Question

1. You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,250,000 million. Over the past five years, the price of land in the area has increased 7 percent per year, with an annual standard deviation of 36 percent. You would like an option to sell the land in the next 12 months for $1,400,000. The risk-free rate of interest is 3 percent per year, compounded continuously.

What is the price of the put option necessary to guarantee your sales price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price of Put Option?

2. A stock is currently priced at $92. The stock will either increase or decrease by 10 percent over the next year. There is a call option on the stock with a strike price of $90 and one year until expiration.

Assume the risk-free rate is 2 percent. What is the risk-neutral value of the option? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Call Value ?

Answer 1

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DERIVATIVES BINOMIAL - Microsoft Excel (Product Activation Failed) Page Layout Formulas File Home Insert Data Review View Add-Ins E AutoSum - Cut A A Wrap Text Calibri 11 General Copy Fill Merge & Center Insert Delete Format Paste в IU* 000 Conditional Format Cell Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Alignment Number Clipboard Font Styles Cells Editing U23 L M N O P R S T V W Y 5 1250000 6 K = 1400000 7 0.03 r = a (A) = 0.36 9 T= 1 10 d,ln(k) 11 12 13 d1 [In(1250000/1400000) (0.03 +0.5*(0.36)^2)(1)]/(0.36*(SQRT(1)]| 14 d1 = 15 -0.05147 16 17 d2 d1 a* SQRT(T) 18 d2 = 0.4115 19 20 e^l-0.03 1) N(d1) 21 0.479476 0.970446 N(d2) 22 0.340364 23 Sheet4 Sheet5 Sheet6 Sheet7 BS Sheet2 Sheet3 BINOMIAL RISK NEUTRAL erences 130% WA 09:56 ENG 22-11-2019

DERIVATIVES BINOMIAL - Microsoft Excel (Product Activation Failed) Formulas File Home Insert Page Layout Data Review View Add-Ins Cut E AutoSum - A A Wrap Text Calibri 11 General Copy Fill Merge & Center Insert Delete Format Paste в IU* 000 Conditional Format Cell Sort & Find & % Format Painter Clear Filter Select Formatting as Table Styles Alignment Number Clipboard Font Styles Cells Editing fox U41 L M P Q T U V W Y 23 24 Value of Put ophon 25 26 P= k.e Nd) -SNEd 27 28 29 1400000*e^-0.03*(1))*(1-0.340364) 1200000 *(1-0.479476) 30 VALUE OF PUT OPTION= 1400000*(0.970446)*(1- 0.340364) 1200000 (1-0.479476) 31 650654.91 32 896196.47 245541.56 33 34 35 36 37 38 39 40 41 Sheet4 BS Sheet5 Sheet6 Sheet7 Sheet2 Sheet3 ΒΙΝΟΜΙAL RISK NEUTRAL erences 130% WA 09:57 ENG 22-11-2019

SUM 2

DERIVATIVES BINOMIAL - Microsoft Excel (Product Activation Failed) File Home Insert Page Layout Formulas Data Review View Add-Ins E AutoSum - Cut Wrap Text Calibri 11 General E Copy Fill Merge & Center Insert Delete Format Paste в IU* +.0 .00 Conditional Format Cell Sort & Find & % .00 0 Format Painter Clear Filter Select Formatting as Table Styles Editing Clipboard Font Alignment Number Styles Cells fox AC56 АН АВ АС AD АЕ AF AG Al AJ АК AL АМ AN AO PRICE INCREASE = 10% 101.20 92*(1+0.1)] 56 82.80 92*(1-0.1)] -10% 57 PRICE DECREASE = 58 PAYOFF 59 МAX [101.20-90, 0] %- MAX [82.80-90, 0] = | 60 IF PRICE INCREASE = 11.20 0.00 61 IF PRICE DECREASE = 62 NOW TO GET 3% RETURN 63 64 WE CAN USE FOLLOWING EQUATION TO FIND RISK NEUTRAL RPROBABILITY PROB(INCREASE)* (15%) + PROB(DECREASE)(-15%) 65 RISK FREE RATE = 2%= (X)(10%)(1-X)(-10%) 66 2% (X)(10%) -10% +(X)(10%) 67 12%= (X)(20%) 68 69 0.6000 PROBABILITY OF INCREASE 70 1-X 0.4000 PROBABILITY OF DECREASE 71 SO THE RISK NEUTRAL : VALUE OF CALL OPTION 72 (PROB(INCREASE)* PAYOFF + PROB(DECREASE)*PAYOFF)/(1+RISK FREE RATE) ((0.6000*11.20) + (0.4000*0))/(1+0.02) 73 VALUE OF CALL OPTION = 74 VALUE OF CALL OPTION= 75 ANSWER VALUE OF CALL OPTION = 6.59 76 Sheet2 RISK NEUTRAL Sheet3 BS Sheet4 Sheet5 Sheet6 Sheet7 BINOMIAL II Rea (- erences 120% EEE WA 09:56 ENG 22-11-2019