Question

The price of a share of stock is currently $50. The stock does not pay any dividend. At the end of three months it will be either $60 or $40. The risk-free interest rate is 5% per year. What is the value of a three-month European put option on this share of stock with a strike price of $50?

Answer 1

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DERIVATIVES BINOMIAL - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins E AutoSum - Cut AC Wrap Text Calibri 11 General ECopy Fill Merge & Center Paste в IU* +.0 .00 .00 0 Conditional Format Cell Insert Delete Format Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Editing Clipboard Font Alignment Number Styles Cells fox AU29 AO AQ AY AZ AN АР AR AS AT AU AV AW AX ВА ВВ |(60-50)/50= 20.00% 29 PRICE INCREASE = (40-50)/50 -20.00% 30 PRICE DECREASE = 31 32 PAYOFF 0.00 [PUT WILL NOT BE EXERCISED] IF PRICE INCREASE = MAX [50 - 60, 0] = 33 MAX [50- 40, 0] = 10.00 [PUT WILL BE EXERCISED] 34 IF PRICE DECREASE = 35 NOW TO GET 5% RETURN [ ANNUAL RATE = 5%, 3 MONTHS RATE 1.25%] 36 37 WE CAN USE FOLLOWING EQUATION TO FIND RISK NEUTRAL RPROBABILITY RISK FREE RATE = PROB(INCREASE)*(20%) PROB(DECREASE)(-20%) 38 1.25% (X)(20%) + (1-X)(-20%) 39 1.25%= (X)(20%)- 20% + (X)(20%) 40 21.25% (X)(40%) 41 42 0.531250 PROBABILITY OF INCREASE 43 1-X 0.468750 PROBABILITY OF DECREASE 44 SO THE RISK NEUTRAL : VALUE OF PUT OPTION 45 (PROB(INCREASE)* PAYOFF + PROB(DECREASE)* PAYOFF)/(1+RISK FREE RATE) ((0.531250*0) (0.468750*10))/(1+0.0125) 46 VALUE OF PUT OPTION = 47 VALUE OF PUT OPTION = 4.62962963 48 VALUE OF PUT OPTION = 49 ANSWER VALUE OF PUT OPTION = 4.63 Sheet4 Sheet5 BS Sheet3 Sheet2 RISK NEUTRAL Sheet6 Sheet7 BINOMIAL 120 % II Rea erences WA 09:08 ENG 01-12-2019