The value of a European call option on the stock with strike k=102k=102 is: 2.03529 and the amount of dollar to invest in the cash account is $28.694
<h3>European call option</h3>
Given:
R=1.02
S0 = 100
u=1/d= 1.05
Strike(k) = 102
First step
Upside Price = u × S0
Upside Price = 1.05 × 100
Upside Price = 105
Downside Price = S0/u
Downside Price= 100×1/1.05
Downside Price= 95.238
Upside Payoff = upside price - strike rate
Upside Payoff =(105 - 102)
Upside Payoff = 3
Second step
Upside probability=(r - q) / u - d
Upside probability=1.02- (1/1.05)÷ 1.05- (1/1.05)
Upside probability=0.0676190/0.0976190
Upside probability=0.692
Probability of downside = 1 - p(upside)
Probability of downside = 1 - 0.692
Probability of downside = 0.30731722
Third step
European call option=[0.692×3+0.30731722×0]×1/100
European call option=2.03529
Let B represent the Dollar to invest
105D -1.05B=3
95.238D-1.02B=0
Solving for B
B=$28.694
Therefore the value of a European call option on the stock with strike k=102k=102 is: 2.03529 and the amount of dollar to invest in the cash account is $28.694
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