Question

Consider a 11-period binomial model with R=1.02R=1.02, S_0 = 100S 0 ​ =100, u=1/d= 1.05u=1/d=1.05. Compute the value of a European call option on the stock with strike K=102K=102. The stock does not pay dividends. Please submit your answer rounded to two decimal places. So for example, if your answer is 3.45673.4567 then you should submit an answer of 3.463.46. 1 point

Answer 1

Answer: 1.76

Explanation:

Given the following :

R=1.02,

S0 = 100

u=1/d= 1.05

Strike(k) = 102

Total Payoff = (probability of upside × upside Payoff) + (probability of downside × downside Payoff)

Upside Price = u × S0 = 1.05 × 100 = 105

downside Price = S0/u = 100/1.05 = 95.24

Upside Payoff = upside price - strike rate =(105 - 102) = 3

Upside probability :

[e^(r - q) - d] / u - d

E = exponential, q = Dividend (Dividend is 0, since the stock does not pay dividend)

d = 1/d = 1/1.05 = 0.9523809

e = 2.7182818

[2.7182818^(1.02% - 0) - 0.9523809] / (1.05 - 0.9523809)

[1.0102521 - 0.9523809] / 0.0976191

0.0578712 / 0.0976191

= 0.5928266

Probability of downside = 1 - p(upside)

P(downside) = 1 - 0.5928266

P(downside) = 0.4071733

Therefore, total Payoff =

(0.5928266 × 3) + (0.4071733 × 0)

= 1.7784798

European. Call option:

Total Payoff / (1 + r%)

1.7784798 / (1 + 1.02%)

=1.7784798/ (1 + 0.0102)

= 1.7784798 / 1.0102

= 1.7605224

= 1.76