Download presentation

Presentation is loading. Please wait.

Published byJailyn Cowden Modified about 1 year ago

1
Modeling of Variance and Volatility Swaps for Financial Markets with Stochastic Volatility Anatoliy Swishchuk Department of Mathematics & Statistics, York University, Toronto, ON, Canada Seminar-April 15, 2004 Department of Statistics, University of Toronto

2
Outline Introduction Stochastic Volatility Model: Heston (1993) Model Solution of the Volatility Equation Property of the Solution Variance and Volatility Swaps Calculation of Expectation and Variance Covariance and Correlation Swaps Numerical Example: S&P60 Canada Index

3
Introduction Cox, Ingersoll &Ross (CIR) (1985)-stochastic variance model; Heston (1993)-asset price has variance that follows a CIR model; Brockhaus & Long (2000)-calculation expectation and variance for volatility swap using analytical approach; He & Wang (RBC Financial Group) (2002)- proposed deterministic volatility for variance and volatility swaps: Query Note for the 6 th IPSW PIMS, Vancouver, UBC, May 2002

4
Stochastic Volatility Model

5
Explicit Solution for Variance

6
Properties of the Process

7
Properties of Variance

8
Variance Swaps

9
Volatility Swaps

10
Calculation E[V]

11
Calculation of Var[V]

12
Calculation of Var[V] (continuation)

13
Calculation of E[V] and Var[V] in Discrete Case (sketch)

14
Calculation of E[V] and Var[V] in Discrete Case (sketch) (continuation )

15
Covariance and Correlation Swaps

16
Pricing Covariance and Correlation Swaps

17
Valuing of Covariance Swap

18
Calculation Covariance for S1 and S2

19
Calculation Covariance for S1 and S2 (continuation I)

20
Calculation Covariance for S1 and S2 (continuation II)

21
Calculation Covariance Swap for S1 and S2

22
Numerical Example: S&P60 Canada Index

23
Statistics on Log-Returns of S&P60 Canada Index for 5 years ( )

24
Estimation of the GARCH(1,1) Process

25
Generating Different Input Variables for the Volatility Swap Model

26
Continuation (Numerical Example )

27
Figure 1: Convexity Adjustment

28
Figure 2: S&P60 Canada Index Volatility Swap

29
Some References

30
Some References (continuation)

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google