Financial Derivatives: Pricing, Applications, and Mathematics
Compact mathematical treatment of derivative pricing and its applications
Summary
Baz and Chacko, both practitioners with academic backgrounds, wrote a compact treatment of derivatives pricing aimed at readers who need the mathematics but not a full textbook.
The structure covers the mathematical preliminaries first, including stochastic calculus, Ito's lemma, Brownian motion and the partial differential equations that pricing requires, then the pricing frameworks: the binomial model, Black-Scholes and its derivation, risk-neutral valuation and the martingale approach, and the equivalence between them. Applications cover equity, currency, commodity and interest rate derivatives, with treatment of term structure models including Vasicek, Cox-Ingersoll-Ross and Heath-Jarrow-Morton, and credit derivatives.
The book is deliberately concise, which is its distinguishing feature relative to Hull and other standard texts. It assumes a reader who wants the derivations and the intuition without the exhaustive coverage, and it explains why each mathematical result is needed rather than presenting the mathematics first.
It is aimed at practitioners in trading, risk and portfolio management and at graduate students, and it requires calculus and probability. It is not an introduction to derivatives as instruments; readers wanting that need a market-structure text first. The 2003 publication means it predates the credit crisis and the subsequent developments in counterparty valuation adjustment, collateral discounting and the multi-curve framework that changed derivatives pricing practice substantially. The core mathematics is unaffected.
Key takeaways 7
- Derivative pricing rests on replication, meaning constructing a portfolio of traded assets that reproduces the derivative's payoff, which determines its price by no-arbitrage.
- Risk-neutral valuation is a computational device rather than an assumption about preferences, since the resulting price holds regardless of any investor's risk aversion.
- Ito's lemma is the essential tool because it gives the dynamics of a function of a stochastic process, which is what a derivative is.
- The binomial model and the Black-Scholes equation give the same answer in the limit, and the binomial version makes the replication argument visible.
- Interest rate derivatives require modelling the whole term structure rather than a single price, which is why they need a different class of model.
- A model's parameters must be calibrated to observed prices, and calibration demonstrates flexibility rather than validity.
- The treatment predates the credit crisis, so counterparty valuation adjustment, collateral discounting and multi-curve frameworks are absent.
Who should read it
Practitioners and graduate students who need derivatives pricing mathematics concisely, with post-crisis developments sought elsewhere.
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