Year 3 · Applied Finance · Advanced Derivatives
Advanced Derivatives
Move from basic option definitions to professional derivatives analysis: volatility surfaces, delta hedging, gamma and vega risk, forward pricing, swaps, option structures, exotic payoffs and derivatives-based risk management.
LEARNING OBJECTIVES
What you should be able to explain after this lesson
01
Explain forward and futures pricing through no-arbitrage relationships.
02
Use delta, gamma, theta and vega to understand nonlinear option risk.
03
Interpret implied-volatility smiles, skews and term structures.
04
Understand dynamic hedging and the mechanics of delta-neutral portfolios.
05
Analyze common option strategies and their payoff trade-offs.
06
Understand interest-rate, FX and equity swaps at a professional level.
07
Identify model, liquidity, basis and counterparty risks in derivative positions.
CONCEPT MAPFrom no-arbitrage pricing to derivatives risk management
Forward prices come from carry and no-arbitrage, not opinion
CORE FACTS · SAME IN EVERY MODE
For a non-income-paying asset, forward value is linked to spot price compounded at the financing rate.
Dividends, storage costs and convenience yield alter the cost-of-carry relationship.
A forward has zero value at inception when the delivery price is set fairly.
Futures and forwards can differ because futures are settled daily and therefore create different cash-flow timing.
BeginnerTeaching style changes, knowledge does not.
A forward price is the future price that makes buying now and carrying the asset equivalent to agreeing today to buy it later. If the two choices were mispriced, traders could create an arbitrage.
FORMULASimple equity forward
F₀,T ≈ (S₀ − PV(Dividends)) × (1 + r)^TThe fair forward price reflects spot, financing cost and income received before maturity.
PROFESSIONAL VOCABULARYCost of carry / cost of carry Convenience yield / convenience yield Basis / basis
Net financing and holding cost embedded in forward pricing.
Non-cash benefit from physically holding a commodity rather than owning a future claim.
Difference between spot and futures or related derivative prices.