Question

1. The table below gives today’s prices of six-month European put and call options written on a share of ABC stock at different strike prices.  The stock does not pay a dividend and the risk-free interest rate is 0% per annum.

Call Price ($)	Strike Price ($)	Put Price ($)
13.1	105	8.2
9.7	110	9.7
7.9	115	12.9

1. Using call options with strike prices of 105 and 110, create a bear spread and show in a table the profit of the spread at maturity as a function of the then stock price. Give the range of stock prices at maturity for which this portfolio of options is profitable.
2. Using put options with strike prices of 110 and 115, create a bull spread and show in a table the profit of the spread at maturity as a function of the then stock price. Give the range of stock prices at maturity for which this portfolio of options is profitable.

Answer 1

(ь) Short put Stike Price B15 Shont put PaicePremium 12.9 derg put Staike price -110 dong put pricelpremiun $9.7 1 ASSume Future expiny dake Stork Prices as ts$90,$95 $100, 6IOS, 110, $1I5 &$120 $l2০s $90 $ho $95 $100 $105 Value of dorg Put option Excise E NE N.E NE NE GBIO- 0 - $I5 - $5 Valueot Shoxt put option Excised N.E NE N.E E E -115+0)25 -$5 I$20 IS -$10 Premium for 3.2 S-2 3-2 both Put eptions CA-T+-9 Net pay ot 3-2 3.2 3.2 3.2 3.2 3.2 3-2 3-2 -$1.8 -$1-8 -8 -8 8 The line chaut will be as follous axta)let pay ofs AKIS) Stock Price ( 120 125 115 0 I00 90 Note This Strotegy is cased enly wben the Investor expects a maderate Aise in unde lying asset (Stock Pice Price

Anshers Short callStrike Price -r05 (Beat Cau SPread Short Call Price /Premiuro$13-10 lorg call price/Premium $97 Long Call Strike price 10 Assume Stockprice on matui y Say $85, $90 $95,$100,$105, $110 &115 $85 $120 $105 $ UD $95 $115 $90 Natue ot he NE-O Excised Notexcisel N.E N.E Ex Not excise NE dong cau (us- 5 NE N.E Excised Value of the N.E NE NE Excised EX =-f0 1S SMFO FIPHy Shert Cal tteot rd sus . Premium for both Calls 3.4 3.4 3-u 3-4 3.4 3-4 3.4 3-4 G93H131) $3.4 -$.6 $3.4 $3.4 # 3.4 -$1.6 -$1-6 Net pay dt$34 The line Chast will be as folloas (rass)Net Paget 55 axis 15 120 - 5 Note This Staategy is used enly ahen the investor expects a decline in price t underly ing asset (Stock Paicee