Question

Use the following information to respond to problems S0= $40; σ= 40%; r = 0.03; D...

Use the following information to respond to problems

S0= $40; σ= 40%; r = 0.03; D = $0; T = 1.

Find the value of an American call option with a strike price of $45 using a two-step binomial model

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Valuation of American Call Option: Call option gives option buyer the right to buy the Stock at a srike price Payoff of Call option Max(S-X,0) where S is stock price and X is exercise price In American Call option can be excercised before the maturity, therefore payoff of the option at each period is compared to holding it for one more period Given the following data: Risk free rate (r) Current Price, So Exercise Price, X 0(Volatility Period Step Period (h) 3.00% 10 12 1Year 0.506 month 14 15 16 17 a) Calculation of u,d,p and 1-p u -exp(o*sqrt(h)) Probability of rise, p -(Exp(rf*h)-d)/(u-d) 0.45612 1.326896 0.753638 19 Uu (EXP(D9*D14)-D19)/(D18-D19) 0.54388 -1-D20 (b) Building Binomial tree of stock Prices 24 First period stock price will either go up Sou or go down Sod as shown below: 26 27 $53.08 -C29 D18 $40.00 31 $30.15 -C29 D19 32 Simillary for next period price will move up and down as each node of period one Final binomial tree of prices is as follows: 35 36 0$40.00 $53.08 $70.43 E37*SD$18 $30.15 $0.00F$36> $C38,E37SD$19, $22.72IF(F$36>-$C39,E38*SD$19,-) 38 39A1 41 42 43 c) Calculation of binomial tree for Call option Step-1: Calculation of Payoff of call option at the maturity of t

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