List of Abbreviations

Transcription

1 List of Abbreviations (CM) 2 ACP AGP AJD ALU API ASIC ATA ATM AVX AXI BAR BIOS BLAST BM BS CAN CAPEX CDR CI CPU CRUD DAL Center for Mathematical and Computational Modelling. Accelerator Coherency Port. Accelerated Graphics Port. Affine Jump Diffusion. Arithmetic Logic Unit. Application Programming Interface. Application Specific Integrated Circuit. AT Attachment. At the Money. Advanced Vector Extensions. Advanced extensible Interface. Base Address Register. Basic Input/Output System. Basic Local Alignment Search Tool. Brownian Motion. Black-Scholes. Controller Area Network. Capital Expenses. Clock Data Recovery. Confidence Interval. Central Processing Unit. Create, Read, Update and Delete. Database Abstraction Layer. Springer International Publishing Switzerland 2015 C. De Schryver (ed.), FPGA Based Accelerators for Financial Applications, DOI /

2 268 List of Abbreviations DMA DRAM DSL DSP EISA EMS FF FFT FIFO FLOPS FPGA FRFT GARCH GNU GPGPU GPIO GPU GSL HDL HFT HLS HP HPC HPRC HTTP HW HW/SW i.i.d. I 2 C ICDF II ILP IP ISA Direct Memory Access. Dynamic Random-Access Memory. Domain-Specific Language. Digital Signal Processor. Extended Industry Standard Architecture. Euler-Maruyama scheme. Flip-Flop. Fast Fourier Transform. First in, First Out. Floating-Point Operations per Second. Field Programmable Gate Array. Fractional Fourier Transform. Generalized Autoregressive Conditional Heteroskedasticity GBM Geometric Brownian Motion. GNU s Not Unix. General Purpose Graphics Processor Unit. General-Purpose Input/Output. Graphics Processor Unit. GNU Scientific Library. Hardware Description Language. High-Frequency Trading. High-Level Synthesis. High Performance. High Performance Computing. High Performance Reconfigurable Computing. Hypertext Transfer Protocol. Hardware. Hardware/Software. Independent and Identically Distributed. Inter-Integrated Circuit. Inverse Cumulative Distribution Function. Initiation Interval. Integer Linear Programming. Intellectual Property. Industry Standard Architecture.

3 List of Abbreviations 269 IT ITM LS LUT MC MCMC MGT MLMC MMU MPEG MPML MSE MSVC MT NAG NRE OCM OPEX OS OTC OTM PC PCI PCI-X PCIe PDE PL PLL PS QE ReST RMSE RN Information Technology. In the Money. Longstaff-Schwartz. Lookup Table. Monte Carlo. Markov Chain Monte Carlo. Multi-Gigabit Transceiver. Multilevel Monte Carlo. Memory Management Unit. Moving Picture Experts Group. Mixed Precision Multilevel. Mean Squared Error. Microsoft Visual C++. Mersenne Twister. Numerical Algorithms Group. Non-recurring Engineering. On-Chip Memory. Operating Expenses. Operating System. Over-the-Counter. Out of the Money. Personal Computer. Peripheral Component Interconnect. Peripheral Component Interconnect Extended. Peripheral Component Interconnect Express. Partial Differential Equation. Programmable Logic. Phase Lock Loop. Programmable Systems. Quadratic Exponential. Representional State Transfer. Root Mean Squared Error. Random Number.

4 270 List of Abbreviations RNG RTL RV SCU SD SDE SerDes SIMD SoC SV SWIP TCO TLP TTM UART URI USB WWW XML Random Number Generator. Register-Transfer Level. Random Variable. Snoop Control Unit. Secure Digital. Stochastic Differential Equation. Serializer/Deserializer. Single Instruction Multiple Data. System on Chip. Stochastic Volatility. Scottish Widows Investment Partnership. Total Cost of Ownership. Transaction Layer Packet. Time to Market. Universal Asynchronous Receiver/Transmitter. Uniform Resource Identifier. Universal Serial Bus. World Wide Web. extensible Markup Language.

5 List of Symbols Options and Markets H payoff function. K strike price of the option. M moneyness of the option. S 0 current price of the asset (asset spot price). S continuous time asset price process. T time to maturity or time to expiration. W S Wiener process for the asset price simulation process. W ν Wiener process for the volatility simulation process. W Wiener process resp. Brownian motion. X price of a financial derivative. Φ cumulative distribution function of the standard normal distribution. α variance process in the SABR model. β distribution parameter in the SABR model. Ŝ discrete time asset price process. ˆν discrete time volatility process in the Heston model. κ mean reversion rate in the Hull-White model. κ mean reversion rate of the volatility in the Heston model. Re real part of a complex number. μ long term average price in the Black Scholes model. ν 0 current volatility. ν volatility parameter in the SABR model. ν continuous time volatility process in the Heston model. ρ correlation between two Brownian motions in Hull-White model. ρ correlation between two Brownian motions in the SABR model. σ volatility of the asset price in the Black-Scholes model. σ volatility in the Hull-White model. σ volatility of the volatility in the Heston model. θ long term average volatility in the Heston model. Springer International Publishing Switzerland 2015 C. De Schryver (ed.), FPGA Based Accelerators for Financial Applications, DOI /

6 272 List of Symbols ϕ characteristic function of the logarithmic stock price. ρ correlation between two Brownian motions in Heston model. a fair price of a european (possibly path-dependent) option. c fair price of a call option. p fair price of a put option. r risk-free interest rate. American exercise feature exercisable at any time until maturity, cf. European exercise feature. at-the-money strike equals spot. call option giving the buyer the right to buy an asset at maturity for the strike price. cap series of caplets. caplet call on the forward interest rate. European exercise feature exercisable only at maturity, cf. American exercise feature. floor series of floorlets. floorlet put on the forward interest rate. implied volatility value of the volatility parameter in a pricing formula equating model and market price. in-the-money intrinsic value is positive. maturity expiration time of a derivative. out-of-the-money intrinsic value is negative. put option giving the buyer the right to sell an asset at maturity for the strike price. strike fixed price at which the owner of the option can trade the underlying asset at maturity. swaption option on the swap rate. Vega sensitivity of a product price with respect to the volatility. Monte Carlo Simulations L total number of levels in a multilevel Monte Carlo simulation. M the multilevel constant. N number executed random experiments. P physical probability measure. Q equivalent (risk-neutral) probability measure. X random variable. A Monte Carlo estimator. E expectation value. μ true expectation value of a random variable X. σ standard deviation. l current level in a multilevel Monte Carlo simulation.

7 List of Symbols 273 Stochastic Processes and SDEs D number of discretization steps in discretized process. X stochastic process. g functional applied to a stochastic process. h step width of an equidistantly discretized process. t time variable. Calibration process ω weight assigned to a particular market price in calibration. calibration process of fitting model parameters to a set of market prices. objective function the function to be minimized in an optimization problem. penalty term stabilizing functional used in the calibration procedure. Parameter sets M model parameters. O observable market parameters. P product parameters. Equity and interest models Bates jump diffusion equity model of Bates. Black-Scholes equity model of Black and Scholes. Black 76 interest rate model of Black. Heston stochastic volatility equity model of Heston. Hull-White interest rate model of Hull and White. Merton jump diffusion equity model of Merton. SABR stochastic volatility interest rate model. Interest rates discount factor price of a zero bond paying one unit of money at a future time. forward rate expected interest rate to be paid between to future points in time. instantaneous forward rate expected interest rate to be paid for an infinitesimal small time step in the future. zero rate interest rate to be paid from today until a future point in time. Product prices ask price lowest price the seller is willing to accept. bid price highest price the buyer is willing to pay. bid-ask spread difference between bid and ask price. market price price at which a financial derivative is traded on the market. model price price of a financial derivative as implied from its model, market and product parameters.