Volume 5 CFA Level 1 Exercise

2. Read and list the new terms in the Section for Option Pricing (Section 8, from p317) in Volume 5, CFA Level 1. - Exercise value (Intrinsic value): The immediate payoff from exercising an option - Moneyness: Relationship between the underlying price and the strike price - o In the money (ITM): Exercise value is positive o At the money (ATM): Underlying price ≈ exercise price o Out of the money (OTM): Exercise value is zero o Deep ITM/OTM: Far from ATM, option has high intrinsic (or none). Time value: Portion of option value beyond intrinsic value, reflecting uncertainty before expiration - No-arbitrage bounds: Upper and lower limits for fair option prices to prevent arbitrage - Replication strategy: Constructing an option’s payoff using the underlying and borrowing/lending - Law of one price: Assets with identical payoffs must have the same price - European option: Exercise allowed only at expiration - Asymmetric payoff: Options differ from forwards/futures due to optionality - Contingent claim: Value depends on a future state of the world - Forward price (F₀(T)): Price agreed today for delivery at future date - Present value of exercise price (PV(X)): Exercise price discounted at risk-free rate; used in valuation - Replication with delta: Hedge ratio showing how much underlying is needed in a replicating portfolio Factors Influencing Option Value 1. Underlying asset value (S₀): Directly affects call/put values 2. Exercise price (X): Higher X => lower call, higher put 3. Time to expiration (T): Longer T => higher time value 4. Risk-free rate (r): Higher r => higher call, lower put 5. Volatility of underlying: More volatility => higher option value 6. Income or cost of holding underlying: Dividends (reduce calls, increase puts); storage/convenience costs affect commodity options 3. Read Chapters 14, 15 in the Textbook, write down and study at least 5 new terminologies/concepts. Chapter 14: Wiener Processes and Ito’s Lemma 1. Markov Property – The future evolution of a stochastic process depends only on its current state, not its past history 2. Stochastic Process – A variable that evolves over time in a way that is partly random 3. Wiener Process (Brownian Motion): A continuous-time process with (i) independent increments and (ii) normally distributed increments with mean 0 and variance proportional to time 4. Standard Wiener Process – A Wiener process with variance rate = 1. 5. Drift Term (μ): Represents the expected average rate of return or change in the process 6. Variance Rate (σ²): Controls the variability (volatility) of changes in the process. 7. Ito Process – A general stochastic process with both drift and volatility components, written as: [ dX = μ(X,t)dt + σ(X,t)dW ] 8. Ito’s Lemma – Provides the differential of a function of a stochastic process, a cornerstone in option pricing derivations 9. Geometric Brownian Motion (GBM): A stochastic process widely used to model stock prices: [ dS = μSdt + σSdW] 10. Lognormal Distribution: If a variable follows GBM, its logarithm is normally distributed. Stock prices under GBM are lognormally distributed 11. Expected Value of Stochastic Process: Average outcome under drift 12. Variance of Stochastic Process: Dispersion around the expected value, driven by volatility Chapter 15: The Black-Scholes-Merton (BSM) Model 1. BSM Model: A theoretical model for pricing European call and put options using risk-neutral valuation 2. Assumptions of BSM: Stock follows GBM, no arbitrage, no dividends, frictionless markets, constant r and σ, continuous trading 3. Risk-Neutral Valuation: A pricing approach assuming investors are risk-neutral, discounting expected payoff at the risk-free rate 4. Lognormal Property of Stock Prices: Stock price distribution at time T is lognormal with parameters (μ, σ) 5. Expected Return of Stock: The average rate of growth under real-world measure vs risk-neutral measure 6. Volatility (σ): The standard deviation of the stock’s continuously compounded return per year