contestada

Consider a 11-period binomial model with r=1.02r=1.02, s_0 = 100s
0 =100,
1.05=u=1/d1.05=u=1/d. compute the value of a european call option on the stock with strike k=102k=102. the stock does not pay dividends. when you construct the replicating portfolio for the option in the previous question how many dollars do you need to invest in the cash account?

Respuesta :

abiolataiwo2015

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

European call option

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:https://brainly.com/question/16998902

#SPJ1

Otras preguntas