Theory and Practice for the FVA: General Instruments and General Models
Presenter: Alexander Antonov: Senior Vice President, Quantitative Research, Numerix
Video Lectures:
xVA general framework: from replications to adjustments Section 1.1 (Running Time: 32:21)
xVA general framework: from replications to adjustments Section 1.2 (Running Time: 44:56)
xVA general framework: from replications to adjustments Section 1.3 (Running Time: 43:19)
xVA general framework: from replications to adjustments Section 1.4 (Running Time: 48:09)
Collateral in Different Currencies Section 1.1 (Running Time: 41:32)
Collateral in Different Currencies Section 1.2 (Running Time: 44:53)
Approximation for General Instruments (including arbitrary callable instruments) (Running Time: 35.46)
- Literature
- Introduction
xVA general framework: from replications to adjustments Section 1.2 (Running Time: 44:56)
- Classical replication/hedging (before the crisis)
- Modern replication/hedging (after the crisis)
xVA general framework: from replications to adjustments Section 1.3 (Running Time: 43:19)
- Pricing equations
- Case studies
- Replication
- Pricing PDE
xVA general framework: from replications to adjustments Section 1.4 (Running Time: 48:09)
- Adjustments
- Comparison
- How to avoid double counting and other traps?
Collateral in Different Currencies Section 1.1 (Running Time: 41:32)
- Foreign currency collateral: pricing PDE via modified replication procedure
- Efficient discount factor for the currency choice option
Collateral in Different Currencies Section 1.2 (Running Time: 44:53)
- Analytical methods for the efficient discount factor calculation (two currency case)
- Numerical experiments
Approximation for General Instruments (including arbitrary callable instruments) (Running Time: 35.46)
- Main idea
- Theoretical and Numerical Issues
- Numerical experiments for a Bermudan option: comparison of the exact FVA with its different approximations
Summary:
1. General multi-currency setup
2. FVA theory framework
- Pricing PDE and its solution by replication
- Probability measure and numeraire
- Generalization
2. Collateral in different currencies
- Replication procedure
- Efficient discount factor for the currency choice option
- Analytical methods for the efficient discount factor calculation (two currency case)
- Numerical experiments
3. Approximation for general instruments (including arbitrary callable instruments)
- Main idea
- Theoretical and Numerical Issues
- Numerical experiments for a Bermudan option: comparison of the exact FVA with its different approximations