QUIZ 3: 1. You have $ 100 to invest. You can invest it in one of two alternatives. The first is to invest it in a stock that is trading for $100. The second is to buy three-month 100- strike calls on the stock that are currently trading at $4 each. You expect the stock price to appreciate with a maximum price after three months of $110. What is the maximum return on investment you can generate using stock and options? 150% (110-100)/100 = 0.1 (stock) Option? (question 4 in the practice) 2. Which of the following statements are true? The maximum possible loss to the seller of a call option is unlimited 3. You sell an IBM call option for $4. The strike price of the option is $120, and the is maturity is one year. At maturity, the price of the IBM stock is $126. Your profit/loss over the entire transaction is: $2 loss 126 – 120 – 4 = 2 4. The largest markets for derivatives based on notional outstanding are Interest rate derivatives 5. The premium of an option is The value of the right but not the obligation to undertake a purchase or sale of the underlying asset The price of the option Is always non-negative 6. You hold the following portfolio: a long position in a European call option on gold with a strike of $975 per OZ, a short position in a European put option on gold with a strike of $975 per oz, and a short forward position in gold with a delivery price of $1,000 per oz. All three contracts expire in one month. The value of your position is Positive 7. If you expect stock volatility to fall but have no particular view of direction, then you should Sell call options 8. An investor who holds a short call option on IBM stock is implicitly Bearish on direction and volatility 9. For a call and put written on the same underlying but at a possibly different strike price Both call and put options may be in the money at the same time 10. I hold a long position in a call option on IBM stock. If the price of IBM goes down and its volatility goes up, then the value of my call option May increase, decrease, or stay the same 11. You anticipate that volatility will increase sharply, and the stock price will fall. Select the most profitable of the following portfolios to hold, given your views: Short stock and long puts 12. The writer of a put option on a stock Has the obligation but not the right to buy the stock 13. You have a long position in a stock that you purchased for $100, and a short position in a put option on the same stock at strike K = 100. At maturity the stock price is $95, and you liquidate your stock and option positions. Your gross payoff is $ -10 14. You anticipate a recession with increased stock volatility and greater negative skewness in stock prices. Which of the following option positions would be most consistent with your view? A strip 15. The 90-, 100-, and 110-strike calls are trading at $12, $5, $3, respectively. The stock price is at $100. What is the maximum net payoff on a long butterfly spread using these options? $5 C(K1)+C(K3)-2C(K2) 12+3-(2*5) – 5 16. The combination of a position in a covered call and a position in a protective put on a stock index (where the options have the same strike and maturity) is similar to: A long position in a balanced index fund (i.e., long stock and long investment at the riskfree rate) 17. If you go short a covered call and buy a protective put portfolio on a given stock (with the options having the same strike and maturity), what you have is A long position in a straddle 18. Suppose your portfolio consists of one share of Goldman Sachs (GS) and a European put option on GS with a strike of $105 and a maturity of a year. At maturity, the value of your portfolio must be Equal to or greater than $105 19. Consider a long position in a 100–strike straddle added to a short position in a 90/110–strike strangle. The underlying is a stock index. This is equivalent to: A short position in a 90-100-110–strike butterfly call spread plus a zero-coupon bond of face value 10. QUIZ 4: 1. The delta of an option measures, approximately, The dollar change in option value for a $1 change in the price of the Underlying 2. The delta of a call option is 0.6. The current price of the call is $5, and the stock is at $100. What is the approximate price of the call if the stock price increases to $100.50? $5.30 5 + 0.6(0.5) – 5.30 3. The delta of a call option is 0.6 The current price of the call is $5 and that of a put at the same strike is $ 4, and the stock is at $100. What is the approximate price of the put if the stock price increases to $100.50? $3.80 0.6 – 1 = -0.4 4 – 0.4 (0.5) = 3.80 4. A stock is trading at $80. You hold a delta-hedged portfolio in which you are short call and long units of the stock. The delta of the call is 0.65 and the gamma of the call is 0.06. If the stock registers an unexpected price decrease of $4, the value of your delta-hedged portfolio will Decrease by approximately $0.48 5. The gamma of an option is The dollar change in the option delta for a $1 change in the price of the underlying. 6. You hold a portfolio of a long position in a call and a short position in a put, both for the same strike and maturity, both written on a non- dividend paying stock. Which of the following statements is most correct? The delta of the portfolio stays the same when the stock price increases 7. The gamma of a put is typically highest when The stock price is in the region of the strike price 8. Gamma is a risk measure that is related to the volatility particularly jump-risk) of the underlying stock. Which of the following is most valid? When you sell vanilla put options it is useful to hedge away gamma to minimize jump risk 9. Which of the following is not an assumption underlying the Black-Scholes model? The dividend rate must be less than interest rate 10. The implied volatility of an option Is the volatility that would have to be plugged into a given option-pricing model to obtain the observed market price. 11. A stock is currently trading at SO = 25.85. It is not expected to pay dividends over the next year. You price a six-month call option on the stock with a strike of K = 15 using the Black-Scholes model and find the following numbers: d1 = 2.115d2 = 1.832 N(d1) = 0.983N(d2) = 0.967 Given this information, the delta of the call is 0.983 (N)d1 12. A stock is currently trading at SO = 25.85. It is not expected to pay dividends over the next year. You price a six-month call option on the stock with a strike of K = 15 using the BlackScholes model and find the following numbers: d1 = 2.115d2 = 1.832 N(d1) = 0.983N(d2) = 0.967 Given this information, the delta of the call is -0.237 13. A stock is currently trading at So = 21.30. It is not expected to pay dividends over the next year. You price a one-month put option on the stock with a strike of K = 22.50 using the BlackScholes model and find the following numbers: d1 =-0.666d2 = -0.738 N(d1)= 0.253N(d2) = 0.230 Given this information, the delta of the put is -0.747 14. Which of the following quantities associated with equity option pricing is model dependent? Implied volatility 15. You hold a portfolio of options on Tesla stock. 200 short calls and 300 long puts. The delta of the calls is 0.38 and the delta of the puts is -0.63. In order to delta hedge this portfolio what should you do? Buy 265 Tesla stocks 16. A share of IBM stock is trading at $200. In one year, it will go up by $50 or down by $50. The annual interest rate is 10 %. Value a European call option of IBM with a strike price of $225. $15.91 QUIZ 5: 1. Firm A can borrow at 5 % fixed or at Libor+100 bps in the fixed and floating rate markets, respectively. Firm B can borrow at % fixed or Libor + 200 bps in the fixed and floating rate markets, respectively. A want to borrow floating and B wants to borrow fixed. If A borrows fixed and B borrows floating, and they enter into a fixed-for-Libor interest-rate swap in which A pays Libor flat, what is the range of fixed rates for B that enables at least one firm or both firms to improve its financing costs (compared to accessing financing in the market directly)? 5% - 7% 2. You enter into a $100 million notional swap to pay six-month Libor and receive 7 %. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360convention. If the floating rate was reset to 6 % on March 25, what is the net amount you will receive on September 25? (March 25-September 25 is 184 days) 433, 333 184/360*0.06*100,000,000 = 30666666.67 184/360*0.07*100,000,000 = 35777777.78 3. An FRN has four remaining payment dates Libor rates as ofto 5.25% 5.18% $.40% 5. 90% Time to payment t=100 days t2=283 days t;= 465 days t4= 648 days The FRN has a face value of $1. The first coupon payment is 5.2 %. What is the value of the FRN? The first coupon payment at initiation 182 days. 1.012 Discount factor = 1/ (1+5.25*100/360) …. The first coupon payment = 5.2 *182/360 ….. …… 1+ …. …. * …. 4. Find the value of the following swap to the fixed recever (short swap). Payment Dates 18 Dec - Yr1 18 Jun - Y12 18 Dec- Yr2 18 Jun -Yr 3 18 Dec -Y1 3 Days from Present 120 303 485 668 850 Discount Factors 0.98396 0.95977 0.93629 0.91697 0.88970 Swap rate: 5 %, LIBOR at last reset: 5 % (182 days to first coupon at initiation) -196.696 5. The main difference between the "short-form" and " forward" methods of pricing a A floatingrate note s: The short form method does not require knowledge of the entire forwards term structure of interest rates 6. A plain vanilla interest-rate swap is an agreement to exchange a series of periodic payments, one computed at a fixed rate and the other at A floating rate indexed to a money market rate in the same currency (e.g. libor) 7. Your firm can borrow fixed at 8% and floating at Libor+1%. You also enter into a fixed-for-Libor swap where the fixed rate is 7.5% (and the swap has the same maturity as the borrowing). What is the cheapest way for the firm to obtain fixed rate financing? Borrow at the fixed rate 8. You have entered into a swap where you receive the fixed rate and pay the floating rate. What is the best way to hedge interest rate risk in this swap from among the following choices? Add a short position in interest rate futures