Tools

Payoff and profit for long and short forwards, futures, calls and puts, with break-evens and the premium's effect.

Forward and futures prices from cost of carry: income, storage costs and convenience yield, and a forward's value during its life.

Price a forward rate agreement from the curve, and value it after rates move, with the settlement amount discounted.

Put–call parity and put–call–forward parity: replicate one instrument from the others and find the arbitrage when prices break parity.

Price an option on a one-period tree by replication and by risk-neutral probabilities, and read the hedge ratio.

Follow a futures position day by day: initial and maintenance margin, variation margin and margin calls, basis and convergence to spot.

Treasury bond futures: conversion factors, quoted and full futures prices, implied repo rates and the cheapest-to-deliver bond.

Black–Scholes–Merton prices with a dividend yield, and delta, gamma, vega, theta and rho, with the working shown.

Back out implied volatility from a price, and see the smile and skew across strikes and expiries.

European and American calls and puts on a multi-period binomial tree, with early exercise marked at each node.

The Black model for options on futures, interest rate caps and floors, and payer and receiver swaptions.

How each Greek moves with the underlying price, time to expiry and volatility, for calls, puts and their combinations.

Build covered calls, protective puts, collars, spreads, straddles, strangles and butterflies, or any combination of legs, with payoff, profit and Greeks.

Combine option and underlying positions into a portfolio and read its net Greeks and value across prices.

Make a position delta-neutral with the underlying, then gamma-neutral with a second option, and test the hedge.

Rebalance a delta hedge along a price path and see how realized against implied volatility drives the hedging profit or loss.

Shock the underlying price, volatility and time, and compare full revaluation with the delta–gamma estimate.

Size beta hedges with index futures and duration hedges with bond futures, and compare hedging an FX or commodity exposure with a forward, an option or a collar.

Price a fixed–floating swap from the curve, value it after rates move, and see it as a portfolio of FRAs.

Price and value a currency swap, with notional exchanges and both legs' cash flows in each currency.

Value equity and total return swaps, where one leg pays the return on a stock or index.

FX forward points from covered interest parity, and FX swaps that pair a spot trade with a forward.

Fix a commodity price with a swap, using the forward curve, storage costs and convenience yield.

Price a credit default swap: hazard rate, fair spread, upfront, risky duration and the position's mark-to-market.

Where volatility and rates closed: the VIX, implied volatility and the risk-free rates the tools use.

The formulas behind every tool, grouped by topic, with each term explained.