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2 years ago

Consider a 11-period binomial model with r=1.02r=1.02, s_0 = 100s

1 answer:

4 0

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

Learn more about European call option here:brainly.com/question/16998902

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