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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
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Realized Variance in Continuous Time
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Payoff Function for Variance Swap
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Realized Volatility (Discrete Time)
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Realized Volatility (Continuous Time)
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Payoff Function for Volatility Swap
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Payoff Function for Volatility-Average Swap
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Payoff Function for Implied Volatility Swap
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Payoff for Variance Swaptions
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Payoff Functions for Volatility Swaptions
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Payoff Function for Volatility and Asset Swaption
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Risk-Neutral Pricing Technique
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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
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1st Approach: Pricing Independently of the Volatility Model
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1st Approach: Pricing Independently of the Volatility Model (cntd)
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1st Approach: Pricing Independently of the Volatility Model (cntd)
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2nd Approach: Pricing by Expectations in a SV Framework
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2nd Approach: Pricing by Expectations in a SV Framework (cntd)
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2nd Pricing Approach: Pricing by Expectations in a SV Framework (cntd)
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2nd Pricing Approach: Pricing by Expectations in a SV Framework (cntd)
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3d Approach: Pricing via PDE
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3d Approach: Pricing via PDE (Model)
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3d Approach: Pricing via PDE (Payoffs)
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3d Approach: Pricing via PDE (Payoffs)
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3d Approach: Pricing via PDE (PDE Itself for the Value V of Derivative)
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3d Approach: Pricing via PDE (Mean-Reverting Model)
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General Stochastic Volatility Models
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Derivation of Certain Expectations
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Derivation of Certain Expectations.I.
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Derivation of Certain Expectations.II.
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Derivation of Certain Expectations.III.
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Derivation of Certain Expectations.IV.
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Derivation of Certain Expectations.V.
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Derivatives Pricing
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Mean-Reverting-Like Process
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Mean-Reverting-Like Process.I.
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Mean-Reverting-Like Process.II.
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Popular SV Models. I.
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Popular SV Models. II.
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Popular SV Models. III.
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Popular SV Models. IV.
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Popular SV Models. V.
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Asymptotical Analysis for Fast Mean-Reversion. I.
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Asymptotical Analysis for Fast Mean-Reversion. II.
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Asymptotical Analysis for Fast Mean-Reversion. III.
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Asymptotical Analysis for Fast Mean-Reversion (Summary).
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Examples: 1. The Variance Swap
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Examples: 2. The Standard-Deviation Swap
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Examples: 3. The Volatility-Average Swap
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Examples: 4. The Implied Volatility- Swap
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Examples: 5. The Volatility-Average Swaption
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The End
• Thank you for Your Attention!