Continuous Time
Payoff Function for Variance Swap
Realized Volatility (Discrete Time)
Realized Volatility (Continuous Time)
Payoff Function for Volatility Swap
Payoff Function for Volatility-Average Swap
Payoff Function for Implied Volatility Swap
Payoff for Variance Swaptions
Payoff Functions for Volatility Swaptions
Payoff Function for Volatility and Asset Swaption
Risk-Neutral Pricing Technique
Three Approaches to the Risk-Neutral Pricing
• Pricing Independently of the Volatility Model
• Pricing by Expectations in a SV Framework
• Pricing via Partial Differential Equations
1st Approach: Pricing Independently of the Volatility Model
1st Approach: Pricing Independently of the Volatility Model (cntd)
1st Approach: Pricing Independently of the Volatility Model (cntd)
2nd Approach: Pricing by Expectations in a SV Framework
2nd Approach: Pricing by Expectations in a SV Framework (cntd)
2nd Pricing Approach: Pricing by Expectations in a SV Framework (cntd)
2nd Pricing Approach: Pricing by Expectations in a SV Framework (cntd)
3d Approach: Pricing via PDE
3d Approach: Pricing via PDE (Model)
3d Approach: Pricing via PDE (Payoffs)
3d Approach: Pricing via PDE (Payoffs)
3d Approach: Pricing via PDE (PDE Itself for the Value V of Derivative)
3d Approach: Pricing via PDE (Mean-Reverting Model)
General Stochastic Volatility Models
Derivation of Certain Expectations
Derivation of Certain Expectations.I.
Derivation of Certain Expectations.II.
Derivation of Certain Expectations.III.
Derivation of Certain Expectations.IV.
Derivation of Certain Expectations.V.
Derivatives Pricing
Mean-Reverting-Like Process
Mean-Reverting-Like Process.I.
Mean-Reverting-Like Process.II.
Popular SV Models. I.
Popular SV Models. II.
Popular SV Models. III.
Popular SV Models. IV.
Popular SV Models. V.
Asymptotical Analysis for Fast Mean-Reversion. I.
Asymptotical Analysis for Fast Mean-Reversion. II.
Asymptotical Analysis for Fast Mean-Reversion. III.
Asymptotical Analysis for Fast Mean-Reversion (Summary).
Examples: 1. The Variance Swap
Examples: 2. The Standard-Deviation Swap
Examples: 3. The Volatility-Average Swap
Examples: 4. The Implied Volatility- Swap
Examples: 5. The Volatility-Average Swaption
References. I.
References. II.
The End
• Thank you for Your Attention!