PSTAT 170 - QUIZ 1 INTRODUCTION TO MATHEMATICAL FINANCE APRIL 15, 2021 HAL W. PEDERSEN The quiz begins at the scheduled time of 11:00am Pacific. The submission window closes at 12:10pm Pacific. You have 70 minutes to complete this quiz and successfully upload your solutions to GauchoSpace. Leave sufficient time to complete your upload. Provide sufficient reasoning to back up your answer but do not write more than necessary. Show all work, do not just write an answer. For questions that use a calculator, make sure to write down the formula you are using that is typed into the calculator. Please make your final results easy to read. This quiz consists of 3 questions. Good luck! Problem 1. Suppose you want to short-sell 1000 shares of Apple stock which has a ask price of $132 and a bid-ask spread of $2. One year later, the ask price is $120 and the bid-ask spread is $1. (a) (4 points) Taking into account only the bid and ask prices (ignoring commissions and interest), what profit did you earn? (b) (6 points) Assume the brokerage fee is quoted as 1% and 0.5% one year later, what profit did you earn in this case? Problem 2. You have purchased one put option and one call option on the same underlying with both options expiring in one year and with strike prices of $30 and $50 respectively. The current price of the underlying is $40.20, the interest rate is zero, and the premium for the combined options is $3.69. (a) (3 points) Draw the payoff and P&L diagrams for the combined option at expi- ration. (b) (3 points) What is the P&L on the option at expiration if the underlying is $47.50? (c) (4 points) Now suppose that you sell the combined options instead. Draw the payoff and P&L diagrams and calculate the P&L if the underlying is $47.50. Problem 3. Assume the effective 6-month interest rate is 2%, the S&R 6-month forward price is $1020, the premium for S&R 1050-strike call option with 6 months to expiration is $71.802, and the premium for S&R 1050-strike put option is $101.214. (1) (5 points) Verify that you earn the same payoff by (a) shorting the S&R index for $1000 and (b) selling a 1050-strike S&R call, buying a 1050-strike put, and borrowing $1029.41. (2) (5 points) Verify that you earn the same profit by (a) shorting the S&R index for $1000 and (b) selling a 1050-strike S&R call, buying a 1050-strike put, and borrowing $1029.41. 1






































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