High performance pricing framework for complex financial derivatives using finite difference methods.
Features:
- Versatile configuration via XML (see the docs)
- Calculate expectation values for risk neutral valuation, utility indifference pricing and other expectation based pricing methods
- Derive optimal/pessimal strategies for payoffs that depend on decisions (like exercise decisions in Bermuda/American options or optimal hedging decisions)
- Provides a novel implementation of the Cryer algorithm for general linear complementary problems (used for American type exercise with more than one exercise region)
- Explicit, Implicit and Crank-Nicholson time-stepping (with Rannacher steps for smooth Greeks)
- Arbitrary dimensional state space, i.e. any number of underlyings and driving factors such as stochastic volatility. Curse of dimensionality (somewhat) weakened through automatic Strang splitting.
- Any combination of von-Neumann and Dirichlet boundary conditions (boundary conditions are solved using a novel implementation of a sparse Sherman-Morrison approach)
- Arbitrary nesting and compounding of derivatives, i.e. calculated prices can be transparantly used as payoffs
- Automatic coarse-grained parallelization through the use of an extended version of Intel's TBB Flow Graph (see below)
- Automatic optimal PDE discretization: the optimal finite difference stencil is derived using non-negative least squares
The software was used to derive numerical results for my dissertation.
- Boost >= 1.54
- Boost Headers (Ubuntu: libboost-dev)
- Boost Filesystems (Ubuntu: libboost-filesystem-dev)
- Boost Program Options (Ubuntu: libboost-program-options-dev)
- Boost System (Ubuntu: libboost-system-dev)
- Threading Building Blocks (Intel TBB) >= 4.4_20160526
- Eigen Template Library >= 3.2 (Ubuntu: libeigen3-dev)
- gcc >= 6.2.0 | >= 4.8.5 | clang >= 3.5.0
- compiling with MS Visual C++ should also work
(see also the travis configuration)
make runo
which uses the config.xml in the same directory.
Alternatively, you can build it with
make opt
and the run it with src/main --config <path>
make run or make debug
Fipster uses its own XML-based configuration format to describe what to calculate. Please refer to the docs and example configurations.
Here is an excerpt of config/positions.xml:
<boundaryConditions id="BCs1" tolerance="1e-14">
<stateVariable nr="1">
<lower type="Dirichlet" inhomSource="futureValue"/>
<upper type="Dirichlet" inhomSource="futureValue"/>
</stateVariable>
</boundaryConditions>
<finiteDifferenceWeights id="BSIsoWAm">
<stencilType>OneDiagonal</stencilType>
<PDE type="BSIso">
<discountingRate>0.05</discountingRate>
<volatility>.5</volatility>
<correlation>0.0</correlation>
<drift>0.05</drift>
</PDE>
<partialDerivativeOrder>2</partialDerivativeOrder>
<higherOrderWeight>0.9</higherOrderWeight>
</finiteDifferenceWeights>
<expectation id="AmExpectation">
<boundaryConditions>BCs1</boundaryConditions>
<finiteDifferenceWeights>BSIsoWAm</finiteDifferenceWeights>
<strangSymmetrization>true</strangSymmetrization>
<timeStepping>
<offset>0</offset>
<stepSize>0.01e6</stepSize>
</timeStepping>
<theta>0.5</theta>
<rannacherSteps steps="2">
<strangSymmetrization>false</strangSymmetrization>
<stepSize>0.005e6</stepSize>
<theta>1</theta>
</rannacherSteps>
</expectation>
<option id="AmOption">
<discountingRate>0.0</discountingRate>
<expectation>AmExpectation</expectation>
<times>
<stop>1e8</stop>
<offset>1e8</offset>
<stepSize>0.01e6</stepSize>
</times>
<exercise>
<implicit>false</implicit>
<value>payoff1</value>
</exercise>
</option>
<solution active="1" id="Decisions0" hedgingPos="true">
<fields>
<option id="AmOption" exercise="always"/>
<option id="Option" exercise="always" skip="2">
<deltaHedging>
<option id="AmOption" exercise="always"/>
</deltaHedging>
</option>
</fields>
<times>
<start>.75e8</start>
<offset>.75e8</offset>
<stop>1e8</stop>
<stepSize>.12e7</stepSize>
</times>
<fixedPlotTime>1e8</fixedPlotTime>
<grid>grid1</grid>
<singleValues>
<at><x>40</x></at>
<at><x>45</x></at>
<at><x>120</x></at>
</singleValues>
</solution>The corresponding program output on a quadcore CPU,
where .x.... is used to indicate which CPU core calculated a certain step:
> src/main --config config/positions.xml
careful: discounting_rate only applies to the expectation, thus it is not suitable to calcuate higher moments of discounted quantites by solving this pde with undiscounted final values
x.....: Parser | create_graph_and_run (parallel)
x.....: Hedging grid (hedging_grid_f):
[("cache hit", 9616979), ("cache miss", 545119), ("continue_nodes", 7), ("edges", 1384335), ("function_nodes", 518), ("joined_function_node", 358862), ("runtime_join_nodes", 420172)]
Cache size of 'boundary_conditions':1
Cache size of 'fdweights':2
Cache size of 'payoff1':2502
Cache size of 'Option':56700
Cache size of 'AmOption':5002
Cache size of 'Expectation1':169200
Cache size of 'AmExpectation':10002
Cache size of 'splitter':2
Cache size of 'timestepping_operator':4
x.....: GRAPH | Start and wait for all
.x....: EXPL FL (0) | START
.x....: EXPL FL| DONE
x.....: EXPL FL (0) | START
x.....: EXPL FL| DONE
..x...: WEIGHTS| for 2 neighbors and 2 of PDE terms
..x...: WEIGHTS| (unconstrained weights) are NOT overdetermined
..x...: WEIGHTS| nSites: 298
..x...: WEIGHTS| Accessing Least Squares TLS
..x...: WEIGHTS| DONE, maxNorm:0.000e+00 in 6.280e-05s
..x...: &gsi: 0x7fabc0002950
..x...: WEIGHTS| DONE systems information in 7.717e-06s
..x...: BCs | START
..x...: BCs | DONE, assembled and inverted: 8.352e-06s
..x...: SPLITIN| START
..x...: SPLITIN| TESTING Split
..x...: SPLITIN| DONE TESTING Split
..x...: SPLITIN| DONE
..x...: WEIGHTS| for 2 neighbors and 2 of PDE terms
..x...: WEIGHTS| (unconstrained weights) are NOT overdetermined
..x...: WEIGHTS| nSites: 298
..x...: WEIGHTS| DONE, maxNorm:0.000e+00 in 5.090e-05s
..x...: &gsi: 0x7fabc0004b20
..x...: WEIGHTS| DONE systems information in 4.658e-06s
..x...: SPLITIN| START
..x...: SPLITIN| TESTING Split
..x...: SPLITIN| DONE TESTING Split
..x...: SPLITIN| DONE
..x...: EXPECT | Accessing Time Stepping TLS
.x....: EXPECT | Accessing Time Stepping TLS
...x..: EXPECT | Accessing Time Stepping TLS
x.....: EXPECT | Accessing Time Stepping TLS
.x....: OUTPUT (Decisions0 at time 100000000 on grid grid1) | START
...x..: OUTPUT (Decisions2 at time 100000000 on grid grid1) | START
[...]
x.....: OUTPUT (Decisions0 at time 76200000 on grid grid1) | START
..x...: OUTPUT (Decisions1 at time 76200000 on grid grid1) | START
.x....: OUTPUT (Decisions2 at time 76200000 on grid grid1) | START
..x...: OUTPUT (Decisions1 at time 75000000 on grid grid1) | START
x.....: OUTPUT (Decisions0 at time 75000000 on grid grid1) | START
...x..: OUTPUT (Decisions2 at time 75000000 on grid grid1) | START