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COMP0043 Numerical Methods for Finance
创建日期：2024-05-17 18:16:57
标签： COMP0043
Numerical Methods for Finance
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COMP0043 Numerical Methods for Finance

Choose one of the following questions and write a program to answer it. You may use
Matlab, C++ or Python. Please ask for permission if you prefer another programming
language.
To reduce grade inflation, the programming style will be weighted more than in the
in-class assessments, so do not just hack something that runs and produces the correct
result, but try also to organise and comment your code as well as format its output in
order to make it easily understandable by a human.
Questions
1. Heston stochastic volatility model
In the Heston stochastic volatility model (1993) the variance evolves with a Feller square-
root process (1951), used also in the Cox-Ingersoll-Ross model for the term structure
of interest rates (1985). The Heston model is more realistic than the older stochastic
volatility model of Stein and Stein (1991), where the variance evolves with an Ornstein-
Uhlenbeck process (1930), because the latter mean-reverting process is Gaussian and thus
its support is R, while the Feller square-root process bounds the variance to R+. For the
system of stochastic di↵erential equations describing the Heston model, see Eq. (1) in
Yiran Cui, Sebastian del Ban˜o Rollin, Guido Germano, “Full and fast calibration of
the Heston stochastic volatility model”, European Journal of Operational Research 263
(2), 625–638, 2017, DOI 10.1016/j.ejor.2017.05.018, available on the Moodle page of
COMP0043, Section 8.
a) Write a script for the Monte Carlo simulation of the Heston stochastic volatility model
combining the script gbp.m that simulates geometric Brownian motion and the script
fsrp.m (formerly cirp.m) that simulates the Feller square root process. The generation
of correlated normal random numbers is described in Course Notes on Computational
Finance, Chapter 2.4, in Tools from Stochastic Analysis for Mathematical Finance: A
Gentle Introduction, Chapter 10.9.7, and in Numerical Recipes in C++: The Art of
Scientific Computing, 3rd edition, Chapter 7.4.
b) Add code to price call and put European options as in the Monte Carlo section of our
Black-Scholes pricing script bs.m. Use the parameters in Table 1 of Cui et al. (2017).
c) Check the price by integrating the characteristic function as in the Fourier transform
section of bsx.m; see Section 3.2 of Cui et al. (2017) for the pricing equation, Eq. (9),
and the characteristic function ; for the latter, use both the expressions of Schoutens
et al. (2004), Eq. (12), and Cui et al. (2017), Eq. (14): they should give the same
result.
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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