Options & Derivatives

Learn how EWMA and GARCH(1,1) models estimate and forecast volatility, including formulas, parameters, maximum likelihood estimation, and practical examples with the S&P 500 and Apple stock.

A swaption gives the holder the right to enter an interest rate swap at a predetermined fixed rate. Learn about payer vs receiver swaptions, Black-76 pricing, exercise styles, and hedging applications.

A convertible bond is a corporate bond that gives the holder the right to convert the bond into shares of the issuer stock, combining bond safety with equity upside potential.

A currency swap is an OTC derivative in which two counterparties exchange principal and interest payments in different currencies. Unlike interest rate swaps, principal is typically exchanged at both inception and maturity, creating unique FX exposure and counterparty credit risk.

Interest rate futures are exchange-traded contracts that allow institutions to hedge and speculate on movements in Treasury bond yields and benchmark rates like SOFR. This guide covers Treasury bond and note futures, the cheapest-to-deliver mechanism, SOFR futures, duration-based hedging with worked examples, and how rate futures compare to forward rate agreements.

Learn how interest rate caps and floors provide insurance against adverse rate movements. Covers caplet and floorlet payoffs, Black-76 pricing, cap-floor parity, and practical hedging strategies for floating-rate borrowers and lenders.

Real options apply option pricing theory to capital investment decisions, recognizing that management flexibility to expand, abandon, or defer projects has quantifiable value beyond what static NPV analysis captures.

Asian options base their payoff on the average price of the underlying asset over a specified period. Learn about average price (fixed-strike) and average strike (floating-strike) types, arithmetic vs geometric averaging, pricing methods, and why Asian options are widely used in commodity and energy markets.

Credit valuation adjustment (CVA) is the market price of counterparty credit risk — a risk-neutral pricing adjustment that reduces the value of an OTC derivative to account for the possibility that the counterparty defaults before all cash flows are exchanged.

Options on futures are derivative contracts where the underlying is a futures contract rather than a stock. Priced using Black’s model (Black-76), these instruments combine futures leverage with options’ asymmetric payoff. This guide covers how they work, how Black-76 prices them, and the key differences from equity options.