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Hedging Strategy Simulation
and Backtesting
with DSLs, GPUs and the Cloud
GPU Technology Conference 2013
Aon Benfield Securities, Inc. Annuity Solutions Group (ASG)
March 20, 2013
This document is the confidential property of Aon Benfield Securities, Inc. (“Aon”), has been prepared by Aon for informational
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licensed affiliate.
Section 1: Problem Description
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 4
Context Equity-Based Insurance Guarantees
– Investment Guarantees embedded in Life Insurance contracts
– Modeled as complex, long-term derivatives contracts
– Examples
• Variable Annuities, Equity-Indexed Annuities
Risk Management and Hedging
– These derivatives create market risks for insurers, e.g.
• Equity market risk
• Interest Rate risk
• Volatility risk
– Systematic risk accretes as the insurer sells more product
– Risk therefore needs to be transferred or hedged
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 5
Hedging Hedging business process (for a single point in time)
– Market quotes used to calibrate the Market Model (Economic Scenario Generator)
– Market Model used to value assets and liabilities
– Monte Carlo simulation offloaded to GPU grid for near real-time risk analytics
– Hedging Strategy rebalances asset positions to reduce (or eliminate) net risk
Liability Cashflow
Projection Model
Scenario Generator
MarketQuotes
Liability Risks
Hedging Strategy
Hedging Asset Models
Asset Risks
Net Risks
Legend
GPU Accelerated
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 6
Simulation-Based Risk Management
Hedging process is simulated through multiple time-steps and multiple scenarios
(generated scenarios, stress scenarios and historical back-testing scenarios)
Notice: Doubly–nested simulation
EconomicScenarios
Time-SeriesData
Scenario Generator
Hedging Simulation
Results
Liability Cashflow
Projection Model
Scenario Generator
Liability Risks
Hedging Strategy
Hedging Asset Models
Asset Risks
Net Risks
Next time step
“Inner Loop”
“Outer Loop”
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 7
Hedging Process in Detail
Scenario Generation (inner-loop)
– This typically refers to Risk-Neutral scenarios (calibrated to Market Quotes)
– There are many different modeling choices and assumptions
• Stochastic Equity (Geometric Brownian Motion, Jump Diffusion, etc)
• Stochastic Interest Rates (Hull-White, LIBOR Market Model, etc)
• Stochastic Volatility (Heston, SABR, etc)
– Could also refer to Real-World scenarios in the context of regulatory capital requirements
Liability Cashflow
Projection Model
Scenario Generator
MarketQuotes
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 8
Hedging Process in Detail Liability Cashflow Projection Model
– Model of complex insurance guarantee payoffs
– Practical approach is to use Monte Carlo method
– Insurance company may have dozens of different models for different products
Liability Risks
– Risk-Neutral Fair Market Value (Economic Risk)
• Sensitivities (Greeks) – Delta, Rho, Vega, etc
– Capital (Balance Sheet Risk)
• Tail measures (similar to VaR) are used by the insurance industry to set regulatory capital
requirements
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 9
Hedging Process in Detail Hedging Strategy
– Goal of hedging is for Asset and Liability Risks to be offsetting
– Many different possible strategies and hedging instruments
• Dynamic Hedging
Continuous rebalancing of assets to match liabilities
Many different possible rebalancing rules
• Static Hedging
Long-term, structured hedges
Often structured as reinsurance deals
• Semi-Static Hedging
Some combination of the two
Liability Risks
Hedging Strategy
Asset Risks
Net Risks
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 10
Hedging Process in Detail
Typical hedging instruments used by insurance companies
Equity
Futures
Interest
Rate
Swaps
Variance
Swaps
Vanilla
Options
Hybrid
Options
Lookback
Options
Structured
HedgeReinsurance
Delta
Rho
Vega
Gamma
Vanna
Vol Skew
Correlation
Policyholder
Behavior
Basis Risk
Ris
ksHedging Instruments
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 11
Simulation-Based Risk Management
Outer-Loop Economic Scenarios
– Real-World scenarios generated from a
model
– Historical Time-Series (back testing)
– Stress Scenarios
Good simulations require realistic Risk-Neutral
and Real-World models
– Wide tails
– Stochastic volatility, jumps
– Interest rate risk
– Mortality and lapse risk
– Intricate connections between Real-World
and Risk-Neutral models
EconomicScenarios
Scenario Generator
EconomicScenarios
Time-SeriesData
Scenario Generator
...Hedging
Simulation Results
“Outer Loop”
“Inner Loop”
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 12
Simulation-Based Risk Management Rationale
“The ability to understand, measure, and weigh risk is at the heart of modern life” 1
Hedging is a risky business
– Riddled with choices – many different, market models (scenario generators), hedging
instruments, hedging strategies, assumptions and parameters
Sensitivity to decisions and assumptions should be studied and documented
Should insist on comprehensive historical and simulation studies of hedging strategy
Simulation-based risk assessments are increasingly part of regulatory requirements for financial
institutions 1 Bernstein, Peter L. 1996. Against the Gods: The Remarkable Story of Risk. New York: John Wiley and Sons.
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 13
Simulation-Based Risk Management Example Variable Annuity Hedging and Business Plan simulation results
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 14
Simulation-Based Risk Management Computational Challenges
Realistic modeling
– Many different complex mathematical models must be implemented by Subject Matter
Experts
– Models must frequently change as businesses and markets evolve
Numerical stability
– Sufficient number of Monte Carlo samples
– Sufficient number of simulation time-steps
– Double precision versus single precision
Computational Steering
– Implementing this logic in a maintainable and efficient manner is a major Software Design
problem in itself
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 15
Simulation-Based Risk Management Nested Simulation Problem
– Simulating hedging leads to a “Doubly-Nested Simulation” problem
– Also called “Stochastic-on-Stochastic” (SoS) simulation
– Example SoS problem:
• 500 policies
• 1000 Risk-Neutral (inner-loop) scenarios, 1200 Risk-Neutral (inner-loop) time-steps
• 5000 Real-World (outer-loop) scenarios, 1200 Risk-Neutral (outer-loop) time-steps
• 10 risk factors (sources of randomness)
• 10 Greeks (“two-sided” sensitivities, i.e. 21 re-valuations )
Result
63 billion valuations
756 quadrillion random samples (may exceed periodicity of RNG!)
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 16
Simulation-Based Risk Management Computational Challenges
Reliability
– Business-critical process– must not fail
• SoS is often part of critical processes such as quarter-end financial reporting
– Grid processing required – prone to random failures
• Huge computational load, requires very large number of parallel processors, continuously
running for multiple days
• More servers and longer run-time increases probability of hardware faults
– Therefore, solution must be highly fault-tolerant at the software level
Section 2: Description of Solutions
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 18
Solutions Computational Challenges in Hedging Simulations
– Realistic modeling
– Numerical stability
– Reliability
Proposed Solution
– Language-Oriented Programming
• “Rather than solving problems in general-purpose programming languages, the
programmer creates one or more domain-specific languages for the problem first, and
solves the problem in those languages”1
• DSLs are an old idea. We propose that they are an excellent fit for GPU programming for
data parallel applications in specialized domains (e.g. financial Monte Carlo)
1http://en.wikipedia.org/wiki/Language-oriented_programming
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 19
Domain Specific Languages Simple DSL Compiler for GPUs
Parser
AbstractSyntaxTree
Business Logic
Front-End JIT Compiler
LLVM IR
LLVM Optimizer
Back-End JIT Compiler
(NVPTX target)
PTX kernel
CUDA Runtime / Driver
GPU
Legend
Supplied by NVIDIA
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 20
Domain Specific Languages Language Parser
– By constraining application to a specific domain, it is relatively simple to define a small formal
grammar and parser for a Domain Specific Language
– Implementation Steps
• Define a Context-Free, Right-Recursive Grammar in Backus-Naur Form (BNF)
• Use the BNF grammar rules to
Use a parser generator (e.g. ANTLR, or Lex/Yacc/Bison), or
Hand-code a recursive descent parser
• Parser outputs an Abstract Syntax Tree (AST) in the host language
Parser2*(X+Y)
Mul
Int
2
Add
Var Var
X Y
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 21
Domain Specific Languages Front-End Compiler
– Using LLVM Compiler Infrastructure simplifies compiler construction
– User must print Abstract Syntax Tree to LLVM IR (Intermediate Representation) and existing
Compiler Infrastructure will “take care of the rest”
Back-End Compiler
– NVIDIA provides CUDA Compiler SDK for handling this part of the tool-chain
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 22
Domain Specific Languages Example DSL Application (PathWise Modeling Studio)
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 23
Domain Specific Languages Benefits
– Productivity
• Business Logic can be implemented by Subject Matter Experts (SMEs), without requiring
programming expertise
• Programming experts can develop and improve software infrastructure without requiring
subject matter expertise
• One SME can implement a Monte Carlo model in 1 week (versus 6-12 months if directly
using general-purpose language, GPUs, grid middleware, and cloud APIs)
– Models implemented in the DSL can be automatically targeted to execute on GPU hardware,
grid middleware and cloud infrastructure
• Massive performance gains are essentially “free” for the DSL user
– Auditing and debugging
• Auditors and SMEs can easily validate and debug business logic, without being exposed to
programming complexities
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 24
Solutions Computational Challenges in Hedging Simulations
– Computational Steering
• Implementing this logic in a maintainable and efficient manner is a major Software Design
problem in itself
Proposed Solution
– General-Purpose High Level Scripting
HPC Middleware
ResultsPython Script
Data Store
GPU Cloud
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 25
Computational Steering Benefits
– Python
• High-level, interactive scripting languages (such as Python) have well documented
productivity benefits for users
• Large number of scientific computing tools available out-of-the-box (e.g. numerical arrays,
plotting, etc)
• Libraries and APIs allow vast majority of computations to be off-loaded to underlying C
function calls
– Providing necessary APIs to integrate seamlessly with DSL models and data
• Grid / Cloud Middleware API
• Data storage API
• Large Scale Optimization library
• Bloomberg Open API
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 26
Solutions Computational Challenges in Hedging Simulations
– Nested Simulation Problem
• Simulating hedging leads to a “Doubly-Nested Simulation” problem
• Also called “Stochastic-on-Stochastic” (SoS) simulation
• Example SoS problem:
63 billion valuations
756 quadrillion random samples (may exceed periodicity of RNG!)
Proposed Solution
– Accelerate simulations using GPU processors
• 35-500x observed gains in Monte Carlo throughput (vs quad-core x86 CPU)
– Distribute computations on GPU clusters
• Linearly scale up to 100s of GPUs
– Burst peak computational demands onto elastic cloud
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 27
GPU Cloud Computing Benefits
– Amazon EC2 offers Cluster GPU Reserved Instances and 10GigE interconnects
– Highly economical when provisioning large clusters for short periods of time
– Example: Quarterly Stochastic-on-Stochastic reporting (1 run per quarterly, 100 GPUs)
GPU cloud compared to a traditional CPU cluster collocated in a data center achieves an
estimated performance per dollar cost efficiency of 1500x
-
200,000.00
400,000.00
600,000.00
800,000.00
1,000,000.00
1,200,000.00
1,400,000.00
Data Center Colocation EC2 Reserved Instances
Annual Infrastructure Cost 100 GPU Cluster, Quarterly Runs
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 28
GPU Cloud Computing Cloud Computing Challenges
– Performance
• Cloud GPUs do not behave in the same way as bare-metal GPUs
• Para-virtualization technology used in by cloud providers leads to significant overheads,
especially in CPU-GPU synchronization critical sections of code
• Our initial attempts to run our models on Amazon’s GPU cloud led to a 200%
performance loss
• Optimizations to our DSL compiler and runtime allowed us to reduce this overhead to 10-
20%
– Integration
• DSL runtime and middleware had to be modified to integrate with cloud API
– Stability
• Fault-tolerance has to be built into application in order to effectively use the cloud
(especially if utilizing spot instances)
Section 3: Conclusion
Aon Benfield Securities, Inc. | Annuity Solutions Group
March 20, 2013 30
Conclusion Simulation-Based Risk Management
– An important risk management tool (hedging simulation and backtesting)
– However commonly avoided in practice due to computational challenges
• Subject Matter Experts must implement complex models
• Doubly-nested simulation
Huge amount of calculations required
Highly complex orchestration required
New technologies are enabling practical, Simulation-Based Risk Management
– Domain Specific Languages
• High-level languages for Subject Matter Experts
• Automatically target low-level hardware and massive parallelism
– High-Level Scripting Languages
• Productive environments for computational steering of large simulations on distributed systems
– GPUs and Cloud Computing
• Massive increases in throughput per dollar for Monte Carlo simulation