This course aims to develop the knowledge of the theoretical foundation of financial models and the application of those models to insurance and other financial risks. This course prepares the Investment and Financial Markets (IFM) examination by the Society of Actuaries (SOA) and the Financial Economics examination (Exam 3F) by the Casualty Actuarial Society (CAS).
Chapter 1: Introductory Derivatives -- Forwards and Futures - 1.1 Derivative Markets (derivative, underlying asset, forward/futures, option, long, short, obligation, exercise, right, regulated exchanges, OTC, hedging, speculation, transaction costs, regulatory arbitrage); 1.2 Forward Contracts (forward, underlying asset, expiration date, forward price, long, short, position, obligation, spot price, payoff and profit, diagrams, no initial payment, fair forward price, no-arbitrage principle, investment strategy, value process, arbitrage strategy, cash flow, no-cost, arbitrage opportunity, free lunch, no-arbitrage pricing principle, arbitrage-free, law of one-price, buy-low-sell-high argument, replicating portfolio, perfect hedge, forward prices, non-dividend-paying stock, discrete dividends, continuous dividend, synthetic long/short forward, expected rate of return, expected stock price greater); 1.3 Variations on Forwards (purchase method, payment time, asset delivery time, payment amount, outright purchase, spot price, forward contract, forward price, fully leveraged purchase, full loan, prepaid forward contract, prepaid forward price, futures contract, exchange-based forward, mark-to-market, daily settlement, liquidity, offset, opposite position, standardization, credit risk minimized, price limit, temporary halt trigger, margin account, initial margin, notional value, multiplier, earn interest, debit/credit, maintenance margin, margin call, additional deposit, close position).
Chapter 2: General Properties of Options - 2.1 Option Contracts (underlying asset, long, exercise, short, exercise date, expiration date, strike price, right, obligation, call, put, European, American, Bermudan, early exercise, position, exercise style, payoff, payoff diagram, moneyness, in-the-money, at-the-money, out-of-the-money, option price, profit, profit diagram); 2.2 Option Strategies (insurance, floor, cap, written covered call, written covered put, synthetic forward, genuine forward, initial payment, put-call parity, bull spread, bear spread, box spread, ratio spread, collar, collar width, zero-cost collar, collared stock, straddle, strangle, butterfly spread); 2.3 Option Comparisons and Price Bounds (moneyness, put-call parity, at any time, European call price bound, European put price bound, American worths more than European, non-dividend-paying, early exercise call sub-optimal, zero risk-free rate, early exercise put sub-optimal, American call price bound, American put price bound, monotonicity, Lipschitz property, convexity, term-to-maturity).
Chapter 3: Binomial Pricing Models - 3.1 Single-Period Binomial Model (two time points, risk-free asset, risky asset constant risk-free interest rate, single-period binomial tree, arbitrage-free, no-arbitrage condition, discounted expectation under risk-neutral world, real-world probability, risk-neutral probability, pricing and hedging European options, replicating portfolio, perfect hedge, cost of replicating portfolio, synthetic call, synthetic put, discounted expected payoff under risk-neutral world, risk-neutral valuation formula, volatility, annualized standard derivation, forward binomial tree); 3.2 Multi-Period Binomial Model (N+1 time points, risk-free asset, risky asset, constant risk-free interest rate, multi-period binomial tree, arbitrage-free, no-arbitrage condition, discounted expectation under risk-neutral world, real-world conditional probability, risk-neutral probability, pricing and hedging European options, replicating portfolio, perfect hedge, cost of replicating portfolio, synthetic call, synthetic put, discounted expected price under risk-neutral world, tower property, risk-neutral valuation formula, volatility, annualized standard derivation, forward binomial tree, iteration.); 3.3 Binomial Models on American Options (early exercise, immediate exercise value, holding value).
Chapter 4: Black-Scholes Option Pricing Model - 4.1 Lognormal Model of Stock Prices (continuous-time, Black-Scholes model, geometric Brownian motion, Brownian motion, lognormal model, lognormal distribution, expectation, first principle, distribution function, survival function, exercise probability, conditional tail expectation, expected payoff); 4.2 The Black-Scholes Formula (continuous-time, two financial assets, risk-free, risky, constant risk-free interest rate, lognormal model, risk-neutral world, risk-neutral valuation formula, Black-Scholes call and put option prices, put-call parity, price bounds).
Chapter 5: Option Greeks and Risk Management - 5.1 Option Greeks (Black-Scholes valuation formula at time t, observed values, model inputs, option characteristics, option Greeks, partial derivatives, sensitivity, change infinitesimally, Delta, Gamma, theta, Vega, rho, Psi, option Greek of portfolio, absolute change, option elasticity, percentage change, option elasticity of portfolio); 5.2 Applications of Option Greeks (risk management via hedging, immunization, adverse market changes, delta-neutrality, delta-hedging, local, re-balance, from-time-to-time, holding profit, delta-hedging, first order, prudent, delta-gamma-hedging, gamma-neutrality, option value approximation, observed values change inevitably, Taylor series expansion, second order approximation, delta-gamma-theta approximation, delta approximation, delta-gamma approximation).
Chapter 6: Exotic Options - 6.1 Introduction to Exotic Options (plan vanilla options, non-standard option characteristics, exotic options, gap, exchange, maxima and minima, chooser, forward start, Asian (arithmetic and geometric), barrier, lookback, compound, shout, path-dependency, path-independent, path-dependent, closed-form valuation formula, binomial model); 6.2 Exotic Options I (payment trigger, strike price, European gap call and put, obligation, negative payoff, decomposition, Greeks, deterministic cash, short risky asset, exchange option, European maximum and minimum contingent claim, decomposition, chooser option, choose, call or put, choosing decision, decomposition, forward start call and put option, strike price determined at intermediate date observed risky asset price, not observed, price); 6.3 Exotic Options II.
1. Lecture Notes.
2. McDonald, R. L. (2013), Derivatives Markets, 3rd edition, Pearson.
1. Bean, M. A. (2018), Actuarial applications of options and other financial derivatives, Investment and Financial Markets Exam Study Note IFM-22-18, Society of Actuaries.
2. Berk, J. B. and DeMarzo, P. M. (2017), Corporate Finance, 4th edition, Pearson.
3. Li, J. S. H. (2018), SOA Exam IFM Study Manual, Summer 2018 edition, ACTEX Learning.
4. Weishaus, A. (2018), SOA Exam IFM: Study Manual, 1st edition, Actuarial Study Materials.
5. White, T. A. (2018), Measures of investment risk, Monte Carlo simulation, and empirical evidence on the efficient markets hypothesis, Investment and Financial Markets Exam Study Note IFM-21-18, Society of Actuaries.
6. Bingham, N. H. and Kiesel, R. (2004), Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives, 2nd edition, Springer.
7. Bjork, T. (2009), Arbitrage Theory in Continuous Time, 3rd edition, Oxford University Press.
8. Bodie, Z., Kane, A., and Marcus, A. J. (2017), Investments, 11th edition, McGraw-Hill Education.
9. Cochrane, J. H. (2005), Asset Pricing, revised edition, Princeton University Press.
10. Hull, J. C. (2018), Options, Futures, and Other Derivatives, 10th edition, Pearson.
11. Lo, A. (2018), Derivative Pricing: A Problem-Based Primer, Chapman & Hall.
12. Shreve, S. E. (2004), Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer.
13. Shreve, S. E. (2004), Stochastic Calculus for Finance II: Continuous-Time Models, Springer.