Black-Scholes summaryBlack-Scholes matches qualitatively and quantitatively the following sensitivities we discussed previously:•Black-Scholes takes these five inputs (?, 𝑋, 𝜎, ?, 𝑟) and tells you what they imply call and put option premia should be▪Also tell you what current replicating portfolio Δ, BisCall PricePut PriceStock price (?)IncreasesDecreasesExercise price (𝑋)DecreasesIncreasesVolatility (𝜎)IncreasesIncreasesMaturity (?)IncreasesUsually IncreasesInterest rate (𝑟)IncreasesDecreasesFinance 367 - Lecture 23Option Valuation18Black-Scholes Option Valuation
10Finance 367 - Lecture 23Option Valuation19Implied volatility•In practice, we observe every ingredient in Black-Scholes formula except 𝜎▪Can estimate 𝜎using past returns, as in Data Exercise 1•Can also reverse the Black-Scholes formula: instead of using 𝜎to find ?and ?, use ?and ?to solve for 𝜎▪“Implied Volatility”, typically annualized▪?and ?high relative to ? ⇒high implied volatility ▪?and ?low relative to ? ⇒low implied volatility ▪Predicts future stock volatility very wellTLSA implied volatility for 6-month ATM options: 72%GOOGL implied volatility for 6-month ATM options: 31%S&P implied volatility for 6-month ATM options: 27%▪Requires fancy Excel spreadsheet or other software (just Google “implied volatility calculator”)▪Available on Yahoo! FinanceImplied volatility over timeGulf warLTCM9/11IraqLehman etc.US Debt DowngradeCovid-19
1Travis JohnsonFinance 367Lecture 24:Mutual Funds, Hedge Funds, Course Wrap-upChapter 4Announcements•Final Exam on Friday, May 15thCovers entire course, with a focus on the last Unity15-20 questions on last unit, 15-20 questions on first three unitsYour choice of 9am-noon or 2-5pmNo need to tell use in advance which one you’ll chose•Same rules as Midterm 3:Open notes, textbook, internet etc.You definitely still need to study!Must be on Zoom call with us, video enabled if possibleNo discussing with anyone else inside or outside class•Main Concepts in Unit 4: forward and futures terminology, hedging & speculating using futures, futures arbitrage pricing, futures curve, put and call option terminology & payoffs, payoffs vs net payoffs, hedging & speculating using options, option strategies, put-call parity (& arbitrage), intrinsic vs time value, general option valuation properties, binomial options pricing (& arbitrage), implied volatility, mutual funds, hedge fundsFinance 367 - Lecture 24Mutual Funds, Hedge Funds, Wrap-up2
2Pre-exam schedule•Pre-exam schedule:TA Review Session:Thursday, May 14thTA office hoursJangwoo Lee Thursday 5/7 5-6pmThomas Lee Monday 5/11 5-6pmChangyong Song 5/13 3-4pmMy office hours (Tuesday 5/12 4-6pm)Finance 367 - Lecture 24Mutual Funds, Hedge Funds, Wrap-up3Mutual fund idea•Investors pool their money, have manager invest itCheap way to get diversificationLess effort than managing your own assetsSave on transaction costsProfessional money manager may do a better job than you would?