About
Nikhil Rajan
Nikhil Rajan
BA Economics, Madras School of Economics (2023 to 2026)
MSc Financial Statistics & Mathematics, LSE (2026 to 2027, incoming)
Location Chennai, India
Email nikhilrajan0502@gmail.com
LinkedIn nikhil-rajan-7bb37a360
Research Interests
Stochastic Modelling Derivative Pricing Credit Risk Market Microstructure Welfare Economics
Chess
FIDE-rated (approx. 1500) · District and State representative

My name is Nikhil Rajan. I am a final-year undergraduate at the Madras School of Economics, heading to post graduation in quant finance at the London School of Economics. What caught my attention was seeing measure-theoretic ideas, especially risk-neutral expectations, show up in actual pricing formulas rather than staying abstract.

Since then, I have been building and testing models around that: simulating GBM paths, pricing options with Monte Carlo, and checking how sensitive outputs are to discretisation, volatility, and parameter shifts. Most of this I have implemented in Python and C++, focusing less on getting a number and more on how stable that number actually is.

I am most interested in the point a model stops giving the same answer once you tweak things like the time step, volatility, or even the scheme you are using. My current projects span market microstructure (liquidity regimes as Markov chains), credit risk (reconstructing the Jarrow-Lando-Turnbull framework from first principles), financial contagion between the S&P 500 and Nifty 50, and a dynamic welfare analysis of sin taxation using Markov consumption models calibrated to NSSO data.

At Madras School of Economics, I have held 7 teaching assistantships covering stochastic processes, game theory, time series analysis, microeconomics, multivariable calculus, and finance. I maintain a CGPA of 9.66 and have been on the Dean's List in every graded semester.

Outside of economics and finance, I am a FIDE-rated chess player who has represented Chennai District at state level. I am drawn to the kind of mathematics and statistics that surprises you.

Research
I  ·  Mathematical Finance
Mathematical Finance
01Liquidity Regimes and Optimal Execution
02Credit Rating Transitions and Defaultable Bonds
03Financial Contagion: S&P 500 and Nifty 50
3 papers →
II  ·  Mathematical Economics
Mathematical Economics
01Optimal Sin Taxation under Stochastic Consumption
02Labour Market Effects of MGNREGA
2 papers →
Teaching

Seven teaching assistantships at Madras School of Economics, spanning mathematics, probability, economics, and finance. Click any card to read what was covered.

∞
May to Jul 2025
MITx MicroMasters: Foundations of Modern Finance I & II
TECO Summer Course
Co-TA with Anagha · 8 Assignments + Final Exam
Topics, Assignments & Notes →
Ω
Sem V · Jul to Nov 2025
Stochastic Processes
Madras School of Economics
Under Prof. Srikant B. Pai
View Topics →
∿
Sem VI · Jan 2026 to Present
Time Series Analysis
Madras School of Economics
Under Prof. Srikant B. Pai
View Topics →
▷▷
Sem VI · Jan 2026 to Present
Game Theory
Madras School of Economics (2nd Year)
Under Prof. Aritri Chakravarty
View Topics →
σ
Sem V · Jul to Nov 2025
Intermediate Microeconomics
Madras School of Economics (2nd Year)
Under Prof. Aritri Chakravarty
View Topics →
∇
Sem IV · Jan to Apr 2025
Multivariable Calculus
Madras School of Economics (2nd Year)
Under Dr. Poorna Pushkala Narayanan
View Topics →
∫
Sem II · Mar 2024
Multivariable Calculus (Peer)
Madras School of Economics (1st Year, Peer)
Under Dr. Poorna Pushkala Narayanan
View Topics →
Notes

Study notes and reference materials prepared during teaching assistantships and independent study. All materials are shared as-is and should be cross-checked against standard references.

📚
Finance · MITx MicroMasters · TECO Summer 2025
Markowitz Portfolio Theory
Mean-variance optimisation from first principles, with worked examples
These notes cover Markowitz Portfolio Theory from first principles: the mean-variance framework, construction of the efficient frontier, the minimum variance portfolio, and the two-fund separation theorem. Worked numerical examples are included alongside the theory. Prepared as a supplementary resource for students in the TECO Summer course on Foundations of Modern Finance.
⚠
These notes have not been formally proofread and may contain minor errors. They are shared as a study aid and should be cross-checked against standard references (Markowitz 1952; Bodie, Kane, Marcus).
Mean-Variance Optimisation Efficient Frontier Minimum Variance Portfolio Two-Fund Separation Worked Examples
📄 markowitz_portfolio_theory.pdf
↓ Open Notes
Education
London School of Economics and Political Science
MSc Financial Statistics & Mathematics
London, United Kingdom · 2026 to 2027
Mathematical Finance
ST409Stochastic Calculus►
Martingales, optional stopping theorem. Poisson processes. BM construction, quadratic variation, the Ito integral. SDEs and diffusions: Ito's formula, Girsanov's theorem. Feynman-Kac connecting SDEs to PDEs. Option pricing under the risk-neutral measure, ruin theory, interest rate models.
MA415Mathematics of the Black and Scholes Theory►
Risk-neutral valuation built from the ground up. Binomial model first: replication portfolios, no-arbitrage, martingale measures. Then continuous time: European claims as risk-neutral expectations, BS PDE via self-financing portfolio arguments, Feynman-Kac and the connection to the heat equation. Barrier options, American options, path-dependent claims. Implied vol and stochastic vol models. FX market extensions.
ST461Mathematics of Market Microstructure►
Part I: HJB equation and dynamic programming under uncertainty. Inventory models and price impact. Optimal execution: Almgren-Chriss and Obizhaeva-Wang frameworks. Avellaneda-Stoikov limit order book model. Part II: asymmetric information in continuous time. Stochastic and Kalman filtering. Kyle model and extensions, Glosten-Milgrom, Glosten's electronic LOB. Part III: DEXes, AMMs, dark pools.
MA417Computational Methods in Finance►
RNG and Monte Carlo basics. Variance reduction: antithetic variates, control variates, importance sampling, quasi-MC. SDE simulation via Euler-Maruyama and Milstein schemes. Finite-difference methods for the BS PDE: explicit and implicit schemes, stability and convergence.
ST463Stochastic Simulation and Calibration►
Monte Carlo and process simulation. GANs for risk management. GLMs as a bridge to deep learning, applied to insurance pricing. Model calibration. RL for hedging and swing option pricing. Main references: Glasserman and Sutton-Barto.
MA435Deep Learning in Finance►
Deep learning for portfolio optimisation, optimal execution, derivative pricing and hedging, vol model calibration. ERM, bias-complexity tradeoff. Feedforward NNs, universal approximation, SGD, backprop, regularisation, RNNs, CNNs. Python throughout. Goodfellow et al. and Horvath et al. as main references.
Statistical Finance
ST425Statistical Inference: Principles, Methods and Computation►
MLE, score functions, Fisher information, Cramer-Rao. Bayesian inference: conjugate priors, MCMC (Gibbs sampler, Metropolis-Hastings). Bootstrap, model selection via AIC/BIC and cross-validation, elements of nonparametric inference. R throughout.
ST436Financial Statistics►
Financial data in R. ARCH-type models and volatility. Markowitz portfolio theory and CAPM. ML in financial forecasting. VaR. Ends with a trading case study.
ST458Machine Learning in Finance►
Extension of ST436. Advanced portfolio optimisation, factor models, large-portfolio constraints, algorithmic trading, deep learning for prediction. R. Main references: Hastie-Tibshirani-Friedman, Dixon-Halperin-Bilokon, Jansen.
Madras School of Economics
BA (Honours) Economics
Chennai, India · 2023 to 2026
CGPA: 9.66 / 10.0  ·  Dean's List: Semester II (9.9), Semester III (10.0), Semester IV (9.77)
Stochastic Processes►
Markov chains in discrete and continuous time: classification of states, stationary distributions. Martingales. BM, Poisson processes. First-passage times and hitting probabilities.
Real Analysis►
Sequences, series, continuity, differentiability, Riemann integration. Metric spaces. Convergence theorems.
Advanced Differential Equations►
ODEs and PDEs, BVPs, phase-plane analysis, Fourier methods. Applications to continuous-time financial and economic models.
Linear Algebra►
Vector spaces, eigendecomposition, matrix factorisation, linear transformations. Transition matrices, PCA, factor models.
Time Series Analysis►
Hamilton's TSA. ARMA, ARIMA, VAR. Unit roots and cointegration, spectral methods.
Econometrics►
OLS, GLS, IV, panel data, treatment effects. Causal inference. Stata.
Game Theory►
Normal and extensive form games. Nash equilibrium, SPNE. Mechanism design, auctions. Applications to IO and policy.
Money and Banking►
Monetary theory, central banking, credit creation, interest rates, policy transmission.
Statistics►
Probability, distributions, hypothesis testing, MLE, Bayesian inference, statistical computing.
Data Science (Python and MATLAB)►
Data wrangling, visualisation, numerical optimisation, simulation, intro ML. Python and MATLAB.
Experience
Research Intern
Madras School of Economics  ·  Advisor: Dr. Naveen Srinivasan
December 2024 to January 2025
  • Studied horizontal innovation and knowledge spillovers within the Romer endogenous growth model using analytical and numerical methods, focusing on long-run productivity implications of innovation intensity.
  • Developed micro-founded models and ran calibrated simulations to examine how the rate and direction of knowledge accumulation shapes steady-state growth trajectories.
Finance Intern
V MACS Yosaney  ·  Chennai, India
May 2024 to July 2024
  • Built an automated tool to generate profit and loss statements, balance sheets, and supporting schedules, improving reporting speed and accuracy across client accounts.
  • Analysed financial statements for MSMEs and evaluated credit products from banks and NBFCs to map documentation requirements, risk parameters, and eligibility thresholds.
  • Worked directly with clients on financial reports and automation projects.
Other
Chess
FIDE-rated  ·  Rating approximately 1500
  • 13th place at the 1st SRM International Open FIDE Rapid Chess Tournament (2022)
  • Captained school team in CBSE Cluster Championships; scored 5.5/6 on Board 1 (2022)
  • 2nd place Under-15 at Talent Chess Academy 2nd FIDE-rated Tournament (2019)
  • Represented Chennai District in Tamil Nadu State Under-17 Open (2018)
App Development
Eminence Class Recognition
  • Developed an education-tech application under India's first project-based learning programme, run jointly by IIT Madras, Rhapsody Plus, Intellect, and UC San Diego.
Articles

Notes and short pieces on topics worth writing about.

I am currently working on a few pieces and will upload them here soon.