Five projects and a full set of course notes from my graduate financial engineering coursework at USC. The projects cover curve construction, lattice and Monte Carlo pricing, volatility modeling, interest rate models, credit, and a 30-year annuity guarantee. Each notebook states its assumptions, derives its formulas, and keeps every result in executed cells.
| Project | Methods | Key result | Open |
|---|---|---|---|
| Term Structure, Swaps, and Lattice Pricing Build the discount curve and price rates products and options off it. |
SOFR bootstrapping under three interpolations · swap and forward-swap pricing · CRR binomial · double-barrier knockout · trinomial tree | Par bonds reprice to exactly 100.00 under all three curves | Open |
| Monte Carlo Option Pricing Price exotics and test how well delta hedging replicates a sold option book. |
Asian and knockout payoffs · correlated baskets · bump-and-revalue Greeks · dynamic delta hedging · least squares Monte Carlo | Weekly hedging of 100,000 calls replicates at 782,038 against 1,134,848 collected | Open |
| Credit Risk Models Model default risk from single names to correlated portfolios. |
Merton structural model · CDS hazard bootstrapping · rating-transition valuation with a crisis stress · one-factor Gaussian tranches · Vasicek loss distributions | Merton calibration backs out a 0.477 percent market spread | Open |
| Volatility, Market Risk, and Real Options Measure market risk and value flexibility under uncertainty. |
GARCH(1,1) by maximum likelihood · VaR and expected shortfall under Vasicek rates · PCA on the Treasury curve · real options on a futures-calibrated tree | Persistence at 0.988; abandonment and expansion price at 7.6228 and 7.9608 | Open |
| Variable Annuity Guarantee Pricing Value a 30-year guaranteed withdrawal benefit from the insurer's side. |
Seeded Monte Carlo · equity correlated with stochastic Vasicek rates · mortality and fee income · risk-neutral and real-world views | 4.6091 per 100 of premium at 5 percent rates; negative 14.7196 at 1 percent | Open |
I wrote these notes chapter by chapter through the course and assembled them into one book, from interest rates and bonds through option pricing, volatility, and rate models to credit risk. Every model is derived step by step and explained in plain terms. Each chapter below opens the PDF at that chapter.
| Ch | Chapter | Topics | Open |
|---|---|---|---|
| 1 | Interest Rates, Bonds, and Futures | Rates and compounding, forward rates, bond pricing, bootstrapping the yield curve, swaps, futures and hedging | Open |
| 2 | Discrete Valuation Models | Option payoffs and strategies, binomial pricing, futures options, the analytical binomial model | Open |
| 3 | Continuous Time Models | Log returns, geometric Brownian motion, Ito's lemma, the Black-Scholes framework, risk-neutral valuation, Monte Carlo | Open |
| 4 | Implied Volatility and Non-Standard Options | The volatility surface, term structure and skew, local volatility, jump diffusion, Heston and Bates, Asian, compound, and FX options, variance swaps | Open |
| 5 | Interest Rate Derivatives and Models | Caps, floors, and swaptions, convexity adjustment, Vasicek and CIR, no-arbitrage models, Hull-White trees, forward rate models | Open |
| 6 | Credit Risk | Rating transitions, structural and reduced form default models, correlated defaults, CDS, CDOs, convertible and callable bonds | Open |
| 7 | Applications | PCA on the curve, VaR and expected shortfall, credit VaR, economic capital, asset liability management, commodity derivatives, real options | Open |