Market Risk For Actuaries (Exams SP9/CM2/CP1)

Define market risk as the unexpected change in an asset's price, capturing both upside and downside, with duration shaped by holding periods, liabilities, and correlations across assets.

Identify market risk by tracing three uncertainty sources: economic factors, fundamental changes, and systemic risk that drive asset prices and returns.

Explore market risk models, linking the log of future stock prices to time-varying mean and variance, and contrast historical GARCH with forward-looking implied volatility from Black-Scholes.

Examine the normality assumption in market risk, its fat tails and volatility implications, and why despite critiques it remains the standard for derivative pricing.

Explore the variance of future returns, including downside and semi downside variance, and connect these measures to second order stochastic dominance and the Sharpe/Sortino ratios.

Explore shortfall models, focusing on the probability of shortfall and the expected shortfall. Learn to compute tail value at risk as the conditional loss beyond a threshold.

Value at risk uses frequency, severity, and duration to quantify potential losses at a confidence level, such as 95% over 10 days, including tail risk and capital implications.

Explore the GARCH model for volatility estimation, showing how alpha and beta capture volatility clustering and mean reverting to the long-run variance.

Learn how to manage market risk by weighing hedging and derivatives, basis and counterparty risk, diversification pitfalls, and strategies to reduce duration, frequency, and severity, including Long-Term Capital Management.

Monitor market risk by measuring asset managers' performance. Use the shop ratio and tino ratio to assess excess returns, noting downside variance and fee incentives to separate skill from luck.

Introduces Brownian motion as background maths for implied volatility, defines delta z, delta t, and epsilon, and shows delta z ~ N(0, delta t) as delta t tends to zero.

Explore the Wiener process as a Brownian motion with drift, where X evolves with mean A t and variance B^2 t, capturing trend and dispersion in market risk.

Explore the Ito process as an upgrade from the Viner process with price dependent drift. Zero volatility yields exponential stock growth; volatility becomes price dependent, hinting at Itô's lemma.

Learn how itô lemma uses log-transformations to turn drift and volatility in itô processes driven by Brownian motion into a tractable stock price model, connecting to the Black-Scholes framework.

Explore the Black-Scholes framework for pricing call and put premiums and deriving forward-looking implied volatility from market prices.

Trace Basel I to Basel III, cover capital adequacy, risk-weighted assets, three-pillar approach, capital conservation and countercyclical buffers, leverage ratio, liquidity convergence ratio, NSFR, and SPV-based securitization.