Derivatives & Market Risk Masterclass: FRM | CFA | Actuarial

Master the time value of money as the foundation of risk management, enabling present value, NPV, IRR, and pricing of loans, bonds, and projects.

Explore the time value of money by calculating future value and present value. See how compounding frequency: annual, semiannual, and continuous shapes growth and key metrics like NPV and IRR.

Master discounting cash flows to value future money today and evaluate investments, loans, and bonds using present value, NPV, duration, and convexity.

Compute net present value by discounting cash inflows and deducting the initial outlay, the gold standard for evaluating investments; positive npv means accept, negative means reject, and zero means indifferent.

Understand the internal rate of return (IRR), the discount rate that makes net present value zero, guiding whether to accept or reject projects relative to the required return and NPV.

Apply NPV and IRR to real-world project scenarios, comparing simple and nonconventional cash flows and mutually exclusive choices to reveal NPV as the clearer measure of value creation.

Apply the time value of money to bonds by discounting coupons and face value to present value under yield to maturity, noting discount, par, premium, and zero coupon cases.

Understand how duration measures a bond's sensitivity to interest rate changes, linking cash-flow timing to price moves, via Macaulay and modified duration for fixed income risk management.

Convexity captures the curvature in the bond price–yield relationship, correcting duration's linear view. Use convexity for more accurate risk estimates, hedging, immunization, stress testing, and scenario analysis in volatile rates.

Combine duration and convexity to forecast bond price changes and manage portfolio risk. Apply immunization and convexity insights for asset-liability balance and enhanced risk control.

This lecture compares valuation and risk methods, uniting NPV, IRR, duration, and convexity to show when to use each tool for capital allocation and risk management.

Apply time value of money and risk management concepts to FRM part one through practical questions on future value, present value, NPV, IRR, bond pricing, duration, and convexity.

Reinforces core time value of money principles and shows how future value, present value, discounting, and compounding underpin risk management, FRM exam concepts like NPV, IRR, duration, and convexity.

Discover how derivatives transfer risk, enable hedging and speculation, and improve price discovery and market liquidity across equities, interest rates, foreign exchange, and commodities.

Explore how hedgers, speculators, and arbitrageurs shape derivatives markets by transferring risk, providing liquidity, and enforcing pricing efficiency through dealers and a robust institutional framework.

Explore derivative payoff structures, comparing linear forwards, futures, and swaps with nonlinear options, and visualize payoffs to master pricing, hedging, and risk management.

Explore arbitrage and fair pricing logic, uncovering the law of one price, no arbitrage, and the cost of carry, with cash-and-carry strategies linking spot and futures.

Consolidate practical derivative principles, key terminology, and common exam traps, covering forwards, futures, options, and swaps, with a concluding quick quiz for FRM, CFA, and university finance courses.

Explore the foundations of market risk across global markets, including systematic and idiosyncratic components, and learn key metrics like value at risk, expected shortfall, beta, duration, and convexity.

Explore value at risk (var) as a risk boundary defined by confidence level, time horizon, and loss, while noting its limitations and the role of expected shortfall.

Explore three var estimation methods—parametric, historical, and Monte Carlo—and learn when to use each, as FRM exams test these distinctions.

Backtest VaR models against real data to verify predictive power, using the Basel traffic light and Cupix and Christoffersen tests to assess frequency and independence, guiding governance and capital decisions.

Learn how expected shortfall replaces VaR to measure tail risk beyond the threshold. It delivers a coherent, stress-aware view used by Basel Frtb regulators.

Learn how stress testing and scenario analysis reveal vulnerabilities in market risk under extreme shocks, linking value-at-risk and expected shortfall to Basel III and Icap regulations, guiding capital planning.

Basel FRTB transforms market risk capital by replacing var with expected shortfall at 97.5%, introducing desk-level validation, stressed calibration, and clearer trading book boundaries for stronger risk governance.

Assess how liquidity risk turns market and funding liquidity into crises, through spreads, margin calls, and forced sales. Learn Basel III LCR, NSFR, stress tests, VaR, and ES integration.

Explore how market and credit risks interact, driving correlated losses, wrong way risk, cva implications, and integrated stress testing under basel iii.

Strengthen your conceptual map of market risk and governance by linking risk types, var and expected shortfall formulas, and stress tests for FRM exam readiness.

Explore what derivatives are, how their value derives from an underlying asset, and their uses in hedging, speculation, arbitrage, and portfolio management, plus key risks.

Explore forwards, futures, options, and swaps as the four core derivatives, their uses for hedging and risk management, and key valuation concepts for the FRM exam.

Explore how forwards, futures, options, and swaps enhance price discovery and market liquidity. See how derivatives enable risk management with hedging, interest rate and currency risk mitigation, and portfolio protection.

Explore forward contracts, their customized over-the-counter mechanics, long and short payoffs, and settlement, highlighting zero-sum risk and hedging applications with a currency forward example.

Futures contracts are standardized, exchange-traded derivatives with daily settlement and margin requirements, supported by clearinghouses that guarantee performance and reduce counterparty risk.

Apply no-arbitrage pricing to forwards and futures by linking spot prices, interest rates, and carry costs; derive forward prices using (1+r)^T or e^{rT} and consider storage and convenience yield.

Learn call and put options, their rights but not obligations, strike prices and premiums, payoffs, and american versus european exercise styles.

Explore option strategies such as spreads, straddles, and hedges to enhance risk-return control; vertical and horizontal spreads express views, while protective puts and covered calls hedge downside.

Master the put-call parity relationship, linking european call and put prices with the same strike and maturity via C – P = S – PV(K), ensuring arbitrage-free pricing.

Explore interest rate swaps: their structure, applications, and valuation. See how fixed and floating legs, notional principal, and net settlement affect corporate and bank risk management.

Learn currency swap mechanics, uses, and exam relevance, including principal exchange, interest payments, and re-exchange at maturity, plus hedging foreign debt and cheaper funding.

Explore equity, credit default, and commodity swaps, enabling synthetic equity exposure, credit risk transfer, and fixed-price hedging, while considering counterparty risk, basis risk, liquidity risk, and systemic risks.

Explore arbitrage-free pricing and its role in derivative valuation, linking spot prices, risk-free rates, and cash flows; apply cost-of-carry forward pricing and put-call parity to prevent arbitrage.

Explore the binomial option pricing model, valuing options with arbitrage-free principles, risk-neutral probabilities, backward induction, and two-move up or down steps on a binomial tree.

Explore yield curve strategies for fixed income risk management, including riding the curve, bullet, barbell, and ladder, and how normal, flat, and inverted shapes guide duration and reinvestment decisions.

Revisit core derivative instruments—forwards, futures, options, and swaps—and review no-arbitrage valuation. Examine hedging, speculation, arbitrage, and portfolio management while noting market, credit, liquidity, operational, and systemic risks.

Distinguish forwards from futures, master call and put mechanics, spreads and hedges, and apply arbitrage-free pricing and the binomial model for FRM Part I.

Explore the mechanics of call and put options, including premium, strike, expiry, moneyness, and the buyer’s rights versus writer’s obligations, and calculate option payoffs.

Master put-call parity, linking european calls, puts, stock, and the risk-free bond to expose arbitrage and synthesize positions for efficient derivatives valuation.

Explore how the binomial option pricing model uses discrete time steps, risk-neutral probabilities, and replication to value derivatives, including european calls and puts, with convergence to Black-Scholes.

Explore implied volatility as the market's forward view of future uncertainty, and map how volatility smiles, skews, and the surface drive option pricing, risk management, and model calibration.

Consolidate all lectures by applying no-arbitrage pricing across forwards, options, and swaps. Develop risk-neutral pricing, binomial valuation, put-call parity, and implied volatility techniques for FRM module five exam readiness.

Explore how risk models quantify market, credit, and operational risk, support capital decisions, and meet Basel and stress-testing standards for informed financial risk management.

Explore market, credit, and operational risk models, including value at risk, stress testing, sensitivity analysis with derivatives greeks, default probabilities, expected loss, and operational loss frameworks.

Explore volatility, correlation, and distributional assumptions as the foundation of quantitative risk management, shaping value at risk, stress testing, and diversification strategies.

Understand value at risk (VAR) as the potential loss over a defined time horizon at a given confidence level, guiding risk management and Basel regulatory decisions.

Explore the historical simulation approach to value at risk, a non-parametric method using 1–3 years of daily returns to revalue a portfolio and estimate losses (95% VaR).

Master the variance-covariance (parametric) approach to value at risk, using mean return, standard deviation, and correlations to compute VAR, noting Basel acceptance and fat tails.

Use Monte Carlo simulation to estimate value at risk by generating thousands of scenarios for portfolios with non-linear payoffs, using distributions for risk factors and percentile thresholds.

Assess the strengths and limitations of value at risk (VaR), including its simplicity and regulatory backing, and the move toward expected shortfall and stress testing.

Explore stress testing as a forward-looking risk tool that complements VAR by evaluating tail risks under extreme scenarios, including sensitivity, scenario, and reverse tests, under regulatory context.

Compare historical and hypothetical scenarios in stress testing to assess portfolio resilience and identify vulnerabilities, while Frem exam requirements emphasize understanding and comparing both approaches.

Identify scenarios that could cause a firm to fail through reverse stress testing, revealing hidden weaknesses. Learn the four-step method from defining the failure point to contingency planning.

Examine regulatory perspectives on stress testing and Basel's shift from value at risk to expected shortfall, and how CCAR, IBA, and Bank of England exercises integrate with ICAP and ELAP.

Integrate value at risk with stress testing to gain a holistic view of financial risk, bridging normal conditions and tail events for regulatory compliance and capital and liquidity planning.

Explore case studies of market crash scenarios, from Black Monday to Covid 19, revealing how correlations spike, models fail under stress, and the need for stress testing and contingency planning.

Practice FRM style questions with solutions to reinforce your understanding of value at risk, historical simulation, stress testing, reverse stress testing, and expected shortfall.

Recap the FRM nano six risk models and stress testing, covering market, credit, and operational risk, volatility, correlation, and distributional assumptions, plus value at risk methods and regulatory context.

Master how to tackle FRM exam questions on risk models by practicing VAR calculations, historical variance and covariance, Monte Carlo methods, and stress testing concepts for real-world scenarios.

Explore how global financial markets trade bonds, equities, currencies and derivatives to enable price discovery, liquidity, capital allocation, risk transfer, and efficiency, while highlighting interconnections and regulation.

Explore the primary market where issuers raise capital through IPOs, government bonds, and corporate debt. Compare the secondary market’s role in liquidity and price discovery on exchanges and OTC.

Identify the three main market participants—issuers, investors, and intermediaries—and explain how their actions drive capital flows, price discovery, and risk management across global primary and secondary markets.

Explore bond basics: face value, coupons, maturity, and price, and learn how present value links coupons to yields, with premium, par, and discount concepts.

Examine government, corporate, and structured bonds, their features and key risks, including credit, liquidity, and rate risk, and learn how diversification and risk management shape fixed income portfolios.

Explore the three fundamental bond risks—interest rate, credit, and liquidity—and how duration and convexity measure price sensitivity, while highlighting their interactions and holistic management.

Compare common and preferred shares to grasp equity features, voting rights, dividends, and liquidation priorities, and apply this framework to Basel III capital adequacy and stress testing.

Examine dividend policies and their link to equity valuation, including policy types and the dividend discount model, plus risk signals for FRM professionals.

Explore market indexes and systematic risk factors that measure performance and drive equity returns. Learn index construction methods—price, market cap, and equal weighting—and their impact on risk and benchmark-based analysis.

Study spot rates, forward rates, and cross rates in the global fx market, and learn hedging, arbitrage, and interest rate parity concepts.

Examine how foreign exchange rates are quoted, interpreted, and applied in practice across direct and indirect quotes, bid-ask spreads, pips, and cross rates, with FRM hedging implications.

Explore currency risk—transaction, translation, and economic exposure—and learn FX hedging with forwards, futures, options, and swaps to manage foreign exchange exposure in global finance.

Explore futures contracts' mechanics and applications: standardized, exchange-traded, margin and daily mark-to-market, enabling hedging, speculation, and arbitrage across assets via clearinghouses.

Explore how margining systems and clearinghouses, as central counterparties emphasized by Basel III, reduce systemic risk in futures markets through initial, maintenance and variation margins, daily mark-to-market, and final settlement.

Explore how futures hedge against losses and enable speculation, learn hedge ratios, optimal hedges via regression, leverage and margin risks, basis risk, and arbitrage to maintain market efficiency.

Compare bonds, equities, fx, and futures to understand their returns, risks, and how hedging and risk management shape portfolios.

Practice FRM style questions with solutions to reinforce bonds, equities, foreign exchange, and futures concepts; develop quantitative, conceptual reasoning and exam-ready risk management skills.

Consolidate essential concepts from bonds, equities, foreign exchange, and futures, and apply risk management through hedging tools, market linkages, and Basel III insights for FRM success.

Explore the Black-Scholes framework, linking geometric Brownian motion to option replication via delta hedging and risk-neutral valuation, deriving European call and put prices and Greeks.

Explore the Greeks: delta, gamma, vega, theta, and rho, and learn how their sensitivities shape option pricing, hedging, and risk management.

Learn how professionals hedge portfolios with delta and vega neutral strategies, decompose P&L using Greeks, and manage gamma, theta, and non-linear exposures to control risk.

Aggregate deltas, gammas, vegas, thetas, and rhos across portfolios to execute scenario-based hedging and connect cross greeks and correlations to VAR, expected shortfall, and Basel IFRS risk frameworks.

Explore how delta, vega, theta, gamma, and rho drive risk and profit. See how capital integration under Basel 3.1 aligns pricing, risk, and PNL.

Capstone workshop integrates Black-Scholes valuation theory, Greeks, hedging, and capital impact in a live multi-option case to value positions, hedge risk, and link results to capital and performance.

Link single-position analysis to portfolio risk by showing how asset interactions, covariance, and correlation shape diversification, portfolio return, and total risk using the variance-covariance framework.

Define value at risk and explain its role as a universal risk metric, and outline its three methods: parametric, historical, and Monte Carlo—plus the key parameters, limitations, and regulatory context.

Evaluate portfolio resilience under adverse conditions using sensitivity analysis, stress testing, and scenario analysis, linking results to Basel 3.1 and IFRS 9 capital planning.

Learn how risk managers use cross hedging and portfolio hedging techniques to reduce exposure when perfect hedges don't exist, using correlation, optimal hedge ratios, and basis risk.

Integrate portfolio risk analytics with governance and capital allocation by uniting VAR, stress testing, and Greeks into a real-time dashboard for risk-informed decision making and value creation.