FRM一级百题巅峰班课件：期权与风险模型.docx

金程教育WWW.GFEDU.NET 专业·创新·增值此预测为考点预测，考题仅为复习参考内部使用资料，严禁传播，否则追究法律责任2020 FRM Part I百题巅峰班 期权与风险模型2020 年 5 月62-62金程教育WWW.GFEDU.NET 专业·创新·增值此预测为考点预测，考题仅为复习参考内部使用资料，严禁传播，否则追究法律责任4. Options and Risk Models4.1. Basic Characteristics of Option4.1.1.1. Option Factors & Pricing Bounds4.1.1.2. Put-call ParityEuropean option: p + S = c + Xe – rTAmerican option: no exact price relationship4.1.1. 重要知识点FactorEuropean CallEuropean PutAmerican CallAmerican PutS＋ ＋ X ＋ ＋T??＋＋σ＋＋＋＋r＋ ＋ D ＋ ＋OptionProxyMin ValueMax valueEuropean callcmax(0, S0 – Xe–rT)S0American callCmax(0, S0 – Xe–rT)S0European putpmax(0, Xe–rT – S0)Xe–rTAmerican putPmax(0, X – S0)X4.1.2. 基础题Q-1. The current stock price of a share is USD 100 and the continuously compounding risk- free rate is 12% per year. The maximum possible prices for a 3-month European call option, American call option, European put option, and American put option, all with strike price USD 90, are:A. 100,100,87.34, 90B. 100,100,90, 90C. 97.04,100, 90, 90金程教育WWW.GFEDU.NET 专业·创新·增值此预测为考点预测，考题仅为复习参考内部使用资料，严禁传播，否则追究法律责任D. 97.04, 97.04, 87.34, 87.34ScenarioLower Bound (USD)Upper Bound (USD)A5.1340.00B5.005.13C34.8740.00D0.1334.87Q-2. Consider an American call option and an American put option, each with 3 months to maturity, written on a non-dividend-paying stock currently priced at USD 40. The strike price for both options is USD 35 and the risk-free rate is 1.5%. What are the lower and upper bounds on the difference between the prices of the call and put options?A. Scenario AB. Scenario BC. Scenario CD. Scenario DQ-3. Jeff is an arbitrage trader, and he wants to calculate the implied dividend yield on a stock while looking at the over-the-counter price of a 5-year put and call (both European-style) on that same stock. He has the following data:Ÿ Initial stock price = USD 85Ÿ Strike price = USD 90Ÿ Continuous risk-free rate = 5%Ÿ Underlying stock volatility = unknownŸ Call price = USD 10Ÿ Put price = USD 15What is the continuous implied dividend yield of that stock? A. 2.48%B. 4.69%C. 5.34%D. 7.71%Q-4. The price of a six-month, USD 25 strike price, European call option on a stock is USD 3. The stock price is USD 24. A dividend of USD 1 is expected in three months. The continuously compounded risk-free rate for all maturities is 5% per year. Which of the following is closest to the value of a put option on the same underlying stock with a strike price of USD 25 and a time to maturity of six months?金程教育WWW.GFEDU.NET 专业·创新·增值此预测为考点预测，考题仅为复习参考内部使用资料，严禁传播，否则追究法律责任A. USD 3.60B. USD 2.40C. USD 4.37D. USD 1.634.2. Trading Strategies Involving Options4.2.1.1. Simple StrategiesØ Covered Call and Protective PutØ Principal Protected Notes(PPN)4.1.1.1. Spread StrategiesØ Bull and Bear SpreadØ Box SpreadØ Butterfly Spread4.1.1.1. Combination StrategiesØ Straddle and Strangle4.2.1. 重要知识点4.1.1. 基础题Q-5. Consider the following bearish option strategy of buying one at-the-money put with a strike price of $43 for $6, selling two puts with a strike price of $37 for $4 each and buying one put with a strike price of $32 for $1. If the stock price plummets to $19 at expiration, calculate the net profit/loss per share of the strategy.A. -2.00 per shareB. Zero – no profit or lossC. 1.00 per shareD. 2.00 per shareQ-6. Which option combination most closely simulates the economics of a short position in a futures contract?A. Payoff of a long call plus a short putB. Profit of a long call plus a short putC. Payoff of a long put plus short callD. Profit of long put plus short call金程教育WWW.GFEDU.NET 专业·创新·增值此预测为考点预测，考题仅为复习参考内部使用资料，严禁传播，否则追究法律责任Q-7. A butterfly spread involves positions in options with three different strike prices. It can be created by buying a call option with a low strike of X1; buying a call option with a high strike X3; and selling two call options with a strike X2 halfway between X1 and X3. What can be said about the upside and downside of the strategy?A. Both the upside and downside is unlimited.B. Both the upside and downside is limited.C. The upside is unlimited but the downside is limited.D. The upside is limited but the downside is unlimited.Q-8. The payoff on a calendar spread is most similar to which of the following option strategies?A. Bull spreadB. Bear spreadC. Long straddleD. Butterfly spreadQ-9. An investor sells a January 2014 call on the stock of XYZ Limited with a strike price of USD 50 for USD 10, and buys a January 2014 call on the same underlying stock with a strike price of USD 60 for USD 2. What is the name of this strategy, and。